SACH-SAWCH

A journey, from SACH to SPMLs

You don't need feet to walk. That was the title of a lecture to our podiatrists in NY & NJ. Simple proof? Amputees running races as fast as anybody else aside from walking to and back from those races – without “feet”. That capability was no accident. Soldiers coming back from the war with parts missing and a need to make them whole again led Inman (et al) to do the seminal work on what did feet and legs actually did. Not so much how big or how fast but what ? There are all kinds of possible make-do things – peg legs for example. However, those were very limiting and the common limiting element was ENERGY. You can do things badly, even quickly. But doing so costs you energy. Disability is more often an inability to sustain the thing you can do. So, the answer was sought to a better question. What do feet and legs do that, working together, conserves energy? When you move the body through space A===>B a steady flat line would seem ideal. Wheels on a chair? Nice, but, not so good when A===>B is through the woods. The anthropologists have not actually caught on (yet) that bipedal-ism is about energy . Long tails to allow bipedal balance are also about that as well. Permissive. Short arms on a toothy predator? Same thing, bigger arms need a bigger tail to balance. Center of mass wants to be close to the two hips axis (if you have hips). It was a neurological development which allowed the modulation of the leg movement mechanism through detected and anticipated momentum and inertial requirements.

The idea is to get the center of mass on a flat uniform speed toward the goal. A===================================================== ======>B A=============================================>B /\_/\__/\_/\__/\_/\__/\_/\__/\_/\__/\_/\__/\_/\__/\_/\__/\_/\__/\_/\__/\_/\__ This is true even when A toward B is over bumpy ground. In a sense the big breakthrough was not the WHEEL but rather THE ROAD which allowed wheels to be worth the trouble to build. But the math – so to speak [control mechanism] needed to be quick. So, simplifying the movement of the center of mass over an irregular ground so that speed requirements would be effective needed a discard of the very flexible limb to body connections (slings of muscles as still exist in the fore limbs (arms) in trade for a connection which spatially does not move relative to the center of mass. The closer to that center the better. Tah-dah!!!! Nature invents articulated HIPS. No, not for 'walking'. No, not for speed either. Big nasty beasts were running all over the place, and plenty fast, eating everything slower moving or which pooped out while trying to escape from a fast hungry runner that didn't seem to tire. Hips simplification leg movement by giving up infinite this way & that way movement in trade for fixed center spherical action. This allows pendulum properties, the energy of one leg is more easily transferred to the other. The linkages below the hips adjust – on the fly – to inertial alterations – adapting to the irregularities of the ground. Wear & tear of impact is also reduced by having the last link (the foot) to be totally inertially adaptive working within a cone of expectation (of graded resistance). Deviations from expectation are SELF adjusted by [IMPORTANT] local (lower spinal cord) reflex arcs. For very big beasts the lower spinal cord was fat and were once called second brains as so many what-if immediate reaction patterns of correction were there – nearer to the needed circuits handling the hind foot details.

So? Those graphs of joint motion “normal” in walking, are very misleading.

Perhaps they are normal for adults walking across an empty room in a leisurely way. No child EVER walks that way unless threatened to do so by an angry parent. In the gait lab: “BILLY!! Just once!! Walk the way mommy walks or we will never get home! No! Over there, across the glass plate!...” Normal” for children should be labeled as how children walk when threatened to walk like adults or else. Why? Kids are not about energy. They are learning the extremes of their walking instrument. A=====>B includes every puddle and challenging obstacle on the way. Therefore OUR first interest should be energy efficient adaptive skills to function in real environments. Failing that? Stepping or wind up toy walking. Those walking robots? Walking? All the ones I have seen are STEPPING and not using optimum energy transfer mechanisms [to save batteries?].

There is so much old and misleading terminology that makes making sense very hard.

It might be useful to first read our bookshelf book: MUD … mired in the footprints of time .

We will wait here..…

Got it? OK. We move on.

