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Transverse Arch?

Discussion in 'Biomechanics, Sports and Foot orthoses' started by sparkyclair, Jun 6, 2008.

  1. All from one isolated second metatarsal? Now that really is a leap of faith.
     
  2. Rob Kidd

    Rob Kidd Well-Known Member

    Whether its a leap of faith or not depends on what one says about it - and of course all you have there is the abstract. As we have been over nefore, this is a key problem with fossils - but it is better, at least IMHO, to say something rather than nothing. However, some basic biology and its quantitative methods. Inside multivariate statistics, one may generally make the assumption that 2 or more standard devaiation units away from a control groups (eg humans) is tantamount to a different species. For instance, in our work of the The Olduvai & STW573 foot assemblages, we noted the tali to be at least 5 standard deviation units away. The biggest problem is a temptation to assume that the specimen represents the mean of that species - and one must be careful not to do this. I am sure that Jerry and Bernie will have done this: I have been working with Bern for over 20 years - he did his PhD with me many moons ago. Did you know that in a previous life he was a Pod? It is, again IHMO, a huge advantage to have a pod background when working with fossil pedal remains. Rob
     
  3. Yep, I get all of that, but how do you make assumptions regarding the proximal transverse metatarsal arch configuration based on one isolated specimen of just the 2nd metatarsal? Answer- you can't; end of extrapolation.

    Five standard deviation units away from the mean in terms of what by the way, what was the quantitative variable in question? How many homo sapiens alive today might show a similar deviation away from that modern-day mean, for what ever variable it was that you measured: more or less than 1?

    Current world population estimate for homo sapiens is 7.055 billion. Question: if we measured every angle and dangle of everyone's talus and calculated the means and variances for those variables, if we assume a normal distribution, how many individuals should fall outside of 5 standard deviations of the mean? You can calculate this, if you have the time and inclination... How many of the present world population would be considered as a different species using the 5 standard deviations technique?
     
  4. Rob Kidd

    Rob Kidd Well-Known Member

    I have not read it yet - perhaps that would be the thing to do next. Rob
     
  5. I was bored and a quick fag packet calculation suggests that given the current world population of 7.055 billion, four thousand two hundred thirty-three of these individuals should be classified as a new species for any given trait displaying a perfectly normal distribution, given the 5 standard deviation rule which Robert Kidd suggested. Have a nice day y'all. :drinks
     
  6. efuller

    efuller MVP

    For the medial longitudinal arch there is upward force distally on the metatarsal head(s) and proximally on the calcaneus and a downward load from the tibia. If we accept the definition that an arch must span something, like a bridge over a river then the center portion would not contact the ground and either end of the arch would be supported by the ground.

    The lateral metatarsals may contact the ground, but the vast majority of the time the medial metarsal bases don't touch the ground. So, the arch cannot support a load in the transverse plane. That is my logic for saying that mechanically there is no transverse arch.

    Eric
     
  7. Rob Kidd

    Rob Kidd Well-Known Member

    Well, let me see now: these are of course standard deviation units in multivariate space - which is not the same as standard deviations away from the mean. For the talus, the dimensions used consisted of 18 linear dimensions of interlandmark distances and two angles. These were then converted to an exponent - either the square root of the natural log - have used both over the years. This is done to remove the positive regression of mean against standard deviation. These were then subjected to both principal components analysis, and canonical variates analysis; it is to the latter that I was referring to in terms of standard deviations units away from the group mean position of humans. And in turn the group mean position of humans - based upon a homogenized group for perhaps ten ethnic groups, spreads over about 1-1.5 standard deviation units - the majority of which is expressed raw size, and a decidely minor component of size-related-shape. If you wish to go beyond this to look at shape differences and "how different" they are, we tend to use the Mahalanobis D2 distance of phenetic similarity; this is good because it accounts for all canonical variates, not just the two plotted to achieve the STU separation. I am uncertain as to whether this clears up your rough and dirty fag packet calculation. Rob
     
