A resource for axes misalignment, nonlinear error and normal gait data

[Allan Carman]

I have put together an excel spreadsheet demonstrating axes misalignment, resulting non-linear errors, correction of these errors, and the derivation of normal gait joint angle data from the varied results presented in the literature. In 3DMA it is important to understand axes misalignment, its source, and its effects on joint angle data. As it is linked to the validity and reliability of joint angle data, poor reliability of current methods and the lack of normative gait joint angle data presented in the literature. The excel file also includes worked examples of post-hoc correction of nonlinear error in joint angle data via correction of respective proximal and distal segment’s axes mis-alignment. To provide a unique approach to 3D gait analysis that identifies and corrects static and dynamic components of axes misalignment. The excel file also demonstrates the non-linear correction of seemingly unrelated gait joint angle data presented in the literature to show, for the first time, normal gait joint angle data.

This will help explain concepts I have mentioned on BiomechL related to different marker sets, filtering joint angle data, limiting joint df’s and global optimisation (inverse kinematics approach) vs 6 df joints. There is a lot of information presented, and it will take time to work through and understand what is presented, but I believe they are valuable concepts and information for those working with 3DMA

I have shared a Google Drive folder containing two files. An Excel file "Normal gait data, axes misalignment and nonlinear error Jan 2017" (45MB) with the data and workings and a word file with the same name with brief explanation of what is in the excel file.

The folder "3DMA Normal Gait Data" is at:

https://drive.google.com/drive/folders/0BwthwD-r-QOUTUFXYzYwVlRUVjA?usp=sharing

or Excel file

https://drive.google.com/file/d/0BwthwD-r-QOUMkk2OGtlZy1OaFk/view?usp=sharing

or Word File

https://drive.google.com/file/d/0BwthwD-r-QOUVXJSU0lLckFnZHc/view?usp=sharing

[Ross Miller]

Re: A resource for axes misalignment, nonlinear error and normal gait data

This looks very nice, thanks Allan.

Ross

[Edward Morra]

Re: A resource for axes misalignment, nonlinear error and normal gait data

Thank you for sharing this data. I was able to connect to your google drive and see the word document and excel spreadsheet listed.

However I was only able to read the word document. I was unable to convert the excel spreadsheet to a Google calc sheet to review it or download it in its excel format.

Would you consider posting a native Google sheet version of your work in the drive?

Thanks,

- Ed -

[Allan Carman]

Re: A resource for axes misalignment, nonlinear error and normal gait data

Edward,

I would like you to get your hands on the Excel file and go though the logic and equations of what I have done. Unfortunately the file is too large to preview in Google Drive or convert to a Google Sheet (at 45MB). You should still be able to download the file. If the file size is going to be a problem to accessing it then I will cut it down into smaller files, although I would like to keep it all together.

Cheers
Allan

[Allan Carman]

Re: A resource for axes misalignment, nonlinear error and normal gait data

Q. Axes-misalignment and non-linear error but what about cross-talk?

Axes-misalignment and non-linear error is commonly called crosstalk in the literature. The effects of knee flex/ext axis misalignment and resulting crosstalk in the non-sagital knee rotations have long been recognized (Blankevoort et al., 1988; Kadaba et al., 1990; Fairgrieve et al., 1997; Baker et al., 1999; Piazza & Cavanagh, 2000). Piazza & Cavanagh (2000) suggest that non-sagital knee rotations measured at large knee flexion angles should be regarded as suspect and recommends a careful examination for crosstalk before basing any conclusions on them. Fairgrieve et al. (1997) and Baker et al. (1999) caution that for non-sagital knee joint rotations non-linear errors can dominate and hide true rotations to the extent that the rotations can become meaningless. Piazza & Cavanagh (2000) suggested that all current motion analysis techniques that rely on estimations of segment axes alignment are subject to axes misalignment and cross talk when calculating ordered joint rotations; including video based, bone pins and radiographic.

There have been a few studies that assess cross talk and incorporate this into 3DMA methods to align segment axes. Such as minimizing cross talk (Baker et al., 1999; Schache et al., 2006), minimize knee adbd/add range of motion (Charlton et al., 2004) or by best fit to known knee abd/add rotational profiles (Piazza & Cavanagh, 2000; Schache et al., 2008). I have presented a more detail view on its cause (static and dynamic components of axes misalignment), how it effects joint angle data, how it can be corrected pre and post calculation of joint angle data, it’s relationship to normal gait joint angle data in the literature, and way it may be incorporated into 3DMA.