SACH / SAWCH This is a really important section. It is the starting point for unlocking disorders of walking. It asks: "If you can't undo what is wrong, can you work around it?" Or substitute? COMPENSATE ? The search for an answer led to so many things. It began with the realization that some hallowed thinking is just plain wrong. Junk. First to fall, shoe rocker bottoms for casts. Two very large manufacturers joined resources in this quest and vastly improved their products by shedding old assumption driven & patented nonsense. But, we begin, here, with war; soldiers coming home from WWII with amputations. Prosthetics. Peg leg? Just fill the gap? Starting with amputation, below the knees - to study what "below knee anatomy needs to do for us. Verne Inman and his associates (Ranchos Los Amigos) did great studies in that quest that had unknowingly duplicated lost studies of Braun & Fisher [from 1895] and which were forgotten in a massive underground catacomb like medical library in what had since become “East Germany”. The data of the B&F's studies had been deeply quoted by Steindler in his orthopaedic text book [without B&F being mentioned, leading to the repeated question " How did he know THAT ?” He described with dead accurate decimal places.

Unaware of the B&F 3D studies, Inman re-described the parameters of normal gait and then broke them down into aspects that - being considered from the functional side - either assisted a functionally normal pattern or not.

But what WAS functional? More exactly, what aspects or combinations allow very low energy usage when humans walk? That, but, amputees in mind, to not get drowned in a useless numbers-only publication title wave. If you can't replace the flesh can you replace what that flesh did? Engineering . This is called Rehabilitation Engineering. The lowest energy to get from point A to point B = STRAIGHT LINE. Use a wheel? On level ground a wheel can do that. On the average over the human millennia how much flat level ground was there? ZERO. The wheel wasn't the first great invention. The cleared ground leveled“ROAD” was. Wheels don't do much in jungles or meadows. Legs take us where wheels cannot go. Over a wall. Up a tree. Through mud. Deep diving. But the big one is and has been uneven ground. We are wanderers. Those paths least taken are bumpy.

Inman told us: On jointed limbs the next lowest energy from A to B would be a low amplitude sine wave approaching a straight line. That path is the path of our center of mass ( a location where we balance). How do humans walk? The center of mass of an adult travels a 2 inch high

sine wave up and down from A to B. Side to side sway is similar. Center of mass is just forward the L5-S1 disc (in the pelvis). It is close to being above a line drawn between the right & left HIP CENTERS. Stow this away. Later, we'll see that the fact that hip centers being fixed in place in

the pelvis thus have a fixed spatial mechanical relationship to the spine is an important evolutionary step which was needed to utilize evolving better movement neurological computation. Above, we see the height of the center of mass near where pelvis attaches to the spine. The hips can go up on right while down on left (or the reverse) which does not displace the center of mass. A stiff line from center of mass to a point on the floor (long peg leg) arcs over a circle path with sharp up to down at the ends of the arc. A small savings is that it does not have to travel the full height as seen in the arc above. Hips can go up and down without the center of mass moving as much. But, we need more. The FOOT. The single most functional bone in the

ankle/foot is the talus (seen prominently in white in inset above). The talus is key to all foot & ankle movement; and yet, it has no muscles or tendons attached to it. It is a spatial adaptive link with several planes of motion with interesting shapes & properties. The cylinder shaped mortise is seen opened here. The Achilles passes the talus to attach to the heel. Others also pass the talus en route to their attachment points. The talus thus moves within an envelope of tension generated by a sheath of passing muscle tendons whose forces (interacting with those generated by ground impact) average and

smooth body travel. It reacts mechanically to change from best guess adaptation to approximated anticipated ground conditions [hard, soft, slippery, tilted etc]. It is a mechanical capacitor averaging oddities, especially of contour. But, what if the forces of unexpected angularity exceed what it can yield to? It breaks. Or, the containing envelope of constraints sprain or break.

To protect our talus in situations where unexpected excesses are likely [hiking], we wear constraints - boots - with firm ankle 'support'. Constraints cost energy as small deviations are now transmitted up the chain of support and not subtracted smoothly from the walking experience. It still beats fractures. We will see later why boots almost have to have heels. Heels a must? See if you can guess why as we later discuss prosthetics. In trying to fit segments of motion to normal relaxed walking on level ground, Inman described 6 “ determinants of gait ” [the things our parts do in harmony to conserve energy by traveling a low sine wave path from A to B. But beware of laboratory conclusions. They fit laboratory conditions – flat level surface. Our walking can adapt such that undulating ground barely changes the path of our body. This mechanism has inertial sensitivity.