    Last edited: Nov 26, 2012
  8. Rob Kidd

    Rob Kidd Well-Known Member

    Here is The Paper referred to earlier by Kevin - Jerry and Bernie I know (Bernie is an old friend and ex-PhD student of mine); Daniel is new to me. Please guys, before people overtly criticise this publication, do please rember that The JHE is an incredibly well thought of, highly referreed journal; this will have been through many remakes before crossing the finish line. Just for your interest, I have also posted the editorial committee; these are very senior, well respected academics in the areas of anatomy and palaeoanthropology. Many are from Stony Brooke - about as high up the **** pile as one can get.......................... Rob
     

    Attached Files:

  9. Eric:

    An arched structure is still an "arch" even though it isn't supported at both ends. Such an arch is called a "cantilever arch", still mechanically an arch, supported at one end of the arch, but unsupported at the other end of the arch.

    In the example below of a cantilever arch, the arch is only supported by the ground on one end and is still mechanically acting as an arch.

    http://www.fabricarchitect.com/2773.html
     

  10. Not really; rather it just adds to obfuscate by virtue of statistical thicket. Lets see if we can hack our way through some of this thicket to see what is being done here.

    Standard deviation units- basically what is being performed here is a transformation to a standard normal distribution. This is often performed when two variables have different units of measurement. It is performed by subtracting the mean and dividing by the standard deviation. I can see how this can be done with an adequate sample, but when one only has a single fossil to work from, then there is no mean and no variance by which to perform the transform. Notwithstanding, even when we convert the data to a standard normal distribution there would still be an expectation for a percentage of a large enough sample to fall beyond 5 standard deviations (standard normal deviates), in the case of the global population of >7 billion, the number of individuals which fall beyond this 5 standard deviation units may run into the thousands (as I demonstrated last night with my "dirty" calculation) does this make them a different species- no.


    Square root / natural log transforms- again these are scale transforms, usually performed to induce linearity into an otherwise non-linear variable, a good example is the Simms-Weinstein filament which employs a log scale.

    Canonical analysis- a form of discriminant analysis. The basic principle of discriminant analysis is to find a series of variables which maximises the separation between the groups. With more than two groups, groups can be further separated by a second combination of the same variables. The combinations are called canonical variates or discriminant functions (Altman, D.G.: Practical statistics for medical students p.359)

    Now, Altman goes on to say that the principle "is based on the strong assumption that all variables have a normal distribution with the same standard deviation within each group". How do we know this when we have a fossil specimen group of n=1?

    Further Altman states that "sample size is again an issue, and it has been suggested that there should be at least five times as many subjects per group as variables examined"; again I ask how is it possible to validly perform such analyses when we have fossil specimens of n=1, i.e. one of the groups has only one "subject"?
     
  11. timharmey

    timharmey Active Member

    Hi Simon
    I know little about maths but I know a woman who knows lots, If you can give me a question to ask her about the above ( one I can ask her that gets to the crux of what the above is about), I can probably give you an idea of what is reasonable
    Tim
     
  12. Hi Tim, thanks for the offer. I have a reasonable understanding of statistics and statistical theory. At the moment I think I'm OK with the stuff being discussed here. What I'm basically saying is that if we take a normal distribution (or even a standard normal distribution) obtained from a very large sample, then the number of individuals who would lie outside of 5 standard deviations from the mean (although a small percentile of the entire population) could still number several thousand individuals (when we are talking sample sizes of >7 billion). Just because we happen to identify one of these outliers, doesn't mean they are from a different species.

    Let me try and give you an example, if we measured the length of the femur of every human on the planet, then we could calculate a mean, +/- 1 standard deviations (SD) from the mean, +/- 2 S.D.... +/- 5 SD. We can even transform the data to a standard normal distribution if we want, either way if the data is normally distributed, we can calculate the proportion of individuals that will fall within each area beneath the normal distribution curve; a proportion of the individuals, say someone who is extremely tall, may have a femoral length which is 5 standard deviations from the mean. While the probability of this is very small, it does not mean it is impossible, and when we have such a large sample to begin with we may find many such people. Nor does it automatically mean that this individual is a member of a different species.