Segment axes-misalignment produces errors in both joint angle data and joint moments; however there is a difference between the two. Due to the non-orthogonal axes and inter-dependency of the ordered rotation sequence used to describe joint rotations, I have referred to the error in joint angle data as non-linear error (highly non-linear equations) instead of cross-talk. Joint moments are expressed relative to orthogonal segment axes and error due to a rotational misalignment about a segment axis is more akin to what people may understand as cross talk.

It has been suggested that because a study is concerned with knee joint moments that erroneous non-sagital knee joint angle data can be ignored. This is nonsense as joint moments are expressed relative to the same segment axes used when calculating knee joint rotations. Due to the large errors in thigh axes-alignment in current methods (plus and minus 10-15 degrees is not uncommon), I would suggest the opposite is true; you need to analyse knee non-sagital joint rotations in gait (or squat or other activity with known or minimal non-sagital knee rotations) to establish axes alignment before calculating joint moments in the activity of interest. Otherwise non-sagital knee moments may be dominated by cross talk from knee fex/ext moments.

I easily get side tracked on related issues!

Cheers
Allan

[Kristian Jones]

Re: A resource for axes misalignment, nonlinear error and normal gait data

I think this looks really interesting but I am struggling to follow the method through the Word and Excel documents.

My understanding is that if I test a participant on three occasions, the error due to axis misalignment will consist of a static offset which differs between the three sessions and a dynamic offset which varies through the movement but is assumed to repeat between trials. I don't understand however, how these offsets are calculated from the data?

Could you provide the explicit method for this process? **I apologise as you have provided such detail already but I am finding it difficult to follow the method in the files given and I am interested to understand the process in full. I'm sure the Excel workbook will be a fantastic resource if I can get over this hurdle.

[Ton van den Bogert]

Re: A resource for axes misalignment, nonlinear error and normal gait data

Allen,

Thanks for including this overview of the history and terminology of this issue. This is very useful to have here.

I think that the crosstalk problem is less severe in non-sagittal moments than in non-sagittal rotations. The non-sagittal rotations are very small, and therefore easily contaminated by the sagittal rotation if the joint coordinate system is slightly altered. The non-sagittal moments are not quite as small, relative to the sagittal moments. Basically, I do not trust non-sagittal rotations (so I assume them to be zero) but I do trust non-sagittal moments obtained during gait.

Ton

[Allan Carman]

Re: A resource for axes misalignment, nonlinear error and normal gait data

Ton,

I agree with what you have said except for the last comment “I do trust non-sagittal moments obtained during gait” as this assumes reliable methods. As seen from data presented in the literature as normal gait, methods can be anything but reliable with 10-15 degrees of thigh axes misalignment common for the mean gait curve about the longitudinal axis.

If we have knee joint moments (Nm/kg) of
Gait Abd/Add = 0.4 and Felx/ext = 0.6 (ratio 1:1.5)
Stair Ascent Abd/Add = 0.46 and Felx/ext = 0.93 (ratio 1:2.0)
Stair descent Abd/Add = 0.57 and Felx/ext = 2.1 (ratio 1:3.7)

Then a (+-) 5 degree error in axis alignment could potentially produce an error of +-13% (sin(5) x 1.5) in abd/add moments due to the component of flex/ext being represented as abd/add. An error in axis alignment of less than 5 degrees and potentially less than 13% crosstalk for gait may well be acceptable. However if the axes misalignment was 10 degrees (26%) abd/add results become poor or at 15 degrees (39%) unusable. Things quickly deteriorate with stair ascent or descent with larger knee flex/ext moments relatively to abd/add moments. A +-15 degree error in axes alignment in stair descent could potentially produce a +-95% error in knee abd/add moments (sin(15) x 3.7) potentially producing knee abd/add moments between 0.03 to 1.11 Nm/kg (ideal was 0.57 Nm/Kg).

Current methods cannot be assumed to be reliable and are highly depend on the implementation (examiner) and therefore I would not trust any non-sagittal knee moment data from any study that has not explicitly established (or at least attempted to measure and correct) axes alignment through an analysis of knee non-sagittal rotations.