That long horizontal scratch on your BMW? Did you actually not notice driving too close to some protruding object? Or was it 'keyed'? If it was a straight line scratch, then it was moving on wheels from A to B. If the scratch is a sine wave, then some moron, WALKING by, did it. The height of the moron can be calculated. The length of one full sine cycle is 75% of the moron's height. Got that, Dr. Watson?

The 6 determinants (of Inman): The capacitor in the ankle (heel/foot) is #6

but we re going ground up, so?

As the heel hits and the ankle lowers and the foot drops flat to the ground we get some height reduction, a lower

radius of arc to travel over. As mass moves forward, above, the calf becomes quite tight and freezes further ankle motion (passive dorsiflexion stops with the shin about 8 to 10 degrees forward tilted – knee center is forward that of the ankle with center of body mass CENTERED on the foot [heel contact to metatarsal heads]. (Not included by Inman, but obvious, toes are feelers not do-ers. Forward roll is over metatarsal heads not toes.). Got that? Toes are detectors. Not doers. Don't blind them. The calf, by making the ankle mechanically solid, diverts the forward roll to over the forefoot (MT heads). That roll lifts the heel which rises off the floor just as center of mass has passed the mid foot. This would otherwise now be a roller coaster car at the top of the first hill. The supporting leg rising – AT THIS POINT – lifts and so flattens the top of hill drop that would otherwise follow. ' Midstance ' is when our center of mass is over the point of floor support. But,for quick eyeballing, use hip over midfoot as close enough, visually. In our method, MIDSWING is when the swinging ankle is at same forward point as the stance ankle (one hides the other on side view).

From heel landing and let down to mid stance the quadriceps controls inertially induced knee FLEXION to shorten the leg (Hip to Ankle line length). Again, inertial sensing. So, knee flexion into midstance [hip above mid-foot] and then follows knee extension past midstance. That, too, happens inertially. Quadriceps does not do it. Not active knee extension? Mostly the center of mass is flying forward by inertia and the knee extends to fill the gap that would otherwise occur. Some length comes from the ankle rise over what moves forward as the forefoot metatarsal head rollover. H ip A nkle R elative Position, a vector. Inman does not note

this detail, but looking at a Hip to Ankle line (a functional virtual invisible leg) the angle to the ground at heel contact and that line as the foot rolls off the forefoot create an arc angle whose apex is well below the floor. If that big arc centered below the floor was a wheel, then a small arc of turn has little rise & fall.

A smaller arc (shorter stride) of a bigger wheel reduces vertical anti-gravity needs. An alternative to sine wave? Another energy saver was hiding from Inman in his own great studies. Look how close this stiff legged BIG wheel arc comes to the sine wave that we just described. However, it needs a centered ground apex as a center of motion or else it becomes a lifting cam which destroys energy and is jarring. The forefoot is too forward for this job … unless....

In this case, plantar flexion (equinus) both increases the wheel's radius (good) and CENTERS the wheel axis to be below the center of mass from

forward travel as from A toward B. A little knee flexion helps sometimes.

[Knee flexion can be looked at as an angle H-K-A. Or, as a line H-A which having magnitude AND direction is both a body and an environment relative VECTOR. [later, but the engineers are now tisking. Tisk tisk.]. Hip – Ankle Relative Position [ HARP] is a room relative vector. Much better than the knee angle although they measure the same think. Knee ankles are for the bozos who want to sound knowledgeable. Vectors are for the knowledgeable who want to make a difference.] Wait. No.. no nooooooooo. Wait wait. Plantar flexion? Really? Equinus, is a good thing? No. It is ' a ' thing. If looking for a work-around, it is there, as an option . But people – patients – don't do THAT! Do they? (Later. The answer = yes). Inman was not aware of this, though. So, at this point, no, not while discussing his determinants. That list should be amended. But, we have more of his original 6 determinants to discuss.