    So, lets say in a few million years time a scientist finds a fossil of this very long femur and notes that it is 5 SD different in length when compared to a relatively small sample of human femurs they take at that time. Should they conclude that the fossil femur was not from a human?

    The problem highlighted is that when someone finds a fossil, we have sample of 1, we do not know anything about the distribution from which this fossil came, was it the "mean", or was it an "outlier"; what proportion of the entire population did this individual represent? Did the process of fossilisation distort the morphology?

    The other point which I'm hoping Robert will discuss with me, is the use of small groups (n=1) within discriminant analyses. It's not a technique I've used before and I'm hoping Robert can enlighten as to it's usage and "abusage".
     
  13. timharmey

    timharmey Active Member

    That makes sense , hope you escaped the west country flood
    Tim
     
  14. Far be it from me to criticise such exalted people and publications, but how do you work out the shape of the proximal transverse arch when all you've got is a second metatarsal?
     
  15. Rob Kidd

    Rob Kidd Well-Known Member

    Not really; rather it just adds to obfuscate by virtue of statistical thicket. Lets see if we can hack our way through some of this thicket to see what is being done here.

    Standard deviation units- basically what is being performed here is a transformation to a standard normal distribution. This is often performed when two variables have different units of measurement. It is performed by subtracting the mean and dividing by the standard deviation. I can see how this can be done with an adequate sample, but when one only has a single fossil to work from, then there is no mean and no variance by which to perform the transform. Notwithstanding, even when we convert the data to a standard normal distribution there would still be an expectation for a percentage of a large enough sample to fall beyond 5 standard deviations (standard normal deviates), in the case of the global population of >7 billion, the number of individuals which fall beyond this 5 standard deviation units may run into the thousands (as I demonstrated last night with my "dirty" calculation) does this make them a different species- no.


    Square root / natural log transforms- again these are scale transforms, usually performed to induce linearity into an otherwise non-linear variable, a good example is the Simms-Weinstein filament which employs a log scale.

    Canonical analysis- a form of discriminant analysis. The basic principle of discriminant analysis is to find a series of variables which maximises the separation between the groups. With more than two groups, groups can be further separated by a second combination of the same variables. The combinations are called canonical variates or discriminant functions (Altman, D.G.: Practical statistics for medical students p.359)

    Now, Altman goes on to say that the principle "is based on the strong assumption that all variables have a normal distribution with the same standard deviation within each group". How do we know this when we have a fossil specimen group of n=1?

    Further Altman states that "sample size is again an issue, and it has been suggested that there should be at least five times as many subjects per group as variables examined"; again I ask how is it possible to validly perform such analyses when we have fossil specimens of n=1, i.e. one of the groups has only one "subject"?

    __________________
     
  16. Lets try to get our heads around this statement from Altman: lets say we have a bag of tali- some of them human and some from gorilla, we want to use discriminant analysis to separate the tali into two groups: gorilla and human. If we only need to measure 1 biometric variable (e.g. length) in the tali to enter into the discriminant analysis to distinguish between human and gorilla tali, then according to Altman and his reference, we need at least five human tali and at least 5 gorilla tali to validly employ this technique; if we can discriminate between human and gorilla tali with only two biometric variables (e.g. length and width), then we should require 10 human tali and 10 gorilla tali to validly perform this form of analysis; if we need to measure 10 biometric variables to discriminate between species, we should require 50 human and 50 gorilla tali to validly perform this analyses. I'm not a paleontologist, I'm just a chiropodist, but I do find this "hard science" interesting. How many fossil specimens are typically entered into such analyses, and how many variables are typically measured when attempting to differentiate between homo sapien tali (or any other bone) and some other species? It seems to me that a bare minimum should be 5 specimens from each group. Which takes me back to my original question- exactly what did you measure, Robert?
     
  17. Yep, that's what I wrote.

    http://www.youtube.com/watch?v=2IlHgbOWj4o , not.
     
