*Interesting new input regarding the Teach-in. Of course I am not
an expert, but I assume the following reason:*

*The sampling frequency of the motion analysis system was too low
to resolve the first (quite sharp) peak. In an impact or push off like
part of the motion I would assume that the only reliable results regarding
the accelerations could be obtained from the force plate. This would explain
why the discrepancy is higher when the motion is performed at higher speed.
When sitting down again, you don't have an 'impact like' situation, so
this would be an indication why there is almost no difference in the results.*

*What do you think about that?*

*Cheers,*

*Karsten*

*-- Univ.Ass. Dipl.Ing. Karsten Schwieger IfS, Department of Biomechanics
Auf der Schmelz 6 A-1150 Vienna, Austria*

*Tel.: ++43-1-9822661-234 Fax: ++43-1-9822661-277*

Dear Karsten,

I also considered the possibility of the sampling rate being the problem. But if so, then doesn't this affect our whole rationale for choosing a sampling (frame) rate based on the Nyquist Sampling theorem? We normally assume that the sampling rate is sufficient if it is 2 (preferably 4) times the highest frequency in the data. For human gait, Winter has shown that there is little signal power beyond the 6th harmonic (usually about 6Hz), and I notice that sit-to-stand researchers often filter at 3Hz.

But the question now arises: should we recalculate the Nyquist frequency and reassess our sampling rate if we are going to differentiate the signal. The results from these experiments and what you say about them would seem to suggest that - but I've never seen it mentioned in any textbooks. Perhaps someone could enlighten us?

Chris -- Dr. Chris Kirtley (Kwok Kei Chi) MD PhD Assistant Professor Department of Rehabilitation Sciences The Hong Kong Polytechnic University Hong Kong

Dear Chris and cga-group, I have two comments (which may be interpreted as questions) regarding the acceleration-by-differentiation problem. 1. You say that there is a discrepancy in the vertical force derived/measured by the two methods. It would be interesting to know if one method is underestimating or the other overestimating the true positive values. I believe this could be approached by looking at the accumulated acceleration over the whole performance, which ideally should equal nil not including gravity. It follows that accumulated force would equal baseline force. Is this so for either of the two methods? 2. This is a shot in the dark, but what about the sampling frequencies of the two methods. If the positive peaks are of shorter duration than the negative ones, could it be that the sampling frequency of the video-based system is too slow to faithfully catch the true positive peaks, thus returning biased peak positive acceleration? As always, thanks for your dedication and enthusiasm Chris! Best regards from the fjord country, Rolf

Rolf Moe-Nilssen, MS, PT, Research fellow, Division for Physiotherapy Science Department of Public Health and Primary Health Care, University of Bergen Ulriksdal 8c, N-5009 Bergen, Norway, email: Rolf.Moe-Nilssen@isf.uib.no voice: +47 55 58 61 70, fax: +47 55 58 61 39

Rolf,

Good idea about the measuring the accumulated acceleration. Here's the means of each trace: Force platform: 629.8507 N Kinematics : 622.7446 N

Since body weight was 64.2 kg, or 629.802 N, I think this confirms that the kinematics are UNDERestimating the accelerations.

Chris -- Dr. Chris Kirtley (Kwok Kei Chi) MD PhD Assistant Professor Department of Rehabilitation Sciences The Hong Kong Polytechnic University Hong Kong

Chris

with regard to Rolf Moe-Nilssen's comments - I think the important point is that integrating the curves over a period of time to include the sit-stand should just give body-weight x the time period (as there is zero acceleration at the start and end of the manoeuvre). From looking at the curves the kinematics actually seems closer to this that the forceplate (although I could be mistaken, the integral would confirm this). Is there a possibility of error on the force-plate? Have you examined the transient response?

Ben Heller (PhD) Clinical Scientist Medical Physics and Clinical Engineering Royal Hallamshire Hospital Glossop Road Sheffield S10 2JF Phone (xx 44)/(0) 114 271 3675

Ben,

Just added up all the points (minus baseline) multiplied by the sampling interval (1/50) and got:

Kinematics: -51.1467 N Forces : 8.047108 N

Is that what you meant? I think its the integral, right?