OK those two were pretty much covered. The pelvis has a roll to play in these 6. With our center of mass held relatively stable by supple links and inertia in forward flight, the hips can ride up on one side if the other side, see-saw like, goes down. So, that goes on the list. But stow this one away for later as well; that pelvic movement can be made to amplify for other purposes. Bird's eye view, looking down:

The pelvis can also advance forward on one side (about 7 degrees) about a vertical axis also passing through the center of mass. Then it trails back to square to the direction of walking to then falls behind by 7 degrees as the other side, linked solidly, goes ahead by 7 degrees. That is a 14 degree vertical axis oscillation of the pelvis facing from 7 degrees toward the right to later be 7 degrees to the left and so on. This oscillation on a vertical axis was noted by Inman to provide longer step reach (length) than legs alone without any anti-gravity cost.

This horizontal pelvic rotation, on a vertical axis: R L R L..., does introduce a lower body torque momentum that needs inertial cancellation. Counter rotation for that is provided by opposite arm swing. Arm swing does that job to avoid energy loss. That is why we swing our arms in contra-lateral coordination. Recurring theme, right motion must sense & react to opposite side activity – AUTOMATICALLY.

The travel speed of the center of mass along this minimally sinusoidal nearly straight A to B path is quite uniform, making Isaac Newton smile. The body moves along, with minimal rise & fall, at uniform speed. Ignore the legs, hand hide them and you get a good idea if what is happening and if it is is working.

There is a very sensitive muscle & timing pattern that transfers any left over energy of the swing of one leg to the stance of the other leg. If progression becomes stop & go then a graph of distance traveled (=d) against time (=t) shows STEPS. “STEPPING”

If our body mass is intermittently slowed, then the graph likewise flattens and looks like a stairway . So, for many reasons this is called STEPPING and not walking . Walking has right-left energy transfer which conserves energy which is kinetic in the pendulum mechanisms of the legs. The swinging leg is a dampened double pendulum while the stance leg is a vertical pendulum (metronome). If these pendulums do not match there is no walking . It becomes stepping . With stepping, nothing gets an energy boost nudge or pull from the other side. Every bit of movement must be consciously muscularly moved, totally. Each step portion becomes a self contained event. There is no energy conservation in stepping.

Stepping can get even worse if stance is unstable. In that case the needed vertical stability must be supplied by additional sustained muscular stabilizing effort (or by a brace).

Stability is the enemy of MOMENTUM ( & mobility ) Braces / AFOs can kill walking by sapping energy through excessive stability , as well as loss of sensibility needed for control and knowing when to transfer energy, and by promoting a difficult rollover fulcrum (toe plates, typical ankle hinges etc). Too free, allows REFLEX kick-back that DECREASES the functional arc. If you prescribe AFOs and think that all AFOs should have ankle hinges, then add yourself to the problem list (in depth later).

Dinosaurs that could easily catch you (even if you were on a 24 speed bicycle) came in two flavors. The original flavor was sling-like hips (hip socket not yet evolved). Over time improved neurology allowed beasts to give up some extreme hip swimming mobility from SLING-LIKE body/leg attachment. Cows, dogs, cats etc are four legged but only have hips in the hind legs. A bone-in-bone socket articulation FIXES the hip centers relative to the body. Early dinosaurs evolved hips because given these constraints their improving neural abilities could sense and alter muscular leg actions more quickly and with better control. Go faster? No. But nearly as fast with height modulation that kept body travel level & uniform in forward speed. ENERGY!! Less energy = less need for food = less hunting, more time between meals, can go longer without food to find new hunting places. Less was more. Do you want to increase your MOBILITY on the dance floor? Drop marbles. Hmm m. Front legs (no hips) actually detract. Predators wanting long runs go vertical off their front legs. Bigger arms need bigger tail = slower? Maybe? Maybe not. Anyway the point is that hip joints are not to allow walking or running. Humans without those (they are among you) can do both. They waddle. It just takes more energy. But with hips it is energy conserving tuned to maximum for walking but with variations that are allowed when there are other needs. The fine tuning of our control mechanism is sharpened by having neurological EXPECTATION . I offer this as another important determinant of gait. We walk much better over ground that is familiar to us. In unfamiliar circumstances we slow and dial in stability patterns for the uncertainties of movement to come. The need to just walk when the energy conservation tricks are thwarted calls upon next best choices (bigger wheel? Still centered below floor???).

This we know, walk too slow and we need more vertical support as we are not flying anymore. Side sway increases with going slow in order to get center of mass more 'supported' on the stance side rather than shoot forward between the average of the two sides as inertia allows.