  18. Rob Kidd

    Rob Kidd Well-Known Member


    Lets take each issue, and see if a little sense may be made.
    First off, to go back to the original posting, My comment was that a "mantra" - a rule of thumb, so to speak, was that a distance of more than about 2 STU's (in multivariate space" was generrtally considered to be indicative of a different species. Not rocket science, not proof, just a working maxim.


    The conversion to an exponent is undertaken after testing to look at the correlation between mean and st. deviation - usually, but not always, in linear variables, there is a positive correlation, which would cause the larger dimensions to be emphasised. With prinicpal components analysis, one way around this is to use the correlation matrix which renders all ST deviations to be the same. Sounds good, but the variation may be the important feature, or at least, an important feature of the biology in question. Jolicour (?SP?) in his work on the multivariate allometry equation, advocated an exponential conversion followed by the covariance matrix, which is what most of us do. In the case of Canonical variates, there is a normalisation, the details of which escape me now, (and I am 1000km from home in a camper van with no books).


    As for your comments about the sample size, from memory we used a sample size of 160-180 specimens, for comparison of the fossil. Then, either 1) the fossil in entered into the calculation as a sample size of 1 - which does mean that it does not enter into the calculation of the multivariate mean or ST dev (but these are calulated for the rest), or 2) it is entered into a matrix of extanct species. Both techniques are valid, but different. For any of the species I have examined - which is not just primates, we work in marsupials as well, we have never found a species spread of greater than perhaps 1-1.5 standard deviation units as judged from a plot of the first and second canonical variates. But then, there is all the further variates - dependent of course on sample size and dimension number; that is why I suggested looking at the Mahanalobis (?SP?) distances, which are based upon all variates, not just the first 2.

    I note your comment about Altments suggestion: if you read around you will find other thoughts of this "5 times as many rule"; it seems to have its origins in the lack of computing capability. Certainly when I started doing this sort of stuff in 1990, My original PC would be fed the question on a Friday night, and produce the answer on Monday morning; now it finds it in less than 5 secoonds. There is no statistical basis for the 5 times rule - at least, that I am aware of. From memory, the Texts held in high regard were:

    Blackith RE and Reyment RA (1971) Multivariate Morphometrics Academic Press, London and New York

    Reyment RA, Blackwith RE and Campbell NA (1984) Multivariate morphometrics Academic Press, London

    Sneath and Sokal (1973) Numerical taxonomy Freeman, San Francisco

    Chatfield C and Collins AJ (1986) Introduction to Multivariate Analysis Chapman and Hall. London and New York

    Jolicoeur P (1963) The Multivariate generalisation of the allometry equation. Biometrics 19: 497-499

    This is all 25 years ago. Since then Ian Dryden (Leeds, then Nottingham) has written some stoking stuff of biological stats

    [While I was writing the above, a bell was ringing in my head - and I have just revisited what I wrote about this stuff for my thesis 25 years ago. It has to do with this: if the number of variables is greater than the groups, there is a greater number of canonical variates than groups. Then, the higher variates on and above group number are not describing overall canonical structure, but are describing within group canonical structure (which may be very interesting) Gene Albrecht (Uni Southern California) wrote much about this stuff in about 1980]


    At the end of the day, if you refer back to my original posting, you will note the caution I suggested with interpretation of fossil finds. You will find studies of this of this sort in the literature going back for about 50 years; the definitive work on the primate talus was from 1973, I think - Lisowski, Albrech and Oxnard, AJPA. Not long before this, the first multivariate study of the Olduvai foot was published in London By Michael Day and Berhard Wood, 1968 I think; there is nothing new in this way of thinking, but yet again, I emphasise caution in interpretation. But then, to say something carefully is better than to say nothing. Rob
     
  19. And to say something based on a sample of one is fraught with error. And I'm guessing from your response, you had one fossil to go on :drinks Now, back to that proximal transverse arch- how do they determine the geometry of the proximal transverse arch based solely upon a second metatarsal?
     
