Plug In Gait Reference Guide
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Plug-in Gait Reference Guide Contents About this guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Regulatory information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Plug-in Gait models and templates . . . . . . . . . . . . . . . . . . . 5 Lower body modeling with Plug-in Gait . . . . . . . . . . . . . . . . . . 6 Upper body modeling with Plug-in Gait . . . . . . . . . . . . . . . . . 18 Full body modeling with Plug-in Gait . . . . . . . . . . . . . . . . . . . 26 Plug-in Gait labeling skeleton templates (VSTs) in Vicon Nexus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Plug-in Gait bones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Complete list of Plug-in Gait bones . . . . . . . . . . . . . . . . . . . . 34 Plug-in Gait virtual markers . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Plug-in Gait joint centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Plug-in Gait lower body forces and moments . . . . . . . . . 40 Plug-in Gait kinematic and kinetic calculations . . . . . . . 43 About Plug-in Gait processes . . . . . . . . . . . . . . . . . . . . . . . . . 44 Segment meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 © Copyright 2016–2018 Vicon Motion Systems Limited. All rights reserved. Vicon Motion Systems Limited reserves the right to make changes to information in this document without notice. Companies, names, and data used in examples are fictitious unless otherwise noted. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic or mechanical, by photocopying or recording, or otherwise without the prior written permission of Vicon Motion Systems Ltd. Vicon® is a registered trademark of Oxford Metrics plc. Vicon Blade™, Vicon Control™, Vicon Lock™, Vicon Lock+™, Vicon Nexus™, Vicon MX™, Vicon Pegasus™, Vicon ProCalc™, Vicon Shogun™, Vicon Studio™, T-Series™, Vicon Tracker™, Vicon Vantage™, Vicon Vero™, Vicon Vertex™, and Vicon Vue™ are trademarks of Oxford Metrics plc. VESA® is a registered trademark owned by VESA (www.vesa.org/about-vesa/). Other product and company names herein may be the trademarks of their respective owners. Vicon Motion Systems is an Oxford Metrics plc company. Email: support@vicon.com Web: http://www.vicon.com Plug-in Gait internal models . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Overview of the Plug-in Gait modeling process . . . . . . . . . . 47 Static vs. dynamic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 The chord function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Lower body kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Upper body kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Angle outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Kinetic modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Plug-in Gait output angles . . . . . . . . . . . . . . . . . . . . . . . . . 74 Angle definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Plug-in Gait kinematic variables . . . . . . . . . . . . . . . . . . . . . . . 78 Upper body angles as output from Plug-in Gait . . . . . . . . . 88 Lower body angles as output from Plug-in Gait . . . . . . . . . . 93 Plug-in Gait output specification . . . . . . . . . . . . . . . . . . . 96 Global (laboratory) co-ordinate system . . . . . . . . . . . . . . . . . 97 Pelvis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Femur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Tibia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Joint kinematic definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Joint kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 © Copyright 2016–2018 Vicon Motion Systems Limited. All rights reserved. Vicon Motion Systems Limited reserves the right to make changes to information in this document without notice. Companies, names, and data used in examples are fictitious unless otherwise noted. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic or mechanical, by photocopying or recording, or otherwise without the prior written permission of Vicon Motion Systems Ltd. Vicon® is a registered trademark of Oxford Metrics plc. Vicon Blade™, Vicon Control™, Vicon Lock™, Vicon Lock+™, Vicon Nexus™, Vicon MX™, Vicon Pegasus™, Vicon ProCalc™, Vicon Shogun™, Vicon Studio™, T-Series™, Vicon Tracker™, Vicon Vantage™, Vicon Vero™, Vicon Vertex™, and Vicon Vue™ are trademarks of Oxford Metrics plc. VESA® is a registered trademark owned by VESA (www.vesa.org/about-vesa/). Other product and company names herein may be the trademarks of their respective owners. Vicon Motion Systems is an Oxford Metrics plc company. Email: support@vicon.com Web: http://www.vicon.com Plug-in Gait Reference About this guide This guide provides in-depth descriptions of Plug-in Gait models and templates, and details of the calculations performed by Plug-in Gait. For information on how to use Plug-in Gait with Vicon Nexus, see Modeling with Plug-in Gait in the Vicon Nexus User Guide. It is assumed that you are familiar with standard motion capture, data processing, and data management in Nexus; and with data visualization, analysis and reporting in Vicon Polygon. For more information on these processes, see the documentation for Nexus and Polygon. Vicon Motion Systems Ltd. 26-Oct-2018 Page 3 of 104 Plug-in Gait Reference Regulatory information For Vicon Nexus regulatory details, see Vicon Nexus regulatory information in the Nexus documentation area of the Vicon website (docs.vicon.com). Vicon Motion Systems Ltd. 26-Oct-2018 Page 4 of 104 Plug-in Gait Reference Plug-in Gait models and templates The following topics contain information on the differences between the Plug-in Gait models, including details of the relevant outputs and marker sets. A description of the labeling skeleton templates that you can use with Plug-in Gait is also available: Lower body modeling with Plug-in Gait on page 6 Upper body modeling with Plug-in Gait on page 18 Full body modeling with Plug-in Gait on page 26 Plug-in Gait labeling skeleton templates (VSTs) in Vicon Nexus on page 31 If you are using Plug-in Gait for gait analysis, the precision of the marker placement is critical for obtaining accurate clinical results. Use the information and illustrations in the above topics to place markers on the patient. Vicon Motion Systems Ltd. 26-Oct-2018 Page 5 of 104 Plug-in Gait Reference Lower body modeling with Plug-in Gait This section describes lower body modeling with Plug-in Gait. It covers the following information: Outputs from Plug-in Gait lower body model on page 6 Marker sets for Plug-in Gait lower body model on page 8 Marker placement for Plug-in Gait lower body model on page 9 KAD marker sets for Plug-in Gait lower body model on page 14 KAD marker placement for Plug-in Gait lower body model on page 15 For details about the labeling skeleton templates to be used with Plug-in Gait lower body models, see Plug-in Gait labeling skeleton templates (VSTs) in Vicon Nexus on page 31. Outputs from Plug-in Gait lower body model Use a Plug-in Gait lower body model if you require the kinematic and kinetic calculation outputs listed in the following table. The output variables are prefixed by the appropriate context (L for left or R for right). Joint angles, force, and moments are expressed in the three anatomical planes: sagittal, frontal, and coronal. Even if the joint powers are scalar, they can also be expressed in the anatomical planes in Vicon Polygon. Forces, moments, and powers are all normalized to the subject's height and body mass. Output Description Kinematics: Angles AbsAnkleAngle The angle between the AJC to KJC vector and the AJC to TOE vector. AnkleAngles Vicon Motion Systems Ltd. Relative. The angles between the shank and the foot. 26-Oct-2018 Page 6 of 104 Plug-in Gait Reference Output Description FootProgressAngles Absolute. The angles between the foot and the global coordinate system. HipAngles Relative. The angles between the pelvis and the thigh. KneeAngles Relative. The angles between the thigh and the shank. PelvisAngles Absolute. The angles between the pelvis and the laboratory coordinate system. Kinetics: Forces AnkleForce The force between the shank and the foot. GroundReactionForce The force exchanged between the foot and the ground while walking. HipForce The force between the pelvis and the thigh. KneeForce The force between the thigh and the shank. NormalizedGRF The ground reaction force expressed as a percentage of the body weight. WaistForce The force between the pelvis and the thorax.a Moments AnkleMoment The moment between the shank and the foot. HipMoment The moment between the pelvis and the thigh. KneeMoment The moment between the thigh and the shank. Vicon Motion Systems Ltd. 26-Oct-2018 Page 7 of 104 Plug-in Gait Reference Output Description WaistMoment The moment between the pelvis and the thorax.a Powers a AnklePower The power between the shank and the foot. HipPower The power between the pelvis and the thigh. KneePower The power between the thigh and the shank. WaistPower The power between the pelvis and the thorax.a This output variable is calculated only if you use a Plug-in Gait model that contains the thorax. Marker sets for Plug-in Gait lower body model All Plug-in Gait marker sets are designed for the Newington-Helen Hayes model on which Plug-in Gait is based. The marker set for Plug-in Gait lower body modeling includes markers for the pelvis and the lower limbs. There are two variations of the standard marker set for the lower body model: A single sacral (SACR) marker for the pelvis Two posterior superior iliac spine (PSIS) markers for the pelvis These markers provide the same function; if you use two PSIS markers, Plug-in Gait calculates the midpoint between them and uses that to perform the calculations. If you use a single SACR marker, you identify that position to Plug-in Gait rather than having it calculated. Using the two PSIS markers has the benefit of providing redundancy, so if one of the pelvis markers is missing, it is possible to reconstruct a virtual marker based on the remaining three markers. You can do this using a Rigid Body Fill in Nexus. Vicon Motion Systems Ltd. 26-Oct-2018 Page 8 of 104 Plug-in Gait Reference Marker placement for Plug-in Gait lower body model To demonstrate where to attach the standard lower body model markers to your patient, the following images show front, back, and side views. Some markers are shown from two views to help you better determine their position on your patient. Important As shown in the following images, some asymmetry is desirable as it helps the auto labeling routine distinguish right from left. In a lower body marker set, you can place the THI and/or TIB markers asymmetrically. Similarly, avoid symmetrical placement of marker clusters or groups of markers and also ensure markers are asymmetrical within each cluster/group. The following image shows the front view. The left lower body markers are not labeled; place markers on the left side in a similar way to those on the right. Important The THI and TIB markers anterior-posterior position is critical for identifying the orientation of the knee and ankle flexion axis. Vicon Motion Systems Ltd. 26-Oct-2018 Page 9 of 104 Plug-in Gait Reference The following image shows the back view. The figure includes the SACR marker variation, which is highlighted in orange. The right lower body markers are not labeled; attach markers on that side in a similar way to those on the left (with some asymmetry, as described above). The following image shows the right side view. The left side view is not shown; attach markers on that side in a similar way to the right markers (with some asymmetry, as described above). The following tables list the markers defined in Plug-in Gait templates for lower body modeling and describe where to place them on the patient: Vicon Motion Systems Ltd. 26-Oct-2018 Page 10 of 104 Plug-in Gait Reference Pelvis marker placement The following markers are positioned on the patient's pelvis: Marker Definition Position on patient Sacral On the skin mid-way between the posterior superior iliac label SACR spines (PSIS) and positioned to lie in the plane formed by the ASIS and PSIS points. LASI Left ASIS Left anterior superior iliac spine RASI Right Right anterior superior iliac spine ASIS LPSI Left PSIS Left posterior superior iliac spine (immediately below the sacro-iliac joints, at the point where the spine joins the pelvis) This marker is used with the RPSI marker as an alternative to the single SACR marker. RPSI Right Right posterior superior iliac spine (immediately below the PSIS sacro-iliac joints, at the point where the spine joins the pelvis) This marker is used with the LPSI marker as an alternative to the single SACR marker. In some patients, especially obese individuals, the markers either can't be placed exactly on the ASIS, or are invisible in this position to cameras. In these cases, move each marker laterally by an equal amount along the ASIS-ASIS axis. The true inter-ASIS distance must then be manually measured and entered in the Properties pane at the bottom of the Subjects tab on the Resources pane. These markers, together with either the SACR marker or the LPSI and RPSI markers, define the pelvic coronal plane. Vicon Motion Systems Ltd. 26-Oct-2018 Page 11 of 104 Plug-in Gait Reference Lower limb marker placement The following markers are positioned on each of the patient's lower limbs. For additional guidance, see the notes at the bottom of the table. Marker Definition Position on patient label Left lower limb markers LTHI Left thigh Over the lower lateral 1/3 surface of the left thigh LKNE Left knee On the flexion-extension axis of the left knee LTIB Left tibia Over the lower 1/3 surface of the left shank LANK Left ankle On the lateral malleolus along an imaginary line that passes through the transmalleolar axis LHEE Left heel On the calcaneous at the same height above the plantar surface of the foot as the toe marker LTOE Left toe Over the second metatarsal head, on the mid-foot side of the equinus break between fore-foot and mid-foot Right lower limb markers RTHI Right Over the upper lateral 1/3 surface of the right thigh thigh RKNE Right On the flexion-extension axis of the right knee. knee RTIB Right Over the upper 1/3 surface of the right shank tibia RANK Vicon Motion Systems Ltd. Right On the lateral malleolus along an imaginary line that passes ankle through the transmalleolar axis 26-Oct-2018 Page 12 of 104 Plug-in Gait Reference Marker Definition Position on patient Right On the calcaneous at the same height above the plantar heel surface of the foot