Chris

-- Dr. Chris Kirtley (Kwok Kei Chi) MD PhD Assistant Professor Department of Rehabilitation Sciences The Hong Kong Polytechnic University Hong Kong

Chris et al.

OK for the sake of arguement I'll come out against the sampling theory explanation of this phenomenon.

First reason is that from a visual examination of the graphs the sampling frequency for the accelerations would appear to be several (say 4 times?) the frequency of the force plate waveform and should therefore satisfy the Nyquist criterion.

Secondly for all that there is some difference in the frequency at which the acceleration phase and decceleration phase are occuring it does not appear to be all that significant and to my mind does not appear sufficient to explain the fact the during decceleration the agreement looks good.

Thirdly if this is the explanation and agreement during acceleration appears to get worse for the faster standing speed why do we not see the problem starting to emerge for the decceleration phase.

I'd still like to see the same data for an even simpler model of C of G (fixed point in pelvis). Richard Baker PhD Gait Analysis Service Manager Musgrave Park Hospital Stockman's Lane Belfast BT9 7JB

Chris, A non-expert comment on the sampling theorem: Even if the Nyquist frequency is the lowest frequency where you get rid of aliasing, I believe it is not a frequency where you may expect true reproduction of any peak amplitudes. If the readers have access to Winter's "Biomechanics and motor control of human movement" (2. ed. 1990) and look up fig.2.17 where two acceleration curves of the same data sampled at 50 Hz and 25 Hz are compared, one can see that a peak acceleration of 14 m/s/s at 50 Hz is reduced to 12,5 m/s/s at 25 Hz (approx.). Even if this is not of significance when looking at the overall signal power, or the overall contribution of the higher harmonics, it appears to me to be of importance when focusing on peak amplitudes in isolation from the rest of the curve. Is this wrongly interpreted? Rolf

Dear Dr. Kirtley,

Some observations:

1. Nyquist's limit does not provide for an exact representation of the original signal, specifically NOT peak amplitudes. It is a minimum frequency for a generally adequate reproduction of the spectrum of the original signal without serious aliasing problems. Video sampling rates are inadequate in many studies that involve changes in direction of movement. I think you are probably on the edge in these observations, due to the directional changes in the motion of body segments and your attempt to derive a "peak" acceleration. This implies an instantaneous measure, while your data is subject to the sampling limits, differentiation, and subsequent low pass filtering, each introducing an uncertainty in the "true" value at any point in time. Identification of any instantaneous peak may be meaningless.

2. The kinematics appear to provide no information regarding the movement of the head, and the relative contribution of the other segments to the calculation of center of mass is unclear. The force platform will show the net force at any point in time, yet your kinematics are based on segments moving in different directions at times and do not include a significant part of the mass being accelerated, the head. The nature of the model for determining the motion of the center of mass is, in my opinion, another likely (and probably more significant) source of your differential result.

Both issues have likely contributed to your problem. Thank you for presenting it and making us think about the significance of the assumptions that go into these types of analysis.

Leonard G. Caillouet Graduate Student, Louisana State University Member, USOC Sport Science & Technology Committee Member, NAA Sport Science & Technology Committee Chairman, National Archery Association Trials Tournaments Committee

Dear Chris and cga-group, I have a comment concerning the acceleration computation by double differentiation of displacement. When a double differentiation of a signal is done the frequency response is multiplied by square w, (w=2*pi*f). That mean that the differentiation make a kind of high pass filtering. But that is the case of the ideal differentiation. In practical we use various method as 2 points difference, 3 points central difference or other techniques, and the transfer function is not square of w. For example for a 2point difference the transfer function is (simple differentiation): (2*fs)*sin(2*pi*f/2fs), where, fs is the sampling frequency, and f the frequency component of signal. In this case the high frequencies are attenuated comparing to the ideal differentiation. This could explain the attenuation of positive peak, in our case( if the positive peak acceleration has higher frequency component than negative peak acceleration). To verify this we most know the value of sampling rate . I suggest to process as follow: - resample the displacement signal by adding more sample (by interpolation) between the actual samples. - Use other method of differentiation. There is other techniques that we can find for example in the : Design of Microcomputer medical instrumentation, W.J Tompkins, J.G. Webster, Prentice -Hall, New jersey, 1981, pp126-136. - It is also possible to study a simple case of mouvement by adding an accelerometer on the marker.