  20. Rob Kidd

    Rob Kidd Well-Known Member

    Have you read the paper of theirs that I posted? I am busy rebuilding my daughters house right now - papers will have to wait. You seem to be asking the question of me - surely the answer is in the Jerry and Bernies paper from the JHE. Rob
     
  21. Rob Kidd

    Rob Kidd Well-Known Member

    Either my PC was misbehaving, or I was having an elderly moment, but I did not see this earlier. Since you asked for it : "Which takes me back to my original question- exactly what did you measure, Robert?" here it is:



    2.2.1.3.1 The talus

    Lisowski et al (1974) describe a series of detailed talar reference positions and I use a modified version of these in the current study.

    The standard talar basal plane was defined as the position the talus assumes when it is resting on the tip of the posterior and lateral tubercles and the most inferior aspect of the head.

    The median sagittal talar plane is the sagittal plane which passes along the midline of the trochlea perpendicular to the standard talar basal plane.

    The coronal talar plane is the plane which passes through the tip of the lateral tubercle perpendicular to the former two planes.

    The median trochlear arc is the shape produced by the intersection of the median sagittal talar plane and the superior trochlear surface.

    The median talar neck plane is the plane which lies in the midline of the neck and is perpendicular to the talar basal plane.

    The trochlea-head plane is the plane which intersects with the most superior points of the trochlear margins and the talar head. This plane is obtained from the position assumed by the inverted talus.


    2.2.1.3.2 The calcaneus

    The standard calcaneal basal plane may be defined as the position assumed by the calcaneus when it is resting upon the medial and (if present) lateral tubercles posteriorly and the most plantarly tip of the cuboid facet anteriorly.

    The median sagittal calcaneal plane is the sagittal plane which passes along the long axis of the calcaneal tuber perpendicular to the standard calcaneal basal plane, effectively dividing it into two equal parts.

    The coronal calcaneal plane is the coronal plane which passes from the most medial point of the sustentaculum tali laterally, perpendicularly to the other two planes

    The median calcaneal tuberosity plane is the plane which lies in the midline of the long axis of the calcaneal tuberosity. In humans it closely approximates to the median sagittal plane but is markedly oblique to this plane in hominoids due to torsion of the calcaneal tuber.

    The talar facet plane is the plane defined by the most superior margins of the articular surface for the talus. This plane may be defined by the positioned assumed by the inverted calcaneus resting upon the talar articular surface.


    The relatively large magnitude of the talus and calcaneus allows the bones to be orientated relative to standard anatomical planes without difficulty. In contrast, the diminutive size of the navicular and cuboid means that definitions of the position of the bone relative to body planes are not practical. Variables are defined in terms of gross morphology of the bones as an alternative.


    2.2.1.3.3 The navicular

    The horizontal plane coincident with the long axis of the bone, bisecting the proximal and distal articular facets, was considered to be analogous to the transverse plane. The corresponding planes perpendicular to this, bisecting the bone into anterior and posterior portions and medial and lateral portions were considered to be analogous to the coronal plane and sagittal plane respectively.


    2.2.1.3.4 The cuboid

    The anatomical position for the cuboid is that in which the bone is positioned resting on its plantar surface; the assumed transverse plane is defined as this surface. The medial face is assumed to be the coincident with the sagittal plane while the assumed coronal plane is perpendicular to it and the transverse plane.

    2.2.1.4 Variable definitions

    Using these standard planes and definitions, the following linear or angular variables were obtained from the four bones:


    2.2.1.4.1 The talus (fig 2.1)
    (After Lisowski et al, 1974)

    1) The maximum medial height is the projected height from the standard basal talar plane to the highest point on the medial margin of the trochlear facet.

    2) The maximum lateral height: is the projected height from standard talar basal plane to the highest point on the lateral margin of the trochlear facet.

    3) The maximum median height of the talus is the projected height from the talar basal plane to highest point on the median trochlear arc.

    The above three measurements were obtained by resting the talus upon a glass plate of known thickness, the measurement being from the underneath surface of the glass to the required maximum height. The thickness of
    FIG 2.1



    the glass was included in the raw data collection to avoid confusion.

    4) The transverse trochlear breadth is the distance between the medial and lateral margins of the trochlear facet taken in the coronal talar plane.