as the toe marker Right toe Over the second metatarsal head, on the mid-foot side of the label RHEE RTOE equinus break between fore-foot and mid-foot Notes Knee markers To locate the precise point for placing the knee markers (LKNE, RKNE), passively flex and extend the knee a little while watching the skin surface on the lateral aspect of the knee joint. Identify where knee joint axis passes through the lateral side of the knee by finding the lateral skin surface that comes closest to remaining fixed in the thigh. This landmark should also be the point about which the lower leg appears to rotate. Mark this point with a pen. With an adult patient standing, this pen mark should be about 1.5 cm above the joint line, mid-way between the front and back of the joint. Attach the marker at this point. If you are using a knee alignment device (KAD), see also KAD marker placement for Plugin Gait lower body model on page 15. Thigh markers The thigh markers (LTHI, RTHI) are used to calculate the knee flexion axis orientation. Place the LTHI marker over the lower lateral 1/3 surface and the RTHI marker over the upper lateral 1/3 surface of the thigh, just below the swing of the hand, although the height is not critical. The anterior-posterior placement of the marker is critical for correct alignment of the knee flexion axis. Try to keep the thigh marker off the belly of the muscle, but place the thigh marker at least two marker diameters proximal of the knee marker. Adjust the position of the marker so that it is lies in the plane that contains the hip and knee joint centers and the knee flexion/extension axis. If you are using a KAD, the precise placement of the thigh markers is not crucial. Tibia markers The tibia markers (LTIB, RTIB) are used to determine the alignment of the ankle flexion axis. Similarly to the thigh markers, place the LTIB marker over the lower 1 /3 surface of the shank and the RTIB marker over the upper 1/3 surface of the shank. The tibial marker should lie in the plane that contains the knee and ankle joint centers and the ankle flexion/extension axis. In a normal patient, the ankle joint axis between the medial and lateral malleoli is externally rotated by around 20 degrees with respect to the knee flexion axis. The placements of the shank markers should reflect this. If you are using a KAD, the ankle dorsi-plantar flexion axis is assumed to be parallel to the knee flexion axis unless: Vicon Motion Systems Ltd. 26-Oct-2018 Page 13 of 104 Plug-in Gait Reference The tibial torsion is manually measured and entered in the Properties pane at the bottom of the SubjectsResources pane. or One marker on each medial malleolus is attached (RMED, LMED). During the static trial, Plug-in Gait automatically calculates the tibial torsion as the angle between the knee flexion and the ankle dorsi-plantar flexion axes. Toe and heel markers If the toe markers (LTOE, RTOE) cannot be placed level with the heel markers (LHEE, RHEE), you must configure Plug-in Gait to compensate for this. For details of the relevant settings, see Plug-in Gait Static pipeline in the Vicon Nexus User Guide. KAD marker sets for Plug-in Gait lower body model In addition to the standard lower body marker sets, an alternative marker set enables you to use a knee alignment device (KAD). The KAD is a light-weight, spring-loaded G-clamp, whose adjustable jaws bridge the knee and whose stem is aligned with the knee flexion axis. One standard-sized marker is fixed to the tip of the stem and two markers are mounted on the ends of two additional rods fixed to the device. The three markers are equidistant from the point where the stem meets the jaws of the clamp, enabling the 3D position of this point, known as the 'virtual knee marker', to be calculated. Instead of the THI and TIB markers in the standard model, the KAD markers (left and right KAX, KD1, and KD2) are used to calculate the orientation of the medio-lateral axes of knee and ankle respectively. The KAD is applied to the patient during a static trial to enable Plug-in Gait to calculate: The offset angle between the knee flexion axis orientation as calculated by using the KAD markers and knee flexion axis orientation as calculated by using the THI markers (Thigh Rotation Offset). When a KAD is present, the ankle dorsi-plantar flexion axis is assumed to be aligned with the knee flexion axis unless the tibial torsion measurement is entered. The angle between the ankle dorsi-plantar flexion axis orientation as calculated by using the KAD and the tibial torsion measurement and the ankle dorsi-plantar flexion axis orientation as calculated using the TIB markers (Shank Rotation Offset). These calculations eliminate the reliance on the anterior posterior position of the THI and TIB markers. Vicon Motion Systems Ltd. 26-Oct-2018 Page 14 of 104 Plug-in Gait Reference A variation of the KAD marker set defines the additional LMED and RMED markers for the medial malleoli. When you use a KAD, the tibial torsion measurement is critical for Plug-in Gait to identify the correct orientation of the ankle dorsi-plantar flexion axis. In fact, if the tibial torsion is left at 0 (zero), the ankle flex axis is assumed to be aligned with the knee flex axis. To enable Plug-in Gait to automatically calculate the tibial torsion measurement, attach the LMED and RMED markers on the medial malleoli of your patient. When the static trial has been processed, you can remove the KAD and the MED markers, and for dynamic trials, place the KNE marker exactly where the KAD pad used to be on the femural epicondyle. KAD marker placement for Plug-in Gait lower body model The following images show front, back, and side views to demonstrate where to attach the lower body model markers to your patient. You do this before capturing a static trial as described in the Vicon Nexus User Guide. Some markers are shown from two views to help you better determine their position on your patient. The following image shows the front view. It includes the knee alignment device (KAD) marker variations, which are highlighted in orange. The left lower body markers are not labeled; attach markers on that side in a similar way to those on the right (with some asymmetry as described in Marker placement for Plug-in Gait lower body model on page 9). Vicon Motion Systems Ltd. 26-Oct-2018 Page 15 of 104 Plug-in Gait Reference The following image shows the back view. It includes the knee alignment device (KAD) marker variations, which are highlighted in orange. The right lower body markers are not labeled in this figure; attach markers on that side in a similar way to those on the left (with some asymmetry as described in Marker placement for Plug-in Gait lower body model on page 9). The following image shows the right side view. It includes the knee alignment device (KAD) marker variations, which are highlighted in orange. The left side view is not shown; attach markers on that side in a similar way to the right markers (with some asymmetry as described in Marker placement for Plug-in Gait lower body model on page 9). If a knee alignment device (KAD) is used, it is attached instead of the LKNE and RKNE markers for the static trial only. Before dynamic capture and modeling, it must be removed and LKNE and RKNE markers attached instead. The KAD markers are constructed in such a way as to enable the model to calculate a position for a virtual knee marker, which corresponds to the external pad. So, the external pad should be positioned as described for the knee marker. Vicon Motion Systems Ltd. 26-Oct-2018 Page 16 of 104 Plug-in Gait Reference The following table shows the KAD marker labels included for static trials. Marker Definition Position Left knee Left KAD axis Label LKAX For the left side, labeling goes counter clockwise from this LKAX marker LKD1 Device 1 Left KAD marker 1 LKD2 Device 2 Left KAD marker2 RKAX Right Right KAD axis knee For the right side, labeling goes clockwise from the RKAX marker RKD1 Device 1 Right KAD marker 1 RKD2 Device 2 Right KAD marker 2 For dynamic trials, the KAD must be removed, and the left or right KNE marker positioned at the same point as the external KAD pad. Vicon Motion Systems Ltd. 26-Oct-2018 Page 17 of 104 Plug-in Gait Reference Upper body modeling with Plug-in Gait This section describes Plug-in Gait upper body modeling, so you can determine if an upper body model will provide the data you require for your clinical analysis. The following topics are covered: Outputs from Plug-in Gait upper body model on page 18 Marker sets for Plug-in Gait upper body modeling on page 20 Marker placement for Plug-in Gait upper body model on page 20 For details about the labeling skeleton templates to be used with Plug-in Gait upper body models, see Plug-in Gait labeling skeleton templates (VSTs) in Vicon Nexus on page 31. Outputs from Plug-in Gait upper body model Use a Plug-in Gait upper body model if you require the kinematic and kinetic calculation outputs listed in the following table. The output variables are prefixed by the appropriate context (L for left or R for right). Output Description Kinematics: Angles ElbowAngles Relative. The angles between the upper arm and the forearm. HeadAngles Absolute. The angles between the head and the laboratory coordinate system. NeckAngles The angles between head relative to thorax. ShoulderAngles Relative. The angles between the upper arm and the thorax. SpineAngles The angles between the thorax relative to the pelvis. Vicon Motion Systems Ltd. 26-Oct-2018 Page 18 of 104 Plug-in Gait Reference Output Description ThoraxAngles Absolute. The angles between the thorax and the laboratory coordinate system. WristAngles Relative. The angles between the forearm and the hand. Kinetics: Forces ElbowForce The force between the upper arm and the forearm. NeckForce The force between the head relative to thorax. ShoulderForce The force between the upper arm and the thorax. WristForce The force between the forearm and the hand. Moments ElbowMoment The moment between the upper arm and the forearm. NeckMoment The moment between the head relative to thorax. ShoulderMoment The moment between the upper arm and the thorax. WristMoment The moment between the forearm and the hand. Powers ElbowPower The power between the upper arm and the forearm. NeckPower The power between the head relative to thorax. ShoulderPower The power between the upper arm and the thorax. WristPower The power between the forearm and the hand. Vicon Motion Systems Ltd. 26-Oct-2018 Page 19 of 104 Plug-in Gait Reference Marker sets for Plug-in Gait upper body modeling The marker set for Plug-in Gait upper body modeling includes markers for the head, torso, and upper limbs. There are two variations of the standard marker set for the upper body model: Additional upper arm (UPA) and forearm (FRM) markers No UPA and FRM markers The UPA and FRM markers are optional; however, using them improves marker tracking during dynamic trials. Marker placement for Plug-in Gait upper body model The following images show front, back, and side views to demonstrate where to attach the upper body markers to your patient. You do this before capturing a static trial as described in the Vicon Nexus User Guide. Some markers are shown from two views to help you better determine their position on your patient. Important As shown in the following images, some asymmetry is desirable as it helps the auto labeling routine distinguish right from left. For upper body modeling, you can place the UPA and FRM markers asymmetrically. Similarly, avoid symmetrical placement of marker clusters or groups of markers and also ensure markers are asymmetrical within each cluster/group. The following image shows the front view. The left upper body markers are not labeled; attach markers on that side in a similar way to those on the right (with some asymmetry as described above). Vicon Motion Systems Ltd. 26-Oct-2018 Page 20 of 104 Plug-in Gait Reference The following image shows the back view. The right upper body markers are not labeled; attach markers in a similar way to those on the left (with some asymmetry as described above). The following image shows the right side view. The left side view is not shown; attach markers on that side in a similar way to those on the right (with some asymmetry as described above). Vicon Motion Systems Ltd. 26-Oct-2018 Page 21 of 104 Plug-in Gait Reference The following tables list the markers defined in Plug-in Gait templates for upper body modeling and describe where to place them on the patient: Head markers The following table describes the markers positioned on the patient's head. To save time, many users buy a headband and permanently attach markers to it. Marker Definition Position on patient Left front Left temple label LFHD head RFHD Right Right temple front head LBHD RBHD Left back Left back of head (defines the transverse plane of the head, head together with the frontal markers) Right Right back of head (defines the transverse plane of the head, back together with the frontal markers) head Important If the back markers cannot be placed level with the front markers, you must configure Plug-in Gait to compensate for this during the subject calibration process. To do this, in the Properties for the Process Static Plugin Gait Model pipeline operation, under Assume Horizontal, select Head. Vicon Motion Systems Ltd. 26-Oct-2018 Page 22 of 104 Plug-in Gait Reference Torso markers The following table describes the markers positioned on the patient's torso. The torso markers (C7, T10, CLAV, STRN) define the thorax sagittal plane; therefore, their lateral positioning is most important. Marker Definition Position on patient 7th On the spinous process of the 7th cervical vertebra label C7 cervical vertebra T10 10th On the spinous process of the 10th thoracic vertebra thoracic vertebra CLAV Clavicle On the jugular notch where the clavicles meet the sternum STRN Sternum On the xiphoid process of the sternum RBAK Right Anywhere over the right scapula back (This marker has no equivalent marker on the left side. This asymmetry helps the autolabeling routine determine right from left on the subject. Placement is not critical as it is not included in the Plug-in Gait model calculations.) Vicon Motion Systems Ltd. 26-Oct-2018 Page 23 of 104 Plug-in Gait Reference Upper limb markers The following table describes the markers positioned on the patient's upper body. Marker labels shown with an asterisk * are optional; however, using them improves marker tracking during dynamic trials. Marker Definition Position on patient label Left upper limb markers LSHO Left On the acromio-clavicular joint shoulder *LUPA Left On the upper lateral 1/3 surface of the left arm (Place upper asymmetrically with RUPA) arm LELB Left On the lateral epicondyle elbow *LFRM LWRA Left On the lower lateral 1/3 surface of the left forearm (Place forearm asymmetrically with RFRM) Left wrist At the thumb side of a bar attached to a wristband on the marker A posterior of the left wrist, as close to the wrist joint center as possible. Loose markers can be used but for better tracking of the axial rotations, a bar is recommended. LWRB Left wrist At the little finger side of a bar attached to a wristband on marker B the posterior of the left wrist, as close to the wrist joint center as possible. Loose markers can be used but for better tracking of the axial rotations, a bar is recommended. LFIN Left Just proximal to the middle knuckle on the left hand finger Vicon Motion Systems Ltd. 26-Oct-2018 Page 24 of 104 Plug-in Gait Reference Marker Definition Position on patient label Right upper limb markers RSHO Right On the acromio-clavicular joint shoulder *RUPA Right On the lower lateral 1/3 surface of the right arm (Place upper asymmetrically with LUPA) arm RELB Right On the lateral epicondyle approximating the elbow joint axis elbow *RFRM RWRA RWRB RFIN Right On the lower lateral 1/3 surface of the right forearm (Place forearm asymmetrically with LFRM) Right At the thumb side of a bar attached symmetrically with a wrist wristband on the posterior of the right wrist, as close to the marker A wrist joint center as possible Right At the little finger side of a bar attached symmetrically with a wrist wristband on the posterior of the right wrist, as close to the marker B wrist joint center as possible Right Just below the middle knuckle on the right hand finger Vicon Motion Systems Ltd. 26-Oct-2018 Page 25 of 104 Plug-in Gait Reference Full body modeling with Plug-in Gait If you require Plug-in Gait full body modeling, use both a lower and an upper body model to provide the data you require for your clinical analysis. This topic explains: Outputs from Plug-in Gait full body model on page 26 Marker sets for Plug-in Gait full body modeling on page 26 Marker placement for Plug-in Gait full body model on page 27 For a description of the labeling skeleton templates to be used with Plug-in Gait lower body, upper body, or full body models, see Plug-in Gait labeling skeleton templates (VSTs) in Vicon Nexus on page 31. Outputs from Plug-in Gait full body model Use a Plug-in Gait lower body and upper body model if you require the kinematic and kinetic calculation outputs listed in Outputs from Plug-in Gait lower body model on page 6 and Outputs from Plugin Gait upper body model. The output variables are prefixed by the appropriate context (L for left or R for right). Marker sets for Plug-in Gait full body modeling There are two variations of the standard lower body model: A single sacral (SACR) marker Two posterior superior iliac spine (PSIS) markers for the pelvis. These markers provide the same function; if you use two PSIS markers, Plug-in Gait calculates the midpoint between them and uses that to perform the calculations. If you use a single SACR marker, you identify that position to Plug-in Gait rather than having it calculated. In addition to the standard lower body marker sets, an additional marker set enables you to use a knee alignment device (KAD). The KAD markers (left and right KAX, KD1, and KD2) are used instead of the THI and TIB markers in the standard model to calculate the orientation of the medio-lateral axes of knee and ankle respectively. Vicon Motion Systems Ltd. 26-Oct-2018 Page 26 of 104 Plug-in Gait Reference A variation of the KAD marker set defines the additional LMED and RMED markers for the medial malleoli. The MED markers enable Plug-in Gait to automatically calculate the tibial torsion measurement. For further information on the KAD and MED markers, see KAD marker sets for Plug-in Gait lower body model on page 14. When you use KAD+MED markers, in order to verify the ankle axis, the Plug-in Gait Static pipeline displays the torsioned tibia instead of the untorsioned tibia. If joint angles are required, you must also run the Plug-in Gait Dynamic pipeline. Marker placement for Plug-in Gait full body model The following images show front, back, and side views to demonstrate where to attach the full body model markers to your patient. You do this when you are capturing a static trial as described in the Vicon Nexus User Guide. Some markers are shown from two views to help you better determine their position on your patient. The following image shows the front view. This view includes the knee alignment device (KAD) marker variations, which are highlighted in orange. If you have chosen to use a Plug-in Gait marker set that includes KAD markers, attach the KAD pad to the patient instead of the THI and TIB markers. For details on the KAD, see KAD marker placement for Plug-in Gait lower body model on page 15. Important As shown in the following images, some asymmetry is desirable as it helps the auto labeling routine distinguish right from left. For a full body set, you can place the THI, TIB, UPA and FRM markers asymmetrically. Similarly, avoid symmetrical placement of marker clusters or groups of markers and also ensure markers are asymmetrical within each cluster/group. The left body markers are not labeled in this figure; attach markers on that side in a similar way (with some asymmetry) to those on the right. Vicon Motion Systems Ltd. 26-Oct-2018 Page 27 of 104 Plug-in Gait Reference Tip To assist with labeling, place the UPA, FRM, THI, and TIB markers at slightly different heights on the left and right sides: Upper 1/3: LUPA, RFRM, RTHI. RTIB Lower 1/3: RUPA, LRFM, LTHI, LTIB Vicon Motion Systems Ltd. 26-Oct-2018 Page 28 of 104 Plug-in Gait Reference The following image shows the back view. This view includes the sacral (SACR) and knee alignment device (KAD) marker variations, which are highlighted in orange. For details on the SACR marker, see Marker sets for Plug-in Gait lower body model on page 8. If you have chosen to use a Plug-in Gait marker set that includes KAD markers, attach the KAD pad to the patient instead of the THI and TIB markers. For details on the KAD, see KAD marker sets for Plugin Gait lower body model. The right body markers are not labeled in this figure; attach markers on that side in a similar way to those on the left (with some asymmetry as described above). The RBAK marker has no equivalent marker on the left side; this asymmetry helps the autolabeling routine determine right from left on the subject. Vicon Motion Systems Ltd. 26-Oct-2018 Page 29 of 104 Plug-in Gait Reference The following image shows the right side view. This view includes the knee alignment device (KAD) marker variations, which are highlighted in orange. If you have chosen to use a Plug-in Gait marker set that includes KAD markers, attach the KAD pad to the patient instead of the THI and TIB markers. For details on the KAD, see KAD marker sets for Plug-in Gait lower body model on page 14. The left side view is not shown; attach markers on that side in a similar way to the right markers (with some asymmetry as described above). For detailed guidance on placing markers on a patient for full body modeling, the following sections: Marker placement for Plug-in Gait lower body model on page 9 KAD marker placement for Plugin Gait lower body model on page 15 Marker placement for Plugin Gait upper body model on page 20 Vicon Motion Systems Ltd. 26-Oct-2018 Page 30 of 104 Plug-in Gait Reference Plug-in Gait labeling skeleton templates (VSTs) in Vicon Nexus The Plug-in Gait biomechanical model calculates joint kinematics and kinetics from the XYZ marker positions and specific subject anthropometric measurements. As with all motion capture and analysis in Vicon Nexus, the information about the marker set as well as the generic relationship between the physical markers attached to a subject is contained in a labeling skeleton template (.vst) file. This template defines a generic model of the chosen marker set. You create a subject in Nexus based on a specific template file and then you calibrate the generic marker set model defined in the template to your particular subject. The calibration process creates a labeling skeleton (.vsk) file which is strictly specific to your subject. Nexus then uses this subject-specific .vsk file to automatically label dynamic motion capture trials for that patient both in real time and in post-processing. Important The labeling skeleton templates included in the supplied .vst files are used only to define the marker set and to enable Nexus to perform automatic labeling. They are not biomechanical models that will output valid joint angles or other kinematic/kinetic variables. To derive valid kinematics or kinetics, use Plug-in Gait or create your own biomechanical model using Vicon BodyBuilder, Python or MATLAB. Vicon Motion Systems Ltd. 26-Oct-2018 Page 31 of 104 Plug-in Gait Reference The following table lists the predefined Plug-in Gait labeling skeleton templates ( .vst files) supplied with Nexus, identifying the portion of the body it applies to for gait analysis. Plug-in Gait Description template file PlugInGait Full body model defining two markers on FullBody Ai. the posterior superior iliac spine (PSIS) Lower Upper body body modeling modeling y y y n vst PlugInGait Lower body model defining two markers LowerBody on the posterior superior iliac spine (PSIS) Ai.vst An extended version of Plug-in Gait that defines additional markers for foot modeling is available. For information about the Oxford Foot Model plug-in, contact Vicon Support. These Plug-in Gait template files are installed under the Nexus ModelTemplates folder (by default, C:\Program Files (x86)\Vicon\Nexus2.#\ModelTemplates). If you create a template of your own, store it in this location, so that it will be immediately available for selection from the drop-down list when you create a subject node based on a predefined template file. (If you choose not to store it in this location, you can instead browse to the relevant location.) Vicon Motion Systems Ltd. 26-Oct-2018 Page 32 of 104 Plug-in Gait Reference Plug-in Gait bones For information on Plug-in Gait bones, see the following topics: Complete list of Plug-in Gait bones on page 34 Plug-in Gait virtual markers on page 38 Plug-in Gait joint centers on page 39 Vicon Motion Systems Ltd. 26-Oct-2018 Page 33 of 104 Plug-in Gait Reference Complete list of Plug-in Gait bones Name Description Name Description PELO Pelvis Origin HEDO Head Origin PELP Pelvis Proximal HEDP Head Proximal PELA Pelvis Anterior HEDA Head Anterior PELL Pelvis Lateral HEDL Head Lateral RFEO Right Femur Origin TRXO Thorax Origin RFEP Right Femur Proximal TRXP Thorax Proximal RFEA Right Femur Anterior TRXA Thorax Anterior RFEL Right Femur Lateral TRXL Thorax Lateral LFEO Left Femur Origin CSPO C Spine Origin LFEP Left Femur Proximal CSPP C Spine Proximal LFEA Left Femur Anterior CSPA C Spine Anterior LFEL Left Femur Lateral CSPL C Spine Lateral RTIO Right Tibia Origin SACO Sacrum Origin RTIP Right Tibia Proximal SACP Sacrum Proximal RTIA Right Tibia Anterior SACA Sacrum Anterior RTIL Right Tibia Lateral SACL Sacrum Lateral Vicon Motion Systems Ltd. 26-Oct-2018 Page 34 of 104 Plug-in Gait Reference Name Description Name Description LTIO Left Tibia Origin RCLO Right Clavicle Origin LTIP Left Tibia Proximal RCLP Right Clavicle Proximal LTIA Left Tibia Anterior RCLA Right Clavicle Anterior LTIL Left Tibia Lateral RCLL Right Clavicle Lateral RFOO Right Foot Origin LCLO Left Clavicle Origin RFOP Right Foot Proximal LCLP Left Clavicle Proximal RFOA Right Foot Anterior LCLA Left Clavicle Anterior RFOL Right Foot Lateral LCLL Left Clavicle Lateral LFOO Left Foot Origin RHUO Right Humerus Origin LFOP Left Foot Proximal RHUP Right Humerus Proximal LFOA Left Foot Anterior RHUA Right Humerus Anterior LFOL Left Foot Lateral RHUL Right Humerus Lateral RTOO Right Toe Origin LHUO Left Humerus Origin RTOP Right Toe Proximal LHUP Left Humerus Proximal RTOA Right Toe Anterior LHUA Left Humerus Anterior RTOL Right Toe Lateral LHUL Left Humerus Lateral LTOO Left Toe Origin RRAO Right Radius Origin LTOP Left Toe Proximal RRAP Right Radius Proximal Vicon Motion Systems Ltd. 26-Oct-2018 Page 35 of 104 Plug-in Gait Reference Name Description Name Description LTOA Left Toe Anterior RRAA Right Radius Anterior LTOL Left Toe Lateral RRAL Right Radius Lateral LRAO Left Radius Origin LRAP Left Radius Proximal LRAA Left Radius Anterior LRAL Left Radius Lateral RHNO Right Hand Origin RHNP Right Hand Proximal RHNA Right Hand Anterior RHNL Right Hand Lateral LHNO Left Hand Origin LHNP Left Hand Proximal LHNA Left Hand Anterior LHNL Left Hand Lateral RFIO Right Finger Origin RFIP Right Finger Proximal RFIA Right Finger Anterior RFIL Right Finger Lateral Vicon Motion Systems Ltd. 26-Oct-2018 Page 36 of 104 Plug-in Gait Reference Name Description Vicon Motion Systems Ltd. Name Description LFIO Left Finger Origin LFIP Left Finger Proximal LFIA Left Finger Anterior LFIL Left Finger Lateral RTBO Right Thumb Origin RTBP Right Thumb Proximal RTBA Right Thumb Anterior RTBL Right Thumb Lateral LTBO Left Thumb Origin LTBP Left Thumb Proximal LTBA Left Thumb Anterior LTBL Left Thumb Lateral 26-Oct-2018 Page 37 of 104 Plug-in Gait Reference Plug-in Gait virtual markers Plug-in Gait creates virtual markers that lie on the axes of a segment's coordinate systems: at the origin, anterior axis, lateral axis, and proximal (vertical) axis. These virtual markers are not necessary for the basic use of Plug-in Gait. Advanced users may use them for exporting the rotational and translational motion of the segments for analysis. The following table lists the virtual markers created for each segment. Virtual marker Segment coordinate system sgmentNameO segment Origin segmentNameA Anterior axis segmentNameP Proximal axis segmentNameL Lateral axis For example, Plug-in Gait would create the following virtual markers for the pelvis segment: PELO: pelvis Origin PELA: pelvis Anterior axis PELP: pelvis Proximal axis PELL: pelvis Lateral axis Vicon Motion Systems Ltd. 26-Oct-2018 Page 38 of 104 Plug-in Gait Reference Plug-in Gait joint centers The following image shows Plug-in Gait joint centers: Vicon Motion Systems Ltd. 26-Oct-2018 Page 39 of 104 Plug-in Gait Reference Plug-in Gait lower body forces and moments The forces calculated by Plug-in Gait and displayed by Vicon Polygon are in the local coordinate frame of the distal segment in the hierarchical kinetic chain. This means that the Ankle joint forces are recorded in the Foot segment