Cheers
Allan

[Ross Miller]

Re: A resource for axes misalignment, nonlinear error and normal gait data

What are everyone's thoughts on the role of center-of-pressure accuracy in all of this?

Suppose hypothetically I have all my joint axes defined perfectly and all my marker data are giving me direct skeletal motion. Won't my moments still potentially be off by quite a bit since my CoP is off by up to a centimeter or so? Especially in non-sagittal planes where the moment arms for the GRF are typically smaller.

Maybe modern force plates with good alignment with the MoCap system are more accurate than that, I'm not sure. +/- 1 cm is the mental thumb rule I've used.

Ross

[Edward Morra]

Re: A resource for axes misalignment, nonlinear error and normal gait data

I was able to download the entire spreadsheet. It is quite comprehensive and valuable to the community, thank you for posting it!

Would you explain how you arrived at the "ideal" data in examples one and two?

- Ed -

[Ton van den Bogert]

Re: A resource for axes misalignment, nonlinear error and normal gait data

Allen,

I agree with your error estimates.

When I said "trust", you can define that word different ways.... Even with 13% or 39% error, you can still recognize the patterns. With good standardization of marker placement protocols, you should be able to use the non-sagittal moments in research and clinic. Whether they are "true", that is another matter.

For the non-sagittal rotations, the errors are easily hundreds of percent, and patterns become completely unrecognizable. They are just too sensitive to axis definitions. So, compared to that, I would say that I "trust" the non-sagittal moments. It's relative.

Ton

[Ton van den Bogert]

Re: A resource for axes misalignment, nonlinear error and normal gait data

I also use 1 cm COP error as a rule of thumb. This would give you about 10 Nm error (VGRF * COPerror) during gait which is a significant fraction of the peak moment, for some joints.

For force plates, my own method was always to motion capture four markers on the corners of the force plate, which are known coordinates in the force plate coordinate system. AMTI and Kistler provide those coordinates. A best fitting rigid body coordinate transformation can then be determined between force plate and mocap coordinate system. This will get you well below 1 cm error.

Instrumented treadmills don't have corners or other calibration points, so you have to do it indirectly. I like the instrumented pole method (Collins et al., Gait & Posture 2009) although I have not personally used it. We use a static weight with a marker on top, which seems OK but does not have a point contact that produces an unambiguous COP.

If you are concerned about systematic COP errors, you could do half of the trials walking in the opposite direction. The COP errors would then have the opposite effect on joint moments. This would only work on a force plate or a bidirectional treadmill, and if you can do motion capture from both sides.

Effect of random COP errors can be reduced by averaging many gait cycles.

Ton

[Morgan Sangeux]

Re: A resource for axes misalignment, nonlinear error and normal gait data

Ton,

Current methods cannot be assumed to be reliable and are highly depend on the implementation (examiner) and therefore I would not trust any non-sagittal knee moment data from any study that has not explicitly established (or at least attempted to measure and correct) axes alignment through an analysis of knee non-sagittal rotations.

Cheers
Allan

Hi Allan,

Firstly thanks for the tremendous resource. I must admit I have some difficulties following the logic through the Excel spreadsheet but that is inevitable working with Excel spreadsheets. I would have probably created a Matlab or Python script, but then some people would not have been able to run the script, whereas everyone can use XL.

Secondly, I agree with your last comment ("highly depend on the implementation (examiner)"). I initially thought functional calibration would provide improved static alignment of the medio-lateral axis of the femur. I reported my findings in 3 previous papers using 3 different data-sets now, against an EOS (bi-plane x-ray system) reference, against a 3D freehand ultrasound reference, and against bi-plane fluoroscopy. The first 2 in healthy adults, and the last one in older adults with 'simpler' prosthetic knees.
However, my latest findings (not reported yet, in children with CP and torsional deformities) tend to show these results do not necessarily translate to every populations/settings. This reminded me of similar findings with hip joint centre functional calibration algorithms, validated ex-vivo or in young (mostly athletic) adults with flying colours but not so great when you actually try to implement it in the clinical setting, at least from my experience and others.

In fact the most promising technique for static calibration of the femur coordinate system from my point of view is medical imaging, with 3D freehand ultrasound. We are currently trying to adapt our research protocol to run in routine clinical practice (i.e. strictly compliant with biomed engineering at the hospital, portable, fast to acquire ~5-10 minutes and easy+fast to process ~10s). There is also EOS, which we have in Melbourne, but that is an expensive piece of equipment to buy :-)

Of course, static alignment is only half the job (cf. the latest STA papers in J of Biomechanics)...