    5) The anterior trochlear breadth is the maximum distance between the trochlear margins parallel to the coronal plane.

    6) The posterior trochlear breadth is the minimum breadth of the trochlear margins taken parallel to the coronal talar plane.

    7) The long dimension of the head is defined as the length of the long dimension of the talo-navicular articulation of the head and is measured obliquely along its long axis.

    8) The short dimension of the head is defined as the length of the short dimension of the talo-navicular articulation of the head and is measured at right-angles to the long dimension. This dimension includes the facet for the spring ligament where identifiable.

    9) The maximum length is the measured distance length from the groove for the tendon of muscle flexor hallucis longus posteriorly to the intersection of the talar neck plane and the articular surface for the navicular.

    10) The maximum breadth is measured from the tip of lateral tubercle to medial talar margin. The dimension is taken in the coronal talar plane.

    11) The trochlear cord is the length of the cord connecting the intersections of the median trochlear arc and the anterior and posterior margins of the superior trochlear facet.

    12) The medial facet length is the maximum distance between the anterior border and posterior tip of the medial facet.

    13) The overall medial trochlear length is the maximum distance between the anterior tip of the medial facet and the posterior extreme of the medial trochlear surface.

    14) The lateral facet length is defined as the maximum distance between the anterior and posterior borders of the lateral facet at their intersection with the superior trochlear surface.

    15) The talar neck length is defined as the maximum distance from the intersection of the median trochlear arc and the anterior border of the trochlear facet, to the intersection of the talar neck plane and the distal extremity of the navicular articulation

    16) The maximum neck diameter is the diameter of the talar neck measured obliquely, coinciding with the long axis of the head.

    17) The minimum neck diameter is the diameter of the talar neck measured at right angles to above, coinciding with the short axis of the head.

    18) The calcaneal facet dimension is defined as the maximum span of the calcaneal facet.

    19) The talar neck-body angle is defined as the angle subtended by the intersection of the median sagittal talar plane and the median talar neck plane.

    20) The talar head torsion angle is defined as the angle subtended by the long bisection of the talar head and the trochlear-head plane.

    In order to allow accurate mensuration of the talar head torsion angle, the talus was carefully positioned with it's neck in line with the camera. This ensures that the true torsion angle is obtained and that it is not distorted due to it's alignment with the camera


    2.2.1.4.2 The Calcaneus (fig 2.2)

    1) The maximum length is the linear measurement from the most posterior point on the calcaneal tuber to the most anterior point on the superior edge of articular surface for the cuboid. It is taken in the median sagittal calcaneal plane.

    2) The sustentaculum breadth is the projected linear measurement taken from the most medial point on the sustentaculum tali to the most lateral point on the posterior talar articular facet. It is taken in the coronal, and parallel to the basal planes.

    3) The calcaneal body is the linear dimension between the most anterior part of the posterior talar facet to
    2.2A & B

    the most posterior point of the tuberosity. It is taken in the median sagittal plane.

    4) The overall articular dimension is the projected distance between the most posterior part of the posterior talar facet to the anterior margin of the anterior facet. It is taken parallel to the median sagittal plane.

    5) The minimum tuber breadth is the minimum dimension from the most medial to the most lateral surfaces of the calcaneal tuber and is taken posteriorly to the talar articulations. It is taken in the median calcaneal tuberosity plane.

    6) The tuberosity breadth is defined as the maximum distance between the medial and lateral margins of the tuberosity. It is taken in a plane perpendicular to the median calcaneal tuberosity plane.

    7) The maximum calcaneal height is the maximum height of the of the calcaneal tuber at its posterior aspect, the calcaneal tuberosity. In humans, because of the upright disposition of the tuberosity, this dimension is almost coincident with calcaneal sagittal plane. In apes, however, because of significant tuber torsion, this measurement is significantly oblique to the calcaneal sagittal plane. No attempt was made, therefore, to rest the bone on it's plantar surface as it would not of achieved homologous positions. The measurement is taken in the calcaneal tuberosity plane.