As kinetic energy is put into the swinging leg to then draw that energy back from it, a prosthetic leg made too light becomes a NERF leg. A prosthesis too light to cooperate in a chain of energy transfers? A prosthesis needs to swing with inertial normality and be tuned as a metronome when in stance to match the opposite intact stance or swinging leg. Absent that, the intact side will instead mimic the abnormal for cyclic symmetry which allows energy passing. Lots of volunteers helped us to see that. Where weight is distributed in the prosthetic matters as that sets the natural speed of the metronome and pendulums.

One big problem for us with Inman's (and Braun & Fischer) works was that the subjects were neurologically normal. There is an entire dimension missing as to what happens when neurology drifts from the evolved ideal of control perfection? For lower leg amputees Inman found that normal gait requirements were attainable by having the prosthetic foot solidly attached at a specific angle ( knee center ahead of ankle center over mid-foot) [shin is NOT VERTICAL, A right angle is a wrong angle . Handle the ankle capacitor and cushioning heel landing by using a wedge of cushion in the heel of the wooden foot (soft pliable toe area). This was the SACH foot prosthesis. Solid Ankle Cushion Heel A 'cushion' is only a cushion if it regains its height by midstance. Less than that it is a back rolling missing heel -a rocker. Not good. Let's look at a very minimal case that shows vividly what SACH really is.

A girl who was born with a missing forefoot but totally normal otherwise. She has a very tiring asymmetrical gait barefoot or in shoes with filler (on the side requiring it). Her walk was not evenly forward and her inability to step fully with her seemingly INTACT right side drew attention and wonder. This right step is well under expected length (arrow points to normal heel contact expected). {75% of radius stature – see mud}

An orthosis with a stop to limit dorsiflexion (solid ankle) and a foot plate stiff to the metatarsal heads (soft at toes) give us a perfectly normal walk. The circle seen is of her 'stature wheel', diameter = stature. Stride, which is two steps R&L, is 75% of the DIAMETER of this wheel. Each step is 75% of the RADIUS of this same wheel. Easy, huh?

The heel is cushioned. As that wedge cushion has no place to exist within the brace, it is put in the shoe heel. Thus prosthetic Solid Ankle Cushioned Heel

= SACH.

It becomes

Solid Ankle Wedge Cushioned Heel = SAWCH when the AFO+shoe need angular forward tilt adjustment that the anatomy isn't allowing.

SAWCH

SOLID ANKLE CUSHION HEEL

SOLID ANKLE WEDGE CUSHION HEEL

Now, about measurements. Should we use arbitrary English or metric? Neither adds anything of value beyond DOCUMENTING a single measurement. That is how it is done... but not by us. Not here. Nothing bad

about it, but, it doesn't even hint at what functional meaning that measurement has.

We will use statures . 1 stature is the subject’s height (which is measured in English or metric). For somebody who is 60 inches tall, one stature is the same as 60 inches. If getting a standing height is difficult, then arm span, finger tips to finger tips, is the same as stature (Marfan's disorder excepted). The center of the stature circle is very close to the center of mass. A semicircle will pass through the center of mass. Are we a wheel?

The stature wheels shows us expected distances and relationships. In well coordinated walking (which depends heavily on overt sensation & general deep primal feed back sensation) there is transfer of energy side to side on two points – a leading heel and a trailing 'toe' {actually metatarsal heads).

The soles of the feet are on the stature circle contour (here moved up a little to better see feet. You will NEVER see this if sensation is impaired. This IS the baton hand-off moment. Many patients with 'CP' have excellent volitional muscle control but look frozen and paralyzed if their sensation is lacking. Give them something to push (cart, chair on wheels) for hand mediated sensory reference and their supposed palsy disappears. Wall touching, sofa rubbing, hand holding may be seen in succession as whatever comes into reach as a spatial reference. 'Curbside' diagnosis at an art show. Adult onset walking difficulty. An early digital camera quick 16/sec 4x4

composite snap shows trailing heel staying on ground too long.