Kamiar AMINIAN, PhD Swiss Federal Institute of Technology Electrical Engineering Department email: aminian@met.de.epfl.ch Metrology Laboratory phone: (+4121) 693.26.17 CH-1015 Lausanne Fax: (+4121) 693.26.14

Thanks to all who've commented so far on the current Teach-in. As I anticipated, there's a lot more to this than meets the eye! I think it's time to try to attempt a summary.

BTW, the page is now back on the main Curtin University server which will probably be quicker:

http://www.curtin.edu.au/curtin/dept/physio/pt/staff/kirtley/cga

You might want to bookmark this. Sorry the URL is so long!

Well, we seems to be still torn between sampling error and model inaccuracies as the cause for the discrepancy, but I'm intrigued by Leon's comment (which I just realised he only sent to me personally):

"Nyquist's limit does not provide for an exact representation of the original signal, specifically NOT peak amplitudes. It is a minimum frequency for a generally adequate reproduction of the spectrum of the original signal without serious aliasing problems. Video sampling rates are inadequate in many studies that involve changes in direction of movement."

and Kamiar's very helpful formulae:

"When a double differentiation of a signal is done the frequency response is multiplied by square w, (w=2*pi*f). That means that the differentiation make a kind of high pass filtering. But that is the case of the ideal differentiation. In practical we use various method as 2 points difference, 3 points central difference or other techniques, and the transfer function is not square of w. For example for a 2point difference the transfer function is (simple differentiation): (2*fs)*sin(2*pi*f/2fs), where, fs is the sampling frequency, and f the frequency component of signal. In this case the high frequencies are attenuated comparing to the ideal differentiation. This could explain the attenuation of positive peak..."

That's certainly news to me, and I'm mosty grateful to Kamiar for the insight.

Leon also has an each-way bet on the model:

"...The nature of the model for determining the motion of the center of mass is, in my opinion, another likely (and probably more significant) source of your differential result."

and Richard has been good enough to play Devil's advocate by lending his support. I especially like his justification:

"...for all that there is some difference in the frequency at which the acceleration phase and decceleration phase are occuring it does not appear to be all that significant and to my mind does not appear sufficient to explain the fact the during decceleration the agreement looks good. If this is the explanation and agreement during acceleration appears to get worse for the faster standing speed why do we not see the problem starting to emerge for the decceleration phase?"

which also made me sceptical of sampling error being the culprit.

Richard suggests we plot the acceleration of a fixed CoM located in the pelvis. This was an easy one to do, since we have a marker on the hip, which will do as a pelvis CoM marker - you can find the graph at

/teach-in/acceleration/acc.gif

The results are quite interesting, in that the acceleration is very much less than before. I have also plotted the aceleration of the shoulder marker for comparison, and - surprise, surprise! - it's much larger. So I think this suggests that it may indeed be the model to blame. Thinking about it, since Chinese people have shorter limbs than Caucasians, I would expect the HAT segment to be heavier, as a percentage of body weight. So this would fit with the data.

We are attempting to confirm this by finding some local anthropometry and also recalculating body CoM acceleration with a higher value for the HAT mass. I'll get back to you with the results.

Meanwhile, thanks all for your contributions - I'm still not discounting the sampling rate as a factor and very much appreciate the insights into the effect of differentiation on choice of sampling rate.

Chris

PS: Just noticed a timely article in this month's JoB...