axis system. Therefore: Ground Reaction force Z will look similar to Ankle Force X Ground Reaction Force Y will look similar to Ankle Force Z Ground Reaction Force X will look similar to Ankle Force Y For the tibia this changes, as the axis orientation now changes: Z force is therefore compression or tension at the joint Y force is mediolateral forces at the joint X force is anteroposterior forces at the joint The positive force acts in the positive direction of the axis in the distal segment on which it acts. A negative force acts in the negative direction along the axis. In Plug-in Gait, we use an external moment and force description. That means that: For the Z axis, a negative force is compression and a positive force, tension For the Y axis, a positive force for the right side is medial and negative lateral For the X axis, a positive force is anterior and negative posterior Vicon Motion Systems Ltd. 26-Oct-2018 Page 40 of 104 Plug-in Gait Reference The following table lists all the lower body forces and moments with their positive and negative descriptors. Description Segment Force or moment +ve -ve axes component descriptor descriptor Foot Compression/Tension Tension Compression Right Foot Medial/Lateral Medial Lateral Foot Anterior/Posterior Anterior Posterior Knee Force X Tibia Anterior/Posterior Anterior Posterior RKnee Force Right Tibia Medial/Lateral Medial Lateral Left Tibia Medial/Lateral Lateral Medial Knee Force Z Tibia Tension/Compression Tension Compression Hip Force X Thigh Anterior/Posterior Anterior Posterior RHip Force Y Right Medial/Lateral Medial Lateral Ankle Force X RAnkle Force Y Ankle Force Z Y LKnee Force Y Thigh LHip Force Y Left Thigh Medial/Lateral Lateral Medial Hip Force Z Thigh Tension/Compression Tension Compression Ankle Foot Dorsi/Plantar flexion Dorsiflexion Plantar Moment X Ankle flexion Foot Abduction/Adduction Adduction Abduction Moment Y Vicon Motion Systems Ltd. 26-Oct-2018 Page 41 of 104 Plug-in Gait Reference Description Ankle Segment Force or moment +ve -ve axes component descriptor descriptor Foot Rotation Internal External Tibia Flexion/Extension Flexion Extension Tibia Varus/Valgus Varus Valgus Tibia Rotation Internal External Thigh Flexion/Extension Flexion Extension Thigh Abduction/Adduction Adduction Abduction Thigh Rotation Internal External Moment Z Knee Moment X Knee Moment Y Knee Moment Z Hip Moment X Hip Moment Y Hip Moment Z Vicon Motion Systems Ltd. 26-Oct-2018 Page 42 of 104 Plug-in Gait Reference Plug-in Gait kinematic and kinetic calculations The following topics describe the way in which Plug-in Gait performs calculations to measure the kinematics and kinetics of subjects. They provide an in-depth understanding of marker placement, and will help you to interpret the results. They describe the geometrical relationships between markers, and segments, and gives fixed values applied to the kinetic segments. Given the same inputs, you should be able to replicate the results. Lower body kinematics on page 50 Upper body kinematics on page 62 Angle outputs on page 68 Kinetic modeling on page 69 The internal structure and the specific algorithms used are not covered. Vicon Motion Systems Ltd. 26-Oct-2018 Page 43 of 104 Plug-in Gait Reference About Plug-in Gait processes The Plug-in Gait Dynamic pipeline consists of the following components: all individual pipeline operations: A quintic spline filter based on code written by Herman Woltring. This filter is intended to be applied to the real marker trajectory data before the modeling stage. No further explicit filtering of the data occurs during the modeling stage. Operations that automatically detect and autocorrelate gait cycle events. The modeling stage, which takes the real marker trajectories, and generates 'virtual' marker trajectories that represent kinematic and kinetic quantities (angles, moments etc.) and representations of the modeled segments. An export operation, to enable you to save your processed trial data to a C3D file. This guide covers only the modeling stage of the process. You can perform modeling on the real marker data independently from the filtering and event detection processes by selecting the appropriate check box in the pipeline. Vicon Motion Systems Ltd. 26-Oct-2018 Page 44 of 104 Plug-in Gait Reference Segment meshes Plug-in Gait outputs virtual markers that are used for several purposes: To calculate variables For visualization purposes, such as to define the positions of meshes (representing bones), which can be displayed in the Polygon application. These mesh outputs are rigidly linked to the calculated rigid body segments but are not necessarily the same. The origins and axes for the meshes are dependent on the meshes contained in the Polygon mesh file. Vicon Motion Systems Ltd. 26-Oct-2018 Page 45 of 104 Plug-in Gait Reference Plug-in Gait internal models Internally, the modeling stage consists of four interdependent models: A kinematic lower body A kinematic upper body A kinetic lower body A kinetic upper body The kinematic models are responsible for the definitions of the rigid body segments, and the calculations of joint angles between these segments. The kinetic models then apply masses and moments of inertia to the segments, and enable the "reactions" that occur on the segments to be calculated. Vicon Motion Systems Ltd. 26-Oct-2018 Page 46 of 104 Plug-in Gait Reference Overview of the Plug-in Gait modeling process To run the models, you must supply the required subject measurements. When you have done this, the stages of the Plug-in Gait modeling process are: The initial stage checks that the required components are present. This includes checks for required markers present in the trial, and subject parameter values. Modeling only continues if these requirements are met. The pelvis markers are the minimum required for the lower body model, and the thorax markers are required for the upper body model. Various static values that can be calculated as being fixed for the whole trial, and are needed for the definitions of the segments, are calculated. The positions of the rigid segments are defined on a frame-by-frame basis. Each segment is defined by an origin in global (laboratory) coordinates, and three orthogonal axis directions. In general, the three axis directions are defined using two directions derived from the marker data. One of these directions is taken as a dominant or principal direction, and used to directly define one of the axes in the segment. The second direction is subordinate to the first, and is used with the first direction to define a plane. The third axis of the segment is taken to be perpendicular to this plane. Then the second axis can be found that is perpendicular to both the first and third axes. All segment axis systems are right-handed systems. The outputs that are required from the modeling are then calculated, based on the frame-by-frame positions of the segments. Vicon Motion Systems Ltd. 26-Oct-2018 Page 47 of 104 Plug-in Gait Reference Static vs. dynamic models The kinematic models are run slightly differently for the static trials, to calculate certain static 'calibration' angles that are required for the dynamic modeling. These differences are noted in the descriptions of the models, otherwise it should be assumed that the model is calculated in the same way for both trial types. When the static modeling is being performed, calculated subject measurements are output to the subject measurements file. This is not done for the dynamic trial, even if new values are calculated internally to enable the model to be run. Vicon Motion Systems Ltd. 26-Oct-2018 Page 48 of 104 Plug-in Gait Reference The chord function To define joint centers, the chord function is used extensively in the Plug-in Gait models. Three points are used to define a plane. One of these points is assumed to be a previously calculated joint center, and a second is assumed to be a real marker, at some known, perpendicular distance (the joint center offset) from the required joint center. (It's called a chord because by definition, the three points (two joint centers and the joint marker) lie on the periphery of a circle.) A modified version of the function calculates the required joint center position when the plane definition marker is rotated out of this plane by a known angle round the proposed joint center axis. For an illustration of this, see Dynamic knee joint center calculation on page 54. Vicon Motion Systems Ltd. 26-Oct-2018 Page 49 of 104 Plug-in Gait Reference Lower body kinematics Lower body fixed values on page 50 Pelvis on page 52 Knee Alignment Device (KAD) on page 52 Knee joint center on page 53 Femur on page 55 Ankle joint center on page 55 Tibia on page 58 Foot on page 59 Lower body fixed values The Newington-Gage model is used to define the positions of the hip joint centers in the pelvis segment. If the InterAsis distance has not been entered in the subject measurements, this is calculated as the mean distance between the LASI and RASI markers, for each frame in the trial for which there is a valid position for each marker. If the Asis to Trocanter distances have not been entered, they are calculated from the left and right leg lengths using the formula: AsisTrocDist = 0.1288 * LegLength – 48.56 This is done independently for each leg. The value C is then calculated from the mean leg length: C = MeanLegLength*0.115 – 15.3, aa is half the InterAsis distance, and mm the marker radius. These are used to then calculate the offset vectors for the two hip joint centers (LHJC and RHJC) as follows: X = C*cos(theta)*sin(beta) – (AsisTrocDist + mm) * cos(beta) Y = -(C*sin(theta) – aa) Z = -C*cos(theta)*cos(beta) – (AsisTrocDist + mm) * sin(beta) where theta is taken as 0.5 radians, and beta as 0.314 radians. Vicon Motion Systems Ltd. 26-Oct-2018 Page 50 of 104 Plug-in Gait Reference For the right joint center, the Y offset is negated (since Y is in the lateral direction for the pelvis embedded coordinate system). The position of the top of the lumbar vertebra 5 (the reference point for Dempster data on page 104) is then estimated as (LHJC + RHJC)/2 + (0.0, 0.0, 0.828) * Length(LHJC – RHJC) where the value 0.828 is a ratio of the distance from the hip joint center level to the top of the lumbar 5 compared to distance between the hip joint centers on the pelvis mesh. Knee and ankle offsets are then calculated by adding half the measured joint width and marker diameter to give the distance from the center point of the marker to the joint center. The general direction of the subject walking in the global coordinate system is then found by looking at the first and last valid position of the LASI marker. The X displacement is compared to the Y displacement. If the X displacement is bigger, the subject is deemed to have been walking along the X axis either positively or negatively, depending on the sign of the X offset. Otherwise, the Y axis is chosen. These directions are used to define a coordinate system matrix (similar to a segment definition) denoted the ProgressionFrame. Note that it's assumed that the Z axis is always vertical, and that the subject is walking along one of these axes, and not diagonally, for example. If the distance between the first and last frame of the LASI marker is less than a threshold of 800mm however, the progression frame is calculated using the direction the pelvis is facing during the middle of the trial. This direction is calculated as a mean over 10% of the frames of the complete trial. Within these frames, only those which have data for all the pelvis markers are used. For each such frame, the rear pelvis position is calculated from either the SACR marker directly, or the center point of the LPSI and RPSI markers. The front of the pelvis is calculated as the center point between the LASI and RASI markers. The pelvis direction is calculated as the direction vector from the rear position to the front. This direction is then used in place of the LASI displacement, as described above, and compared to the laboratory X and Y axes to choose the Progression Frame. Vicon Motion Systems Ltd. 26-Oct-2018 Page 51 of 104 Plug-in Gait Reference Pelvis First the pelvis segment coordinate system is defined from the waist markers. The origin is taken as the midpoint of the two asis markers. The dominant axis, taken as the Y axis, is the direction from the right asis marker to the left asis marker. The secondary direction is taken as the direction from the sacrum marker to the right asis marker. If there is no sacrum marker trajectory, the posterior markers are used. If both are visible, the mean is used. If just one is visible, then that one is used. The Z direction is generally upwards, perpendicular to this plane, and the X axis generally forwards. The position and scale of the pelvis is thus determined by the two asis markers, since they determine the origin of the coronal orientation of the pelvis. The posterior sacral markers (or psis markers) determine only the anterior tilt of the pelvis. Their actual distance behind the asis markers and lateral position is immaterial, allowing a sacral wand marker to be used, for example. If the asis markers are also used to calculate the inter asis distance, they are therefore also used to determine the lateral positions of the hip joint centers within the pelvis segment. It is important for these to be as accurate as possible, since they affect the determination of the femur segments, and thus influence both the hip angles, and also the knee joint angles. Knee Alignment Device (KAD) For the model to determine the knee and ankle joint centers, the markers must be very carefully positioned, and it is the responsibility of clinical staff to use their anatomical knowledge to position markers such that the model is able to make as good an approximation to the joint centers as possible. The dynamic model uses the Thigh and Shank wand markers to define the plane of containing the joint centers, and one method of marker placement is to carefully position these markers to align with your judgment of where the joint centers are. Alternatively, the Knee Alignment Device (KAD) may be used. This must be placed on the patient during the static trial to indicate the plane of the knee joint center. Then the model calculates the relative angle of the Thigh wand marker, and this angle is used in the dynamic trial to determine the joint center without the KAD. This technique relies on the accurate placement of the KAD, rather than the accurate placement of the wand marker. Vicon Motion Systems Ltd. 26-Oct-2018 Page 52 of 104 Plug-in Gait Reference Knee joint