Follow up of correct diagnosis = cyst in spinal canal. This art viewer was unaware of his missing sensibility until it was specifically tested. Inman's determinants have no provision for sensory loss. Also, being focused on injured soldiers needing prosthetics, there is great (with a glitch) depth of thinking about stance mechanics. It is, however, weak in swing phase considerations which have (aside from weight distribution) little to do with the foot. The Ranchos researchers also gave us

this graphic pearl. Y = energy needed X = walking speed. D=

Walking at normal pace is crazy energy efficient at the comfortable speed (lowest curve at arrow). A= energy curve if one leg is stiff (knee etc).

A at best pace cannot walk holding hands with D as D's energy will exceed running full out. Mommy, pick me up. Energy cost = social cost.

So, we have seen isolated left abnormality of foot structure manifest as abnormal right leg function. We have seen that invisible sensory things can fool us to misdiagnose motor problems (palsies). Here it comes – oooooo – much of what we see as wrong in cerebral palsy walking is neither cerebral nor palsy. We have a lot of ground to cover.

Before club foot was considered to be surgically amenable, such untreated feet served to torture the owner. Prosthetic mechanics outpaced club foot remedy and so prosthetics around the abnormality was used (man on left is standing on his well disguised right tip toe.). Women tended to prefer amputation of ugly dysfunctional actual feet to more cosmetic functional prosthetics. Recurring theme: We don't need the thing. We need what the thing should do.

SACH, but not only prosthetics? Include similar acting orthotics. We saw an example. But maybe even casts? Not casts meant to immobilize & align injury, but casts meant to protect and guide early mobilization. How about casts?

Testing this required certain manufacturing ability for it to be practical – that is, clinically useful. Our having been pivotal in the development and manufacture of fiberglass casting tape(s) there were three companies very interested in the associated things that go along with that, cast shoes and cast like boots and so forth. Were the old 'truths' true? Interestingly the top executives of several companies got personally involved, even serving as subjects and victims to our science! Start with real need.

1 4 Look. A high school girl, basketball high scorer, on a team in the championships. Bad timing. She has bilateral heel pain. Miss the championships? On left (#1) is what was then called a plaster cast 'rubber walker' typically attached to the bottom of plaster casts at a balance point so it would roll and allow 'walking' (no way – it is what we now call 'stepping'). Well, after having seen what missing one forefoot can do, you can imagine what these will do? Her gait is seen on the right above (#4). It was unsteady even just walking. Hard to sustain. Her steps were extremely short. It is similar to walking on very short stilts. The missing plantar lengths of the rubber base and missing forward toe rollover (apex of gait arc below floor) is badly missed. Could these lead a basketball team to victory? Nnnnnn..no. Not a chance. But let us test this prosthetic idea (#2 ) without the cushioned heel. Forward shin tilt with wooden sole shoes varying in shape and forward rolling point (thank you Darco). Shoes with wood stiff bottom flat or rocker bottom was impossible to walk at all if the cast did not have the required forward tilt. It was not practical even when the casts were optimally tilted forward. It was hard to even walk just a few steps. So, there is nothing to show. No pictures. No chance at basketball. 2 3

The flexible, cast shoe with an array of stack-able wedges of varied compression strengths (Thanks 3M) let us play with 'functional dorsiflexion' given a starting ankle fixed plantar-flexion that we could offset with the heel wedges. Over #3 above . The bottom of shoe to tibia angle – varies with wedges. Now we had a SAWCH mechanism. Solid ankle Wedge Cushion Heel – that is – a wedge cushion in the shoe heel not the cast nor orthosis nor prosthesis. Engineering wise, this should not matter. That is too much for an actual patient to be asked. She did play when we found her the best treatment combination by torturing our exec volunteers. Her team won. She scored high (wearing two casts).

Another volunteer subject, an adult fit jogger with nothing to treat but who was involved in the fiberglass cast product development needs. Notice the sweat and the jack-knife posture. In this trial, he is wearing two casts with 5 degrees of plantar-flexion. The sweat is from trying to walk unsuccessfully in 'walker' fitted casts, then “rocker bottom” cast shoes. What you do not see, off to the right of this image, before a black screen (used for strobe lighting) is the wheelchair needed to get him to where he stands (only briefly) with much strain. The jack-knife forward lean (butt out) is

typical of stiff plantar-flexion when heels are impossibly urged to be flat down or balance deficits require it. How would our basketball girl & this fellow do with SAWCH shoes?