JT Journal of biomechanics. DA AUG 01 1997 v 30 n 8 PG 851 AU Giakas, G. AU Baltzopoulos, V. TI Optimal digital filtering requires a different cut-off frequency strategy for the determination of the higher derivatives. SI 0021-9290(19970801)30:8L.851:ODFR;1-

-- Dr. Chris Kirtley (Kwok Kei Chi) MD PhD Assistant Professor Department of Rehabilitation Sciences The Hong Kong Polytechnic University Hong Kong

Dear cga subscribers

I think this is a very useful discussion. I will go straight to the point.

I assume that the force platform data accurately describe the acceleration of the centre of mass; its calculation is quite simple. >From the other hand, the calculation of the CM acceleration using the kinematic data requires the following consecutive steps. 1. The recording of specific markers in 2-D (so we have one source of error here), 2. Filtering (did that happen here ?) 3. The use of an anthropometric model (another source of error) 4. Differentiation of the displacement of the CM (amplification of noise)

My points / questions are: 1. Did you first calculated the acceleration of CM and then filtered the data (so move step 2 at the end) ? If yes, then there is a problem here. I will not expand this since I don't know the sequence.

2. I do not think there is a problem with the sampling frequency in this case, because then I would expect problems during the deceleration period also.

3. Similarly, I have the same comment for the type of differentiation. A quick check I had using analytical differentiation of Fourier series and splines revealed about the same outcomes as with 1st order finite differences. Of course a higher order would have a smoothing effect.

4. The whole signal is non-stationary. Theoretically, and this is well confirmed by the force data also, there are no frequency components before and after the Sit-to-stand movement. The fact that the whole signal is used for filtering in this case, will probably result in underestimation of the peak accelerations.

5. Considering all the above, I think that the data derived using kinematic analysis are quite faithful.

6. Finally since the underestimation of acceleration occurs only during the acceleration period, I would like to see what would be the result of reversing the signal, during its data processing. Are we still going to have an underestimation of the acceleration phase ?

Thank you very much for your attention, and I look forward to seeing more opinions on this topic.

Giannis

-- Giannis Giakas Division of SHE Staffordshire University Stoke-on-Trent ST4 2DF

Tel : +44 1782 294292 Fax : +44 1782 747167 Email: g.giakas@staffs.ac.uk http://www.staffs.ac.uk/sands/scis/sport/giannis/gian1.htm

Dr. Kirtley,

Thank you for including my comments in your message, as I mistakenly replied only to you. I still wonder about the lack of kinematic data for the head. How can we expect an accurate model of the movement of the center of mass of the body with no info regarding the motion of the head, which acts as another segment in the system?

Also, I believe that Kamiar is correct in his description of the effect of differentiation, though those classes are a couple of decades in my past...but unless the characteristic frequencies of the two directions were very different this would not explain the diferential result for the positive and negative accelerations. As you said, I'm betting on both sides but I think the much larger problem is to be found in the treatment of c.m.

Leon.

You'll no doubt be interested to know that we've just finished analysing the experiments suggested by the Teach-in discussion last week. I must say I have been pleasantly suprised by what we've found!

On looking at the videos more closely we decided to put a marker on the head and include its acceleration in the calculation (previously it was lumped into a HAT segment). As you will note from my BIOMCH-L message, we've had to estimate some of the anthropometry involved, but I'm pretty confident about the results.

It seems that the missing acceleration is indeed accounted for by the head! The head does a nodding action, and it is its abrupt downwards deceleration (= upwards acceleration) that is responsible for the missing segment of the force trace:

So the CGA virtual prize for this week goes to Leonard Caillouet of Louisana State University for insisting that we include the head in our analysis - just goes to prove that you ignore segments of the body to your peril when analysing human movement.

Well done, Leon! And thanks again to all who contributed to the discussion.

Chris -- Dr. Chris Kirtley (Kwok Kei Chi) MD PhD Assistant Professor Department of Rehabilitation Sciences The Hong Kong Polytechnic University Hong Kong