center Static knee joint center calculation on page 53 Dynamic knee joint center calculation on page 54 Static knee joint center calculation If a KAD is being used in the static model, firstly a virtual KNE marker is determined by finding the point that is equidistant from the three KAD markers, such that the directions from the point to the three markers are mutually perpendicular. For the right knee, the markers RKAX, RKD1, RKD2 must be labeled in a clockwise direction, and for the left knee, the markers LKAX, LKD1, LKD2 must be labeled anticlockwise. That is, if the two KD markers are positioned anteriorly, the upper marker should be KD1. The joint center KJC is then determined using the chord function with the HJC, KNE and KAX. The HJC-KJC and KJC-KNE lines will be perpendicular, and the KJC-KNE line has a length equal to the knee offset (KO). The thigh marker rotation offset ( ) is then calculated by projecting its position on to a plane perpendicular to the HJC-KJC line. Vicon Motion Systems Ltd. 26-Oct-2018 Page 53 of 104 Plug-in Gait Reference If a KAD is not being used in a static trial, then processing proceeds exactly as for a dynamic trial. Note that for static trials without a KAD, the anterior-posterior position of the KJC is determined by the position of the THI wand marker, and the value of wand offset value that is entered (if you do not enter a value, a value of zero is assumed). Correct determination of the KJC (and the AJC) is very important, especially for the kinetic calculations. In the clinic, you have to assess which method of marker positioning gives the best estimate of the KJC: using a KAD or using the THI marker. Dynamic knee joint center calculation In the dynamic model, the KJC is determined using the modified chord function, from the global position of the HJC, the thigh wand marker (THI), and the knee marker (KNE), together with the knee offset (KO), and thigh wand angle offset ( ) from the subject measurements. KJC is found such that the KNE marker is at a distance of KO from the KJC, in a direction perpendicular to the line from the HJC to KJC. It is also found such that the angle between the KJC-KNE line and the KJC-THI line, projected onto a plane perpendicular to the HJC-KJC line, is the same as the thigh wand offset angle. There is only one position for the KJC that satisfies these two conditions. Vicon Motion Systems Ltd. 26-Oct-2018 Page 54 of 104 Plug-in Gait Reference Femur The femur origin is taken as the knee joint center. The primary Z axis is taken from the knee joint center (KJC) to the hip joint center (HJC). The secondary axis is taken parallel to the line from the knee joint center to the knee marker (or virtual knee marker, for static KAD trials). This in fact directly gives the direction of the Y axis. For both the left and the right femur, the Y axis is directed towards the left of the subject. The X axis for both femura is hence directed forwards from the knee. Note that in a static trial although a KAD determines the plane in which the knee joint center lies, it does not directly determine the lateral orientation of the "knee axis" which is implicitly defined as the Y axis of the femur segment. The lateral orientation is defined by the vertical orientation of the Z axis (the line joining the hip and knee joint centers). The Y axis may pass either above or below the KNE marker. Ankle joint center The ankle joint center is determined in a similar manner to the knee joint center (see Knee joint center on page 53). Static ankle joint center calculation on page 55 Dynamic ankle joint center calculation on page 57 Static ankle joint center calculation In static trials with a KAD, the KAX marker is used to define the plane of the knee axis, and the plane of the ankle axis is assumed to be parallel to this. A value for Tibial Torsion can be entered, and the plane of the in which the Ankle joint center lies will be rotated by this amount relative to the plane containing the KAX marker. Thus the AJC is found using the modified chord function, such that it has a distance equal to the ankle offset from the ANK marker (AO), and such that the ANK-AJC line forms an angle equal to the Tibial Torsion with the projection of the KAX-AJC line into the plane perpendicular to the KJC-AJC line. Note that Tibial Torsion is thus considered as an external rotation of the ankle axis relative to the knee axis. Vicon Motion Systems Ltd. 26-Oct-2018 Page 55 of 104 Plug-in Gait Reference The shank marker rotation offset is then calculated by projecting its position onto the same plane. Note that this value takes into account the value of the tibial torsion, and in general, you would expect it to be slightly less than the value for Tibial Torsion, if the TIB wand marker is conventionally placed. Vicon Motion Systems Ltd. 26-Oct-2018 Page 56 of 104 Plug-in Gait Reference Dynamic ankle joint center calculation In the dynamic trial, and static trials without a KAD, the ankle joint center is calculated from the knee joint center, shank wand marker and ankle marker with the ankle offset and shank rotation offset using the modified chord function. Thus the ankle joint center is at a distance of ankle offset from the ankle marker, and the angle between the KJC-AJC-ANK plane and the KJC-AJC-TIB plane is equal to the tibia rotation offset. Vicon Motion Systems Ltd. 26-Oct-2018 Page 57 of 104 Plug-in Gait Reference Tibia Tortioned tibia on page 58 Untortioned tibia on page 58 Tortioned tibia The tibial rotation offset as determined by the static trial already takes into account the tibial torsion. Thus a Tortioned Tibia is defined with an origin at the AJC, the Z Axis in the direction from the AJC to the KJC, the Y axis leftwards along the line between the AJC and ANK marker, and the X axis generally forwards. This is representative of the distal end of the tibia. Untortioned tibia A second tibia is also generated representing the tibia before tibial torsion is applied, by rotating the X and Y axes of the Tortioned Tibia round the Z axis by the negative of the tibial torsion (i.e. externally for +ve values). This represents the proximal end, and is used to calculate the knee joint angles. Vicon Motion Systems Ltd. 26-Oct-2018 Page 58 of 104 Plug-in Gait Reference Foot Static foot on page 59 Dynamic foot on page 61 Static foot calculation The heel marker is used in the static trial, and the model effectively makes two segments. For both segments, the AJC is used as the origin. The main foot segment is constructed using the TOE-HEE line as the primary axis. If the settings for the model have the foot flat check box selected (ie you have selected Left Foot and/or Right Foot in the Assume Horizontal properties for the Process Static Plugin Gait Model pipeline operation), then HEE is moved vertically (along the global Z axis) to be at the same height as TOE. This line is taken as the Z axis, running forwards along the length of the foot. The direction of the Y axis from the untortioned tibia is used to define the secondary Y axis. The X axis thus points down, and the Y axis to the left. Vicon Motion Systems Ltd. 26-Oct-2018 Page 59 of 104 Plug-in Gait Reference A second foot segment is constructed, using the TOE-AJC as the primary axis, and again the Y axis of the untortioned tibia to define the perpendicular X axis and the foot Y axis (the 'uncorrected' foot). The Static offset angles (Plantar Flexion offset and Rotation offset) are then calculated from the 'YXZ' Cardan Angles between the two segments (rotating from the 'uncorrected' segment to the heel marker based foot segment). This calculation is performed for each frame in the static trial, and the mean angles calculated. The static plantar-flexion offset is taken from the rotation round the Y axis, and the rotation offset is the angle round the X axis. The angle round the Z axis is ignored. Vicon Motion Systems Ltd. 26-Oct-2018 Page 60 of 104 Plug-in Gait Reference Dynamic foot calculation In the dynamic trial, the foot is calculated in the same way as for the 'uncorrected' foot. The resulting segment is then rotated first round the Y axis by the Plantar Flexion offset. Then the resulting segment is rotated around its X axis by the rotation offset. Vicon Motion Systems Ltd. 26-Oct-2018 Page 61 of 104 Plug-in Gait Reference Upper body kinematics Upper body fixed values on page 62 Head on page 63 Thorax on page 63 Shoulder joint center on page 64 Clavicle on page 64 Elbow joint center on page 65 Wrist joint center on page 66 Humerus on page 66 Radius on page 66 Hand on page 67 Upper body fixed values A shoulder offset value is calculated from the Subject measurement value entered, plus half the marker diameter. Elbow, wrist and hand offset values are also calculated from the sum of the respective thickness with the marker diameter divided by two. A progression frame is independently calculated in just the same way as for the lower body. C7 is tested first to determine if the subject moved a distance greater than the threshold. If not, the other thorax markers T10 CLAV and STRN are used to determine the general direction the thorax was facing in from a mean of 10% of the frames in the middle of the trial. Note that in principle it could be possible to arrive at different reference frames for the upper and lower body, though the circumstances would be extreme. Vicon Motion Systems Ltd. 26-Oct-2018 Page 62 of 104 Plug-in Gait Reference Head The head origin is defined as the midpoint between the LFHD and RFHD markers (also denoted 'Front'). The midpoint between the LBHD and RBHD markers ('Back') is also calculated, along with the 'Left' and 'Right' sides of the head from the LFHD and LBHD midpoint, and the RFHD and RBHD midpoint respectively. The predominant head axis, the X axis, is defined as the forward facing direction (Front - Back). The secondary Y axis is the lateral axis from Right to Left (which is orthogonalized as usual). For the static processing, the YXZ Euler angles representing the rotation from the head segment to the lab axes are calculated. The Y rotation is taken as the head Offset angle, and the mean of this taken across the trial. For the dynamic trial processing, the head Offset angle is applied around the Y axis of the defined head segment. Thorax The orientation of the thorax is defined before the origin. The Z axis, pointing upwards, is the predominant axis. This is defined as the direction from the midpoint of the STRN and T10 to the midpoint of CLAV and C7. A secondary direction pointing forwards is the midpoint of C7 and T10 to the midpoint of CLAV and STRN. The resulting X axis points forwards, and the Y axis points leftwards. The thorax origin is then calculated from the CLAV marker, with an offset of half a marker diameter backwards along the X axis. Vicon Motion Systems Ltd. 26-Oct-2018 Page 63 of 104 Plug-in Gait Reference Shoulder joint center The clavicles are considered to lie between the thorax origin, and the shoulder joint centers. The shoulder joint centers are defined as the origins for each clavicle. Note that the posterior part of the shoulder complex is considered too flexible to be modeled with this marker set. Initially a direction is defined, which is perpendicular to the line from the thorax origin to the SHO marker, and the thorax X axis. This is used to define a virtual shoulder 'wand' marker. The chord function is then used to define the shoulder joint center (SJC) from the Shoulder offset, thorax Origin, SHO marker and shoulder 'wand'. Clavicle The clavicle segment is defined from the direction from the joint center to the thorax origin as the Z axis, and the shoulder wand direction as the secondary axis. The X axis for each clavicle points generally forwards, and the Y axis for the left points upwards, and the right clavicle Y axis points downwards. Vicon Motion Systems Ltd. 26-Oct-2018 Page 64 of 104 Plug-in Gait Reference Elbow joint center A construction vector direction is defined, being perpendicular to the plane defined by the shoulder joint center, the elbow marker (LELB) and the midpoint of the two wrist markers (LWRA, LWRB). The elbow joint center is defined using the chord function, in the plane defined by the shoulder joint center, the elbow marker and the previously defined construction vector. Vicon Motion Systems Ltd. 26-Oct-2018 Page 65 of 104 Plug-in Gait Reference Wrist joint center After the elbow joint center is calculated, the wrist joint center (WJC) is calculated. In this case the chord function is not used. The wrist joint center is simply offset from the midpoint of the wrist bar markers along a line perpendicular to the line along the wrist bar, and the line joining the wrist bar midpoint to the elbow joint center. Humerus After the wrist joint center is defined, the Humerus is calculated with its origin at the EJC, a principal Z axis from EJC to SJC, and a secondary line approximating to the X axis between the EJC and the WJC. Radius The radius origin is set at the wrist joint center. The principal axis is the Z axis, from the WJC to the EJC. The secondary line approximating to the Y axis is taken as the Y axis of the Humerus segment. Vicon Motion Systems Ltd. 26-Oct-2018 Page 66 of 104 Plug-in Gait Reference Hand The hand is defined by first defining its origin. The chord function is used again for this, with the WJC, FIN marker and Hand Offset. The midpoint of the wrist bar markers is used to define the plane of calculation. The principal Z axis is then taken as the line from the hand origin to the WJC, and a secondary line approximating the Y axis is defined by direction of the line joining the wrist bar markers. Vicon Motion Systems Ltd. 26-Oct-2018 Page 67 of 104 Plug-in Gait Reference Angle outputs The output angles for all joints are calculated from the YXZ Cardan angles derived by comparing the relative orientations of the two segments. The knee angles are calculated from the femur and the Untortioned tibia segments, whilst the ankle joint angles are calculated from the Tortioned tibia and the foot segment. In the case of the feet, since they are defined in a different orientation to the tibia segments, an offset of 90 degrees is added to the flexion angle. This does not affect the Cardan angle calculation of the other angles since the flexion angle is the first in the rotation sequence. The progression angles of the feet, pelvis, thorax and head are the YXZ Cardan calculated from the rotation transformation of the subject's Progression Frame for the trial onto each segment orientation. Vicon Motion Systems Ltd. 26-Oct-2018 Page 68 of 104 Plug-in Gait Reference Kinetic modeling The kinetic modeling parts