[Allan Carman]

Re: A resource for axes misalignment, nonlinear error and normal gait data

This is to answer questions about the ideal gait curve used and to help understand the approach presented in the excel spread sheet. Which as pointed out can be difficult to follow from someone else's work.

The ideal gait curves were derived from an in-house reliability study of 11 healthy young adults tested on three separate days over a one week period. I used a 7 segment lower body, 6DF, least squares, marker cluster design, using virtual joint centers as part of the cluster for each segment. The same model was used for my 30 participant normal gait example in the spread sheet, with the same assumptions:

1. The static offset in axes alignment (during subject calibration procedure) is constant within a session (same marker placement) but variable between sessions.
2. The dynamic offset in axes alignment (skin movement during movement trial) is variable within a movement trial but is repeatable between sessions for a given subject, marker placement and movement pattern.

In the original reliability study the process of introducing a static correction to refine axes alignment within the subject calibration procedure was very much experimental. Where offsets were adjusted, gaining an understanding how joint angle data were affected, while looking for common dynamic offsets (skin movement artifact patterns) within subjects, as well as similar skin movement artifact patterns across subjects and similar gait joint angle patterns across all subjects. There is the influence of my own perceptions and judgment on the differences ROM and variability of knee abd/add between stance and swing phases.

This ideal joint angle data is therefore my best guess given a surface marker cluster design and an understanding of static (defining segment axes) and dynamic (skin movement) errors and how they affect joint angle data.

The approach to correcting the three examples and the data from the literature was a two part process, also using the two assumptions mentioned. Initially the static offsets were introduced. There was no set procedure to defining the static offsets, it again was a matter of adjusting offsets to minimise difference to the ideal curves, while looking for similarities in the dynamic offsets. In this first step dynamic offsets were automatically produced for the given static offset so as to minimise the difference to the ideal curves. Then common (mean) dynamic offsets were calculated for different trials of the same participant or across different studies with similar design. In the second part of the approach, the whole procedure was repeated with the same static offsets used in the first part but with the common dynamic offsets representing common patterns of skin movement artifact.

In the initial reliability study and the 30 participant example the approach is different and represents how identifying and correcting static (subject calibration) and dynamic (skin movement) offsets may be implemented in 3DMA. Deriving the static segment axes offsets were completed in the subject calibration procedure. In an iterative process the traditional marker based static subject calibration was performed as an initial estimate of axes alignment, a sample gait trial was analysed, and refinements to the static axes alignment made (offsets introduced) and calibration and analysis processes repeated as the offsets were refined to minimise differences between knee non-sagittal rotations and the ideal. The spread sheet shows the second part of the approach in identifying the dynamic offset component of axes misalignment. This was achieved by calculating the common differences between the hip and knee non-sagittal rotations relative to the respective ideal gait curves. This common differences to the ideal for abd/add and ext/int rotations for the hip and knee was used to correct thigh dynamic alignment during the gait cycle (skin movement) given the assumption that the shank has minimal skin movement. When correcting static and dynamic offsets for the 30 participants, each subject was analysed individually.

You may have noticed that when identifying and correcting dynamic axes alignment for the 30 participants I used one of two alternative hip abd/add rotation patterns and one of three alternative Hip ext/int patterns instead of the respective single ideal curve for each participant. This was purely speculative given that there appeared to be several alternative normal gait patterns for these two joint rotations. It will take a new study to see if this holds up or was something peculiar to this group.

My marker based ideal produced greater knee abd/add during stance and a leading shift in joint angles in the swing phase when compared to the bone pin study of Lafortune et al. (1992). If there were a second bone pin or radiographic study to support this result then I would replace my marker based ideal used in the spread sheets with this ideal. In so doing changing the marker based dynamic skin movement artefact profile during gait.

This will be difficult to fully understand from the examples and the best way is to collect data from several individuals on repeated days, apply the approach and see what you find. What I have presented is not perfect and is still evolving. I would recommend that you do not try this initially with global optimization methods as this will introduce a new random source of axes misalignment that will be difficult or impossible to correct.

Cheers
Allan