Basketball? Hmm. Not exactly walking, but dead on why this girl was doing this.

Science!! Strobe captures her doing a lay up basketball dunk (ball is red, white, & blue). Our jack-knife fellow in SAWCH shoes set to 'functional dorsiflexion' grabbed a PT exercise ball and dribbled it including passing the ball under his legs. There was competition in the air. Hurdles? OK.

Beat that!

He eventually did clear three foam blocks, but this image so clearly shows the SAWCH concept. The shin is NOT perpendicular to the shoe sole. The wedge height was whatever would produce that functional dorsiflexion. Cushion isn't just soft, it recoils fully as midstance is approached.

Walking & chewing gum... running dribble (PT exercise ball).

Pages of measurements were presented that FOUND that SAWCH beat rocker bottom massively (almost no data for rocker bottom as subjects could hardly move in them – at all. Even flat stance jack-knifed was impossible). Should be convincing. The execs who had to shoot & kill their own existing product lines wanted SOMETHING that just couldn't be blamed on – whatever... Numbers don't sell. We needed a killer test.

Executive basketball game. Two teams from coin flips and players from Darco, Aircast, and 3M. Team SAWCH vs Rockers!! It is on. It was a massacre. No baskets for the rockers. Three digit score for SAWCH & points climbing fast - well before half time. Blue faces on the Rocker bottom team and tongues way too visible. Let's stop here & switch shoes! We ended when the score (quickly) evened up. Execs don't like losing, even for science. Quit at a draw. Suddenly all sorts of products were replacing rocker everything but interestingly design people did their best to color the boot sides to look rocker-ish (for the many who can't abide changing what they were taught). This was the birth of high performance by way of casts and a subset of cast braces when immobility is not the purpose. SAWCH, born of SACH. But, was this really about ENERGY? Calculating from motion video is a beast with huge assumptions that are required... Sweat & inability to perform are quite convincing but do not MEASURE. In a range of reasonable expectation, just how tight a measurement is needed? How much is too much because it fails? So, on to engineering student volunteers doing participation projects.

Build two AFOs (per volunteer) that can be finely adjusted degree by degree in the range of 'functional dorsiflexion' as it was called, plus or minus 5 degrees. Monitor cardiac output, O2 consumption, CO2 production and also take it outside to uphill and downhill driveways, and to the park on the walking and running paths and on grass all with fine GPS spatial tracking sensitive to height changes. Numbers numbers numbers... but nothing we didn't already know. Hills are harder & require more energy. “Functional dorsiflexion” is a real thing – a sweet spot, where energy loss is least. Basically the arc traveled through stance has to be near symmetrical to a vertical midpoint line. The apex the of that arc traveled by center of mass is well below the floor. What happened to Inman's sine wave?

Warning: Proceed at your own risk. Geek speak begins here!

When an actual math relationship as an equation is beastly nasty to apply in real time keeping up with the process, engineers ask: Do we really need THAT particularly complex or hard to produce equation? We are not interested in going from negative infinity to positive infinity, just from minus a small amount to plus that same small amount in a potentially useful range. Does some other calculation or mechanism nearly coincide within that very narrow range?

There is a field of math (& engineering) which is focused on exactly that. This simplification is common especially with gravity being useful to have around and the need for having hyperbolic cosines at the ready. If you did that once, can you use something simpler if you are only working within a much narrower bounds? See right? The red curve is complicated. The green is simple, Staying between the two blue pointers, the simple green math will get you there.

Yes. So you see the use of a stiff leg acting like a metronome – an arc pivoting from below & the apex below the floor can be approximated by bringing the arc apex up to the floor surface by standing tip-toe. That also moves the pivot in line with the center of the travel arc (with a touch of knee flexion to help center the pivot point). What??? Does that mean a flexed knee with a plantar flexed foot (equinus) is FUNCTIONAL??? It works quite well for horses and in a pinch, when the Inman determinants are thwarted, in humans as well. That common area in the graph above could also be sine wave & wheel. So, knee flexion and plantar flexion of the foot are NOT necessrily abnormal? Hmm, this is how academics can be rotten clinicians.