of the model simply assign masses and radii of gyration to the segments defined in the kinematic model. An estimate of the position of the center of mass is required in the segment. This is defined as a point at a given proportion along a line from the distal joint center (normally the origin of the segment) towards the proximal joint center of a "typical" segment. The masses of each segment are calculated as a proportion of the total body mass. The principal axes moments of inertia are calculated from (mass) normalized radii of gyration from these tables too. In general the moment is considered to be zero around the longitudinal axis of most segments. Since experimental data were not available, estimates have been made for the radii of gyration of the pelvis and thorax. You can change these values in the Properties pane of the Process Dynamic Plug-in Gait Model pipeline operation. The following diagram shows the kinetic hierarchy. Vicon Motion Systems Ltd. 26-Oct-2018 Page 69 of 104 Plug-in Gait Reference Note that the clavicles are not considered to have mass in themselves, so reactions for the humerus segments are consider to act directly on the thorax. Vicon Motion Systems Ltd. 26-Oct-2018 Page 70 of 104 Plug-in Gait Reference The feet are only 'connected' to the forceplates where forceplate measurements and marker data indicate a match. Only one segment is chosen to be in contact with a given forceplate for each frame. Note also that the "untortioned" tibiae are used for the kinetic modeling. This means that where the KAD and a tibial torsion have been used, and the proximal frame is chosen to reference the ankle moments, the flexion and abduction moments will not correspond to the axes used to calculate the ankle angles. Having said that, the axes are calculated with a "floating axis" definition, so even for corresponding segments the axes will not be coincident. Even though the "untortioned" tibiae are used for the reference frames, a difference in moments will be observed if the trial is processed with a different tibial torsion. When the tibial torsion is applied in the static trial, the ankle joint center is moved backwards, then the "untortioned" tibia is calculated by rotating the tortioned tibia round the Z axis, keeping the ankle joint center in position. Thus, for a given trial, as tibial torsion is increased, and the joint center is rotated backwards around the ankle marker, the ankle flexion moment will generally become more positive. Segment CoM Mass Radius of gyration Pelvisa 0.895 0.142 0.31 Femur 0.567 0.1 0.323 Tibia 0.567 0.0465 0.302 Foot 0.5 0.0145 0.475 Humerus 0.564 0.028 0.322 Radius 0.57 0.016 0.303 Handb 0.6205 0.006 0.223 Thoraxc 0.63 0.355 0.31 Headd see below 0.081 0.495 Vicon Motion Systems Ltd. 26-Oct-2018 Page 71 of 104 Plug-in Gait Reference a) Pelvis: The center of mass is defined along a line from the midpoint of the hip joint centers, to the center of the top surface of the Lumbar 5 vertebra. For simplified scaling, this distance is defined as 0.925 times the distance between the hip joint centers, and the Lumbar5 is defined as lying directly on the Z axis (derived by inspection from the bone mesh used in Polygon). The radius of gyration for the pelvis is an estimate, and is applied round all three axes. b) Hand: The length of the hand in this model is defined as the distance from the wrist joint center to the finger tip. An estimate of 0.75 is taken as the proportion of this length to the "Knuckle II" reference point referred to in the Dempster data on page 104. c) Thorax: The thorax length is taken as the distance between an approximation to the C7 vertebra and the L5 vertebra in the Thorax reference frame. C7 is estimated from the C7 marker, and offset by half a marker diameter in the direction of the X axis. L5 is estimated from the L5 provided from the pelvis segment, but localized to the thorax, rather than the pelvis. The positions are calculated for all frames in the trial, and averaged to give the mean length. The Center of mass is deemed to lie at a proportion of 0.63 along this line. d) Head: The center of mass of the head is defined as being 0.52 * the distance from the front to the back of the head along the X axis from the head origin (the midpoint of the front head markers). The length of the head used for the inertial normalization is the distance from this point to the C7 vertebra (the mean position localized to the head segment). The inertia value for the head is applied around all three axes. Vicon Motion Systems Ltd. 26-Oct-2018 Page 72 of 104 Plug-in Gait Reference Whole body center of mass The center of mass is calculated whenever the head or thorax segment is present. A weighted sum of all the centers of mass of all the segments is made, where segments are defined by markers. The sum is still made if segments, such as the hands, for example, do not have markers. The center of mass is the center of mass of all the modeled segments. Caution Note that this center of mass algorithm has not been clinically tested, and may be misleading in some clinical situations. In particular, the thorax segment is modeled kinetically as a rigid body which includes the mass of the abdomen (which is not independently modeled). The markers which define the thorax are at the top of the thorax, and the center of mass is assumed to be on a line directed towards the L5 vertebra. Any bending of the trunk in the upper lumbar region will cause this assumption to fail, which may cause a significant error in the position of the center of mass for the whole body. The projection of the center of mass onto the floor is made simply by setting the Z value to zero. Vicon Motion Systems Ltd. 26-Oct-2018 Page 73 of 104 Plug-in Gait Reference Plug-in Gait output angles The output angles for all joints are calculated from the YXZ Cardan angles derived by comparing the relative orientations of the segments proximal (parent) and distal (child) to the joint. The knee angles are calculated from the femur and the Untorsioned tibia segments, while the ankle joint angles are calculated from the Torsioned tibia and the foot segment. In the case of the feet, because they are defined in a different orientation to the tibia segments, an offset of 90 degrees is added to the flexion angle. This does not affect the Cardan angle calculation of the other angles because the flexion angle is the first in the rotation sequence. The progression angles of the feet, pelvis, thorax and head are the YXZ Cardan calculated from the rotation transformation of the subject's progression frame for the trial onto each segment orientation. The following topics provide further details. Angle definitions on page 75 Plug-in Gait kinematic variables on page 78 Upper body angles as output from Plug-in Gait on page 88 Lower body angles as output from Plug-in Gait on page 93 Vicon Motion Systems Ltd. 26-Oct-2018 Page 74 of 104 Plug-in Gait Reference Angle definitions Plug-in Gait uses Cardan angles, modified in the case of the ankle angles, to represent both: Absolute rotations of the pelvis and foot segments and Relative rotations at the hip, knee, and ankle joints These angles can be described either as a set of rotations carried out one after the other (ordered). For more information about the use of Cardan angles to calculate joint kinematics, refer to Kadaba, Ramakrishnan and Wooten (1990) and Davis, Õunpuu, Tyburski and Gage (1991) (see Plug-in Gait references). The rotations are measured about anatomical axes in order to simplify their interpretation. For more information on joint angle descriptions, including the issues of gimbal lock and Codman's Paradox, see: Ordered rotations on page 75 Angle goniometric description on page 76 Ordered rotations To describe an angle using ordered rotations, the following are true: One element is 'fixed'. For absolute rotations the laboratory axes are fixed. The proximal segment axes are fixed for relative rotations. The second element 'moves'. This means the segment axes move for absolute rotations and distal segment moves for relative rotations. A joint angle is then defined using the following ordered rotations: The first rotation (flexion) is made about the common flexion axis. The other two axes, abduction and rotation, are afterwards no longer aligned in the two elements. The second rotation (abduction) is made about the abduction axis of the moving element. The third rotation (rotation) is made about the rotation axis of the moving element. Vicon Motion Systems Ltd. 26-Oct-2018 Page 75 of 104 Plug-in Gait Reference Angle goniometric description In addition to using ordered rotations, joint angles can also be described using goniometric information. Using goniometric definitions, a joint angle is described by the following: Flexion is about the flexion axis of the proximal (or absolute) element. Rotation is about the rotation axis of the distal element. Abduction axis 'floats' so as always to be at right angles to the other two. Cardan angles work well unless a rotation approaching 90 degrees brings two axes into line. When this happens, one of the possible rotations is lost and becomes unmeasurable. Fortunately, this does not frequently occur in the joints of the lower limbs during normal or pathological gait. However this may occur in the upper limb and particularly at the shoulder. For more information, see Gimbal lock on page 76 and also Codman's Paradox on page 76 below. Gimbal lock Gimbal lock occurs when using Cardan (Euler) angles and any of the rotation angles becomes close to 90 degrees, for example, lifting the arm to point directly sideways or in front (shoulder abduction about an anterior axis or shoulder flexion about a lateral axis respectively). In either of these positions the other two axes of rotation become aligned with one another, making it impossible to distinguish them from one another, a singularity occurs and the solution to the calculation of angles becomes unobtainable. For example, assume that the humerus is being rotated in relation to the thorax in the order Y,X,Z and that the rotation about the X-axis is 90 degrees. In such a situation, rotation in the Y-axis is performed first and correctly. The X-axis rotation also occurs correctly BUT rotates the Z axis onto the Y axis. Thus, any rotation in the Y-axis can also be interpreted as a rotation about the Z-axis. True gimbal lock is rare, arising only when two axes are close to perfectly aligned. Codman's Paradox The second issue however, is that in each non-singular case there are two possible angular solutions, giving rise to the phenomenon of "Codman's Paradox" in anatomy (Codman, E.A. (1934). The Shoulder. Rupture of the Supraspinatus Tendon and other Lesions in or about the Subacromial Bursa. Boston: Thomas Todd Company), where different combinations of numerical values of the three angles produce similar physical orientations of the segment. This is not actually a paradox, but a consequence of the Vicon Motion Systems Ltd. 26-Oct-2018 Page 76 of 104 Plug-in Gait Reference non-commutative nature of three-dimensional rotations and can be mathematically explained through the properties of rotation matrices (Politti, J.C., Goroso, G., Valentinuzzi, M.E., & Bravo, O. (1998). Codman's Paradox of the Arm Rotations is Not a Paradox: Mathematical Validation. Medical Engineering & Physics, 20, 257-260). Codman proposed that the completely elevated humerus could be shown to be in either extreme external rotation or in extreme internal rotation by lowering it either in the coronal or sagittal plane respectively, without allowing any rotation about the humeral longitudinal axis. To demonstrate Codman's Paradox, complete the following steps: 1. Place the arm at the side, elbow flexed to 90 degrees and the forearm internally rotated across the stomach. 2. Elevate the arm 180 degrees in the sagittal plane. 3. Lower the arm 180 degrees to the side in the coronal plane. Observe that the forearm now points 180 degrees externally rotated from its original position with no rotation about the humeral longitudinal axis actually having occurred. 4. Note the difficulty in describing whether the fully elevated humerus was internally or externally rotated. This ambiguity can cause switching between one solution and the other, resulting in sudden discontinuities. A combination of gimbal lock and Codman's Paradox can lead to unexpected results when joint modeling is carried out. In practice, the shoulder is the only joint commonly analyzed that has a sufficient range of motion about all rotation axes for these to be an issue. Generally, if you are aware of the reasons for the inconsistent data, you can manipulate any erroneous results by adding 180 or 360 degrees. As Plug-in Gait uses Cardan (Euler) angles in all cases to calculate joint angles, they are subject to both Gimbal Lock in certain poses, and the inconsistencies that occur as a result of Codman's Paradox. Plug-in Gait includes some steps to minimize the above effects by trying to keep the shoulder angles in consistent and understandable quadrants. This is not a complete solution however, as the above issues are inherent when using Cardan (Euler) angles and clinical descriptions of motion. Vicon Motion Systems Ltd. 26-Oct-2018 Page 77 of 104 Plug-in Gait Reference Plug-in Gait kinematic variables When gait cycle events have been defined, derived kinematic quantities are calculated and written to file. Note that throughout this section, axes are described as follows: Transverse axes are those axes which pass from one side of the body to the other; Sagittal axes pass from the back of the body to the front; and Frontal axes pass in a direction from the center of the body through the top of the head. Vicon Motion Systems Ltd. 26-Oct-2018 Page 78 of 104 Plug-in Gait Reference List of kinematic variables calculated by Plug-in Gait The following table lists all the kinematic variables calculated by Plug-in Gait. It includes information describing each variable in terms of ordered rotations or goniometric definitions. For example, knee rotation is a relative angle measured between the thigh as the proximal segment and the shank as the distal segment. Its 'goniometric' axis is fixed to the shank as the distal segment. Incidentally, this angle, although always calculated, is often omitted from reports because it is so difficult to measure with precision. Foot rotation and foot progression, also known as foot alignment, are not expressed in terms of goniometric axes, since the ankle angles are not calculated as strict Cardan angles. Both rotations measure the alignment of the foot. The first is relative to the