    8) The posterior talar articular surface a: length is measured from the antero-lateral to postero-medial margins along the long axis of the facet

    9) The posterior talar articular surface b: breadth is measured from the antero-medial to the postero-lateral margins perpendicular (8) above.

    10) The dorso/plantar cuboid facet dimension is the projected measurement from the most dorsal to the most plantar margins of the cuboid facet. It is taken in the median calcaneal sagittal plane.

    11) The medio/lateral cuboid facet dimension is taken at right-angles to 10) above and is from the most medial to the most lateral margins of the facet.

    12) The sustentaculum tali projection is the measurement of the distance the sustentaculum projects medially from the surface of the calcaneum. It is measured in the calcaneal coronal plane and perpendicular to the other two planes.

    13) The cuboid facet angle is the angle subtended by the cuboid facet when viewed from the lateral aspect and the talar facet plane.


    2.2.1.4.3 The Navicular (fig 2.3)

    1) The long talar facet dimension is defined as the maximum dimension of the talar facet.

    2) The short talar facet dimension is defined as the minimum dimension of the talar facet.

    3) The long cuneiform facet dimension is defined as the maximum dimension of the cuneiform dimension measured in the transverse plane.

    4) The maximum short cuneiform dimension is defined as the maximum span of the short cuneiform dimension and is measured in the sagittal plane.

    5) The minimum short cuneiform dimension is defined as the minimum span of the short cuneiform dimension and is measured in the sagittal plane.

    FIG 2.3

    6) The maximum navicular breadth is measured in the anatomical position.

    7) The maximum navicular height is measured in the anatomical position.

    8) The sagittal plane thickness is the maximum dimension between the talar facet posteriorly and the cuneiform facet anteriorly measured with respect to the sagittal plane.

    9) The tuberosity projection is the maximum projection of the navicular tuberosity medially beyond the margin of the talar facet.


    2.2.1.4.4 The Cuboid (fig 2.4)

    1) The long metatarsal facet dimension is defined as the maximum dimension with respect to the transverse plane of the metatarsal facet.

    2) The short metatarsal facet dimension is defined as the minimum dimension with respect to the sagittal plane of the metatarsal facet.

    3) The long calcaneal facet dimension is as in 1) above but for the calcaneal facet.

    4) The short calcaneal facet dimension is as in 2) above but for the calcaneal facet.

    5) The medial dorsal length is defined as the distance from the most dorsal and medial point of the metatarsal facet to the most dorsal and medial tip of the calcaneal facet.

    6) The medial plantar length is defined as the distance from the most plantar and medial point of the metatarsal facet to the most plantar and medial point of the calcaneal facet.

    7) The lateral length is defined as the distance from the metatarsal facet to the calcaneal facets measured on the lateral side.

    8) The overall breadth is measured from the medial side of the bone perpendicularly to the lateral side of the bone with reference to the assumed coronal plane.

    9) The overall depth is measured from the most plantar to the most dorsal points of the bone while resting in the assumed anatomical position.


    You will find many of these in standards texts, particularly for the talus, however, those for the other bones are my work alone. I have been using them for over 25 years.

    You will find subsets of these in perhaps 20 publications over the last two decades. Rob
     
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    Cross stability in conventional shoes by the use of spring steel insoles: a pedobarographic effect study with observational application
    Becker NL, Obens T, Weisser J, Flick S.
    Orthopade. 2014 Sep;43(9):825-32. doi: 10.1007/s00132-014-2310-6.
     
  23. how does this rubbish still get printed

    There is no distal transverse arch end of story,
     
  24. scotfoot

    scotfoot Well-Known Member

    According to a very recent paper (1) , appendages can be "geometrically flat, yet functionally curved " . So does the human foot have a functional , distally placed ,transverse arch ? Going by the content of "Contribution of the transverse arch to foot stiffness in humans " the answer would appear to be yes .

    Paper (1) Contribution of the transverse arch to foot stiffness in humans
    https://arxiv.org › physics
    by A Yawar - ‎2017
    15 Jun 2017
    Gerry
     
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