shank, and the second is measured as an absolute angle in the laboratory's transverse plane. Absolute angles are measured relative to laboratory axes with the sagittal and transverse axes automatically selected according to the direction of walking. In Plug-in Gait, the laboratory axis closest to the subject's direction of progression is labeled the laboratory sagittal axis. Each variable is listed in the following table: Angle Goniometric Description Absolute Pelvic tilt is normally calculated about the laboratory's rotation Pelvic tilt transverse axis. If the subject's direction of forward progression is closer to the laboratory's sagittal axis, however, then pelvic tilt is measured about this axis. The sagittal pelvic axis, which lies in the pelvis transverse plane, is normally projected into the laboratory sagittal plane. Pelvic tilt is measured as the angle in this plane between the projected sagittal pelvic axis and the sagittal laboratory axis. A positive value (up) corresponds to the normal situation in which the PSIS is higher than the ASIS. Pelvic obliquity Absolute Pelvic obliquity is measured about an axis of rotation perpendicular to the axes of the other two rotations. This axis does not necessarily correspond with any of Vicon Motion Systems Ltd. 26-Oct-2018 Page 79 of 104 Plug-in Gait Reference Angle Goniometric Description rotation the laboratory or pelvic axes. Pelvic obliquity is measured in the plane of the laboratory transverse axis and the pelvic frontal axis. The angle is measured between the projection into the plane of the transverse pelvic axis and projection into the plane of the laboratory transverse axis (the horizontal axis perpendicular to the subject's axis of progression). A negative pelvic obliquity value (down) relates to the situation in which the opposite side of the pelvis is lower. Pelvic Absolute rotation Pelvic rotation is calculated about the frontal axis of the pelvic co-ordinate system. It is the angle measured between the sagittal axis of the pelvis and the sagittal laboratory axis (axis closest to subject's direction of progression) projected into the pelvis transverse plane. A negative (external) pelvic rotation value means the opposite side is in front. Hip flexion Relative /extension Hip flexion is calculated about an axis parallel to the pelvic transverse axis which passes through the hip joint centre. The sagittal thigh axis is projected onto the plane perpendicular to the hip flexion axis. Hip flexion is then the angle between the projected sagittal thigh axis and the sagittal pelvic axis. A positive (Flexion) angle value corresponds to the situation in which the knee is in front of the body. Hip ab /adduction Relative Hip adduction is measured in the plane of the hip flexion axis and the knee joint centre. The angle is calculated between the long axis of the thigh and the frontal axis of the pelvis projected into this plane. A positive number corresponds to an adducted (inwardly moved) leg. Vicon Motion Systems Ltd. 26-Oct-2018 Page 80 of 104 Plug-in Gait Reference Angle Goniometric Description Relative Hip rotation is measured about the long axis of the rotation Hip rotation thigh segment and is calculated between the sagittal axis of the thigh and the sagittal axis of the pelvis projected into the plane perpendicular to the long axis of the thigh. The sign is such that a positive hip rotation corresponds to an internally rotated thigh. Knee Relative The sagittal shank axis is projected into the plane flexion perpendicular to the knee flexion axis. Knee flexion is /extension the angle in that plane between this projection and the sagittal thigh axis. The sign is such that a positive angle corresponds to a flexed knee. Knee ab Relative This is measured in the plane of the knee flexion axis /adduction and the ankle center, and is the angle between the (Knee long axis of the shank and the long axis of the thigh valgus projected into this plane. /varus) A positive number corresponds to varus (outward bend of the knee). Knee Relative rotation Knee rotation is measured about the long axis of the shank. It is measured as the angle between the sagittal axis of the shank and the sagittal axis of the thigh, projected into a plane perpendicular to the long axis of the shank. The sign is such that a positive angle corresponds to internal rotation. If a tibial torsion value is present in the Session form, it is subtracted from the calculated knee rotation value. A positive tibial torsion value therefore has the effect of providing a constant external offset to knee rotation. Ankle dorsi Relative The foot vector is projected into the foot sagittal /plantar plane. The angle between the foot vector and the flexion sagittal axis of the shank is the foot dorsi/plantar flexion. A positive number corresponds to dorsiflexion. Vicon Motion Systems Ltd. 26-Oct-2018 Page 81 of 104 Plug-in Gait Reference Angle Goniometric Description rotation Foot Relative rotation This is measured about an axis perpendicular to the foot vector and the ankle flexion axis. It is the angle between the foot vector and the sagittal axis of the shank, projected into the foot transverse plane. A positive number corresponds to an internal rotation. Foot-based This optional angle is defined similarly to ankle dorsi dorsi /plantar flexion, but it is measured in a plane /plantar containing the knee and ankle centers and the toe flexion marker. Foot Absolute progression This is the angle between the foot vector (projected into the laboratory's transverse plane) and the sagittal laboratory axis. A positive number corresponds to an internally rotated foot. Head tilt Absolute Head tilt is normally calculated about the laboratory's transverse axis. If the subject's direction of forward progression is closer to the laboratory's sagittal axis, however, then head tilt is measured about this axis. The sagittal head axis is normally projected into the laboratory sagittal plane. Head tilt is measured as the angle in this plane between the projected sagittal head axis and the sagittal laboratory axis. A positive value (up) corresponds to forward head tilt. Head obliquity Absolute Head lateral tilt is measured about an axis of rotation perpendicular to the axes of the other two rotations. This axis does not necessarily correspond with any of the laboratory or head axes. Head lateral tilt is measured in the plane of the laboratory transverse axis and the head frontal axis. The angle is measured between the projection into the plane of the transverse head axis and projection into the plane of the laboratory transverse axis (the horizontal axis Vicon Motion Systems Ltd. 26-Oct-2018 Page 82 of 104 Plug-in Gait Reference Angle Goniometric Description rotation perpendicular to the subject's axis of progression). A negative head obliquity value (down) relates to the situation in which the opposite side of the head is lower. Head Absolute rotation Head rotation is calculated about the frontal axis of the head co-ordinate system. It is the angle measured between the sagittal axis of the head and the sagittal laboratory axis (axis closest to subject's direction of progression) projected into the head transverse plane. A negative (external) head rotation value means the opposite side is in front. Thorax tilt Absolute Thorax tilt is normally calculated about the laboratory's transverse axis. If the subject's direction of forward progression is closer to the laboratory's sagittal axis, however, then thorax tilt is measured about this axis. The sagittal thorax axis is normally projected into the laboratory sagittal plane. Thorax tilt is measured as the angle in this plane between the projected sagittal thorax axis and the sagittal laboratory axis. A positive value (up) corresponds to forward thorax tilt. Thorax obliquity Absolute Thorax obliquity is measured about an axis of rotation perpendicular to the axes of the other two rotations. This axis does not necessarily correspond with any of the laboratory or thorax axes. Thorax obliquity is measured in the plane of the laboratory transverse axis and the Thorax frontal axis. The angle is measured between the projection into the plane of the transverse thorax axis and projection into the plane of the laboratory transverse axis (the horizontal axis perpendicular to the subject's axis of progression. Vicon Motion Systems Ltd. 26-Oct-2018 Page 83 of 104 Plug-in Gait Reference Angle Goniometric Description rotation As the thorax segment is defined with the frontal Z axis point downward a positive (up) thorax obliquity angle relates to the situation in which the opposite side of the thorax is lower. Thorax Absolute rotation Thorax rotation is calculated about the frontal axis of the thorax co-ordinate system. It is the angle measured between the sagittal axis of the thorax and the sagittal laboratory axis (axis closest to subject's direction of progression) projected into the thorax transverse plane. As the thorax segment is defined with the frontal Z axis point downward a positive (internal) thorax rotation value means the opposite side is in front. Neck Relative The sagittal head axis is projected onto the plane flexion perpendicular to the thorax sagittal axis. Neck flexion /extension is then the angle between the projected sagittal head axis and the sagittal thorax axis around the fixed transverse axis of the thorax. A positive (flexion) angle value corresponds to the situation in which the head is tilted forward. Neck Relative The angle between the long axis of the head and the lateral long axis of the thorax around a floating transverse flexion axis. Neck rotation Relative Neck rotation is measured about the long axis of the head. It is measured as the angle between the sagittal axis of the head and the sagittal axis of the thorax, around a floating frontal axis. As the thorax frontal axis points downward while the head frontal axis points upward, a positive angle therefore refers to rotation of the head toward the opposite side. Vicon Motion Systems Ltd. 26-Oct-2018 Page 84 of 104 Plug-in Gait Reference Angle Goniometric Description Relative Spine flexion is the angle between the sagittal thorax rotation Spine flexion axis and the sagittal pelvis axis around the fixed /extension transverse axis of the pelvis. A positive (flexion) angle value corresponds to the situation in which the thorax is tilted forward. Spine Relative The angle between the long axis of the thorax and the lateral long axis of the pelvis, around a floating transverse flexion axis. Spine Relative rotation It is measured as the angle between the sagittal axis of the thorax and the sagittal axis of the pelvis, around a floating frontal axis. As the thorax frontal axis points downward while the pelvis frontal axis points upward, a positive angle therefore refers to rotation of the thorax toward the opposite side. Shoulder Relative Shoulder flexion is calculated about an axis parallel to flexion the thorax transverse axis. Shoulder flexion is the /extension angle between the projected sagittal-humerus axis and the sagittal-thorax axis around the fixed transverse axis. of the thorax. A positive (flexion) angle value corresponds to the situation in which the arm is in front of the body. Shoulder ab /adduction Relative The angle is calculated between the transverse axis of the humerus and the transverse axis of the thorax around a floating sagittal axis. A negative number corresponds to an abducted (outwardly moved) arm. Vicon Motion Systems Ltd. 26-Oct-2018 Page 85 of 104 Plug-in Gait Reference Angle Goniometric Description Relative Shoulder rotation is measured about the long axis of rotation Shoulder rotation the humerus segment and is calculated between the sagittal axis of the humerus and the sagittal axis of the thorax around a floating frontal axis. The sign is such that a positive shoulder rotation corresponds to an internally rotated humerus. Elbow Relative Elbow flexion is the only kinematic parameter flexion calculated at the elbow as the segment definitions of /extension the Humerus and radius result in two of the axes being shared. Elbow flexion is calculated between the sagittal radius axis and the sagittal humerus axis around the fixed transverse axis of the humerus. A positive number indicates a flexion angle. Wrist Relative Wrist flexion is the angle between the sagittal hand flexion axis and the sagittal radius axis around the fixed /extension transverse axis of the radius. A positive (flexion) angle value corresponds to the situation in which the wrist bends toward the palm. Wrist ab Relative /adduction The angle is calculated between the transverse axis of the hand and the transverse axis of the radius around a floating sagittal axis. A positive number corresponds to the hand abducting toward the thumb. Wrist rotation Relative Wrist rotation is measured about the long axis of the hand segment and is calculated between the sagittal axis of the hand and the sagittal axis of the radius around a floating frontal axis. The sign is such that a positive wrist rotation corresponds to the hand rotating in the direction of the thumb. Vicon Motion Systems Ltd. 26-Oct-2018 Page 86 of 104 Plug-in Gait Reference For more information, see also: Complete pelvis position description A pelvis in which the three markers all lay in the horizontal plane and the line joining the ASIS markers was parallel to a laboratory axis, would have zero tilt, obliquity and rotation. To visualize the pelvic angles, start with a pelvis in this neutral position, tilt it about the transverse axis by the amount of pelvic tilt, rotate it about its (tilted) sagittal axis by the amount of pelvic obliquity and rotate it about its (tilted and oblique) frontal axis by the amount of pelvic rotation. The pelvis is now in the attitude described by those degrees of tilt, obliquity and rotation. The transverse and frontal plane kinematics of all joints are influenced by the mathematics involved with embedded axes. The following is an example which demonstrates the effect of using embedded axes to calculate "pelvic obliquity" in a static trial: If a calibration device, designed with 15 degrees of pelvic tilt and level ASIS markers, is statically rotated 20 degrees from a lab's axis of progression, a report generated by Plug-in Gait will show 10 degrees of pelvic obliquity. For more clarification about the effect of embedded axes on joint kinematics, refer to Kadaba, Ramakrishnan and Wooten (1990). Complete hip position description A thigh whose long axis was parallel to the frontal pelvic axis, and in which the knee flexion axis was parallel to the pelvic transverse axis, would be in the neutral position (described by zeroes in all three angles). To move from this neutral position to the actual thigh position described by the three angles, first flex the hip by the amount of the hip flexion, then adduct by the amount of hip adduction, then rotate the thigh about the (flexed and adducted) long axis of the thigh, and it is in the position described by those three angles. Complete knee position description A neutral shank is positioned such that the shank is in line with the thigh and the ankle flexion axis is parallel to the knee flexion axis. From this position, flex the knee by the amount of knee flexion, bend inward by the amount of valgus/varus, and rotate by the amount of knee rotation, to produce the actual position described by those three angles. Vicon Motion Systems Ltd. 26-Oct-2018 Page 87 of 104 Plug-in Gait Reference Upper body angles as output from Plug-in Gait The following tables display the upper body segment angles from Plug-in Gait. All upper body angles are calculated in rotation order YXZ. As Euler angles are calculated, each rotation causes the axis for the subsequent rotation to be shifted. X’ indicates an axis which has been acted upon and shifted by one previous rotation, X’’ indicates a rotation axis which has been acted upon and shifted by two previous rotations. Vicon Motion Systems Ltd. 26-Oct-2018 Page 88 of 104 Plug-in Gait Reference Left upper body angles Angles LHeadAngles LThoraxAngles LNeckAngles LSpineAngles LShoulderAngles LElbowAngles Vicon Motion Systems Ltd. Positive rotation Axis Direction 1 Backward Tilt Prg.Fm. Y Clockwise 2 Right Tilt Prg.Fm. X' Anti-clockwise 3 Right Rotation Prg.Fm. Z'' Clockwise 1 Backward Tilt Prg.Fm. Y Clockwise 2 Right Tilt Prg.Fm. X' Anti-clockwise 3 Right Rotation Prg.Fm. Z'' Clockwise 1 Forward Tilt Thorax Y Clockwise 2 Left Tilt Thorax X' Clockwise 3 Left Rotation Thorax Z'' Clockwise 1 Forward Thorax Tilt Pelvis Y Anti-Clockwise 2 Left Thorax Tilt Pelvis X' Clockwise 3 Left Thorax Rotation Pelvis Z'' Anti-Clockwise 1 Flexion Thorax Y Anti-clockwise 2 Abduction Thorax X' Anti-clockwise 3 Internal Rotation Thorax Z'' Anti-clockwise 1 Flexion Humeral Y Anti-clockwise 2 - Humeral X' - 26-Oct-2018 Page 89 of 104 Plug-in Gait Reference Angles LWristAngles Vicon Motion Systems Ltd. Positive rotation Axis Direction 3 - Humeral Z'' - 1 Ulnar Deviation Radius X Clockwise 2 Extension Radius Y' Clockwise 3 Internal Rotation Radius Z'' Clockwise 26-Oct-2018 Page 90 of 104 Plug-in Gait Reference Right upper body angles Angles RHeadAngles RThoraxAngles RNeckAngles RSpineAngles RShoulderAngles RElbowAngles Vicon Motion Systems Ltd. Positive rotation Axis Direction 1 Backward Tilt Prg.Fm. Y Clockwise 2 Left Tilt Prg.Fm. X' Clockwise 3 Left Rotation Prg.Fm. Z'' Anti-clockwise 1 Backward Tilt Prg.Fm. Y Clockwise 2 Left Tilt Prg.Fm. X' Clockwise 3 Left Rotation Prg.Fm. Z'' Anti-clockwise 1 Forward Tilt Thorax Y Clockwise 2 Right Tilt Thorax X' Anti-clockwise 3 Right Rotation Thorax Z'' Anti-clockwise 1 Forward Thorax Tilt Pelvis Y Anti-Clockwise 2 Right Thorax Tilt Pelvis X' Anti-clockwise 3 Right Thorax Rotation Pelvis Z'' Clockwise 1 Flexion Thorax Y Anti-clockwise 2 Abduction Thorax X' Clockwise 3 Internal Rotation Thorax Z'' Clockwise 1 Flexion Humeral Y Clockwise 2 - Humeral X' - 26-Oct-2018 Page 91 of 104 Plug-in Gait Reference Angles RWristAngles Vicon Motion Systems Ltd. Positive rotation Axis Direction 3 - Humeral Z'' - 1 Ulnar Deviation Radius X Anti-clockwise 2 Extension Radius Y' Clockwise 3 Internal Rotation Radius Z'' Anti-clockwise 26-Oct-2018 Page 92 of 104 Plug-in Gait Reference Lower body angles as output from Plug-in Gait The following tables display the lower body segment angles from Plug-in Gait. All lower body angles are calculated in rotation order YXZ except for ankle angles, which are calculated in order YZX. As Euler angles are calculated, each rotation causes the axis for the subsequent rotation to be shifted. X’ indicates an axis which has been acted upon and shifted by one previous rotation, X’’ indicates a rotation axis which has been acted upon and shifted by two previous rotations. Vicon Motion Systems Ltd. 26-Oct-2018 Page 93 of 104 Plug-in Gait Reference Left lower body angles Angles LPelvisAngles LFootProgressAngles LHipAngles LKneeAngles LAnkleAngles Vicon Motion Systems Ltd. Positive rotation Axis Direction 1 Anterior Tilt Prg.Fm. Y Anti-clockwise 2 Upward Obliquity Prg.Fm. X' Anti-clockwise 3 Internal Rotation Prg.Fm. Z'' Clockwise 1 - Prg.Fm. Y - 2 - Prg.Fm. X' - 3 Internal Rotation Prg.Fm. Z'' Clockwise 1 Flexion Pelvis Y Clockwise 2 Adduction Pelvis X' Clockwise 3 Internal Rotation Pelvis Z'' Clockwise 1 Flexion Thigh Y Anti-clockwise 2 Varus/Adduction Thigh X' Clockwise 3 Internal Rotation Thigh Z'' Clockwise 1 Dorsiflexion Tibia Y Clockwise 2 Inversion/ Adduction Tibia X'' Clockwise 3 Internal Rotation Tibia Z' Clockwise 26-Oct-2018 Page 94 of 104 Plug-in Gait Reference Right lower body angles Angles RPelvisAngles RFootProgressAngles RHipAngles RKneeAngles RAnkleAngles Vicon Motion Systems Ltd. Positive rotation Axis Direction 1 Anterior Tilt Prg.Fm. Y Anti-clockwise 2 Upward Obliquity Prg.Fm. X' Clockwise 3 Internal Rotation Prg.Fm. Z'' Anti-clockwise 1 - Prg.Fm. Y - 2 - Prg.Fm. X' - 3 Internal Rotation Prg.Fm. Z'' Anti-clockwise 1 Flexion Pelvis Y Clockwise 2 Adduction Pelvis X' Anti-clockwise 3 Internal Rotation Pelvis Z'' Anti-clockwise 1 Flexion Thigh Y Anti-clockwise 2 Varus/Adduction Thigh X' Anti-clockwise 3 Internal Rotation Thigh Z'' Anti-clockwise 1 Dorsiflexion Tibia Y Clockwise 2 Inversion/ Adduction Tibia X'' Anti-clockwise 3 Internal Rotation Tibia Z' Anti-clockwise 26-Oct-2018 Page 95 of 104 Plug-in Gait Reference Plug-in Gait output specification The following topics provide definitions to enable you to reliably reconstruct the segment co-ordinate systems using Plug-in Gait outputs in third-party modeling software. Global (laboratory) co-ordinate system on page 97 Pelvis on page 98 Femur on page 99 Tibia on page 100 Foot on page 101 Joint kinematic definitions on page 102 Joint kinetics on page 103 The Plug-in Gait model consists of seven segments (including the left and right side): Pelvis Femur (left and right) Tibia (left and right) Feet (left and right) When Plug-in Gait Static calculations are performed, a scaling length for each of the 7 segments is written to the subject's .mp file. The Plug-in Gait Dynamic process outputs joint kinematics and kinetics to a .c3d file, which also defines them in terms of their order and sign conventions. For information about the definition of the Plug-in Gait model itself and the algorithms used to locate the segment co-ordinate systems and calculate the segment lengths from skin fixed marker data, see Plug-in Gait kinematic and kinetic calculations on page 43. The marker names used here are from the standard Plug-in Gait marker definitions. For precise definitions of their location, see Plug-in Gait models and templates on page 5. Vicon Motion Systems Ltd. 26-Oct-2018 Page 96 of 104 Plug-in Gait Reference Global (laboratory) co-ordinate system The laboratory co-ordinate system is required here as a reference for the pelvis kinematics. The lab system is also used later in the definition of the foot co-ordinate frame. The global Z axis defines the vertical, i.e. perpendicular to the lab floor. The global X and Y axes are in the plane of the lab floor, with X often defining the direction if normal walking along the laboratory walkway. Vicon Motion Systems Ltd. 26-Oct-2018 Page 97 of 104 Plug-in Gait Reference Pelvis The origin of the pelvis co-ordinate system in Plug-In Gait is the midpoint of the vector connecting the two asis landmarks (LASI and RASI). The co-ordinate system of the pelvis is reconstructed from the surface markers on the ASIS and PSIS landmarks, but should be considered to be related to the bony geometry of the pelvis as follows. The Y axis is lateral (to the left) and is directed from the right hip joint centre (RHJC) to the left hip joint centre (LHJC), where the HJC are defined as the centre of the spherical part of the femoral head: The Z axis is then perpendicular to Y and the vector between the sacrum (SACR) and the midpoint of the asis landmarks: where: (The sacral marker is not always used, and this landmark can be calculated as being at the midpoint of the vector connecting the LPSI and RPSI markers). The X axis is naturally the cross product of the Y and Z pelvis axes: In the Plug-in Gait model, the pelvis Y axis is assumed to be parallel to the vector between the LASI and RASI markers, but the definition above is more suitable when constructing a co-ordinate system from known hip joint centers. The length of the pelvis segment calculated by the Plug-in Gait model is equal to the inter-hip distance: Plug-in Gait also outputs the inter-asis distance, which can also be used to assist in reconstruction of the morphology of the pelvis. Vicon Motion Systems Ltd. 26-Oct-2018 Page 98 of 104 Plug-in Gait Reference Femur The accuracy/validity of the femoral coordinate system is affected by the estimation of the knee joint center location as well as the knee flexion extension axis. These two estimations are reliant upon your providing accurate marker placement and subject measurements. The co-ordinate axes are aligned with the long axis of the femurs and the knee flexion axes as follows. The Z axis of the femur is directed from the knee joint center to the hip joint center: The X axis is anterior and is perpendicular to the knee flexion axis, : Finally, the Y axis is lateral (to the left for both legs) and is given by: The scaling length of the femur is simply the distance from the knee joint center to the hip joint center: Vicon Motion Systems Ltd. 26-Oct-2018 Page 99 of 104 Plug-in Gait Reference Tibia The Tibia effectively has two co-ordinate systems: a proximal one for calculating knee joint angles and a distal one for calculating ankle joint angles. Both segments have their origins at the ankle joint center (AJC) and are defined in a manner similar to the femoral segments. Again, the location of the ankle joint center and ankle flexion axis calculated by Plug-in Gait are reliant upon your providing accurate marker placement and subject measurements. Firstly, the proximal system uses the knee joint center, ankle joint center and the knee flexion axis, : The distal coordinate system is then rotated about the long axis of the tibia (Z) such that it is aligned with the ankle flexion axis, : The scaling length of the tibia is the distance from the ankle joint center to the knee joint center: Vicon Motion Systems Ltd. 26-Oct-2018 Page 100 of 104 Plug-in Gait Reference Foot The origin of the foot segments of the Plug-in Gait model is located at the ankle joint centers. The foot co-ordinate system is defined in a rather more complex manner within the Plug-in Gait model than is necessary to recreate the motion of the bones from the Plug-in Gait kinematics output. Firstly, the system Z axis is equal to the vector from the toe to heel markers (HEE and TOE), projected into the plane of the laboratory floor (X-Y plane): Where: The X axis is then perpendicular to this and the ankle flexion axis and is directed vertically: And finally, the Y axis is naturally the cross product of these two axes: The scaling length of the foot is the distance from the ankle joint center to the toe marker: Vicon Motion Systems Ltd. 26-Oct-2018 Page 101 of 104 Plug-in Gait Reference Joint kinematic definitions The following table specifies how the rotations within each of the joints of the model are ordered as trajectories in the .c3d file. Note Angles are always given in the .c3d file as degrees. For all of the joints, the joint co-ordinate system method of reporting kinematics has been used to specify flexion, abduction, and rotation. It is difficult to give a consistent definition of these angles for all of the joints due to the differing meaning of flexion etc. Instead, the axis in the proximal segment embedded co-ordinate system about which each of the rotations takes place (together with the order these rotations should be applied) is given in the following table showing Euler angle specification: Joint 1st Component 2nd Component 3rd Component Order Global Pelvis Tilt (Y) Obliquity (X) Rotation (-Z) 1,2,3 Left Hip Flexion (-Y) Adduction (-X) Rotation (-Z) 1,2,3 Left Knee Flexion (Y) Adduction (-X) Rotation (-Z) 1,2,3 Left Ankle Flexion (-Y)1 Inversion (Z) Rotation (X) 1,3,2 Right Hip Flexion (-Y) Adduction (X) Rotation (Z) 1,2,3 Right Knee Flexion (Y) Adduction (X) Rotation (Z) 1,2,3 Right Ankle Flexion (-Y)1 Inversion (-Z) Rotation (-X) 1,3,2 1. The feet segments are peculiar to the rest of the model, not only because of the different rotation order, but also because the orientation of the foot at zero degrees flexion is straight upwards, that is, the toe will point towards the knee. An offset of +90 degrees should be applied in order to point the foot forwards. Vicon Motion Systems Ltd. 26-Oct-2018 Page 102 of 104 Plug-in Gait Reference Joint kinetics The output from Plug-in Gait also contains forces, moments and powers for each of the segments. Note Forces, moments and powers are given in the .c3d file in Newtons, Newtonmeters and Watts respectively. For both forces and moments, the reaction frame can be specified within Plug-in Gait to be proximal, distal, or in the global frame. For each of the forces, the components in the .c3d file match the co-ordinate directions described in this document. For the moments, however, the order they are stored in the .c3d file matches the rotation order shown in the table in Joint kinematic definitions on page 102, and therefore do not correspond to any of the segment embedded co-ordinate systems. Vicon Motion Systems Ltd. 26-Oct-2018 Page 103 of 104 Plug-in Gait Reference The following table lists the components of the moments in terms of the axes about which they act. Joint 1st Component 2nd Component 3rd Component Left hip -Y X Z Left knee Y X Z Left ankle (prox.)1 Y X Z Left ankle (dist.)1 Y Z -X Right hip -Y -X -Z Right knee Y -X -Z Right ankle (prox.)1 Y -X -Z Right ankle (dist.)1 Y -Z X 1. Due to the differing alignment of the foot and tibia segment co-ordinate systems, the components of the ankle moment differ depending on whether they are represented in the proximal, distal or global co-ordinate systems. References Dempster, WT. (1955) Space requirements of the seated operator. WADC Technical Report 55–159, Wright-Patterson Air Force Base, OH. Vicon Motion Systems Ltd. 26-Oct-2018 Page 104 of 104
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