We don't throw publications at problems. We start with 'Are you having a problem' ? Then, looking at what is happening, ask: “Do the findings better fit the stated problem or simply respond to it or minimize it?” More forgiving: Could it be true that SOME of the knee flexion and SOME of the plantar flexion is compensatory. This is like getting off a long bus ride one block too soon. Can live with it. Functionally, every zig needs a zag. The zig may be hard to see when the zag is obvious but compensatory. If mobility control treatments are rendered by single joint, the chances of catastrophe are great unless this is taken into account. We do not want to excise compensatory mechanisms. We want the patient to not require using them. For example we have two structural zigs in the leg, They are quite out of balance. Short of surgery, how to make do? Increase both zigs in a way that centers them offsetting displacement at another level. Is THAT legal? It is written into the constitution. The.... Constitution of what we are – survivors.

Copernicus Copernicus? This is as good a place to introduce an old idea that nobody thought to apply to walking. And since we are going ground up, it makes sense to not have to back track on this later. If you were a super high paid gear maker back in the days when the sun went around the earth and some planets meandered back & forth in the sky, then you were in high demand to make the boxes of gears it took to simulate that in a model that you crank. Epicycles. With enough epicycle gears, you can trace any path you like, including sun circles and Mars doing a celestial two step.

BUT … IF - instead of centering the EARTH – you center the sun? Most of the gears go away. Boxes of them. You only need one gear per planet.

Gear makers go to the bread lines… So given a person walking over uneven ground seeking to travel a level low amplitude sinusoidal path at steady velocity, we need to solve many

simultaneous equations as the ground undulates and the limb segments change angular interrelationships in a nonlinear (periodic) way.

Walking epicycles. Wow. What a mess! No? No. Not a mess.

On the right is a tall computer (Gould RTM – super fast) and a disk drive costing (then) a fortune. The drive was FULL. No more space. Massive data on thousands of cases of walking disorders including everything that impairs walking plus normal volunteer data from endless experiments - disabling

them with braces designed to impair in certain ways. Plan was to find what we can do to a normal person, mostly young gymnasts, to make them look like an abnormality of interest.

Thousands of graphs; each with thousands of 3D data samples and we were now out of disc space and so out of business. Yaaaaahhhhhh!!!!! Unless... Unless, we dissect that data to see how it might compress. We chose Fourier discrete methods. Not a single case in all that data needed more than 6 “harmonics” (pairs of numbers, turning circle side & speed – same as gears). Result: Exact matches. Graphs on transparent paper held to the light were the same (Thanks Jack Jolly, Rutgers engineering who generated stacks of comparisons). But (thankfully) only six harmonics (12 numbers) per case? Cases with a wide range of abnormalities? Think this way. What we do well, we do with the anatomy that we have. But, abnormality cannot do anything you can dream up. Abnormality is also constrained by our anatomy. A knee can't be anywhere. It is tethered by the hip. It reacts to the same ground. This meant that WE are bearers or users of maybe 6 functionally linked gears! We identified five consistent anatomic but abnormal often conjured another. We solve our needs with them or we fail with them as well. So humans have 5 to 6 built-in gears (or wheels)? Or five plus a spare? Was there an ability to combine the built-in gears to generate a different required 6th gear? Yes. What is a harmonic, again? It is a number pair. The first number is the gear size (amplitude or in electronics = power = circle radius ) and the second number of the harmonic is theangular velocity at which that gear is turning at that functional moment in time. A full gait cycle might be from right heel strike to the next right heel strike. If continuous walking is being followed then each full cycle repeats making this a periodic process, like what a wooden horse on a merry-go-round is doing, same thing over and over.

The built-in Gears (gait harmonics) Bottom-up: Forefoot - ('met heads') to ankle center is the spoke of that wheel. (Axis at end of foot) Heel - Heel tip to ankle center is a spoke of a second (smaller) wheel. Shin - Ankle center to knee (shin) is the spoke of a large wheel. Femur - Knee to hip joint ( spoke of a femur wheel ) CmH - Center of mass (an inertial reality without a visible presence) to hip center. This top wheel spoke is nearly the same as the forefoot wheel. Can swap. Being of similar size the CmH & forefoot wheels are able to share adapting to the smaller ground changes. If the forefoot is insufficient then the CmHip wheel gets the remains. This is why vertical hip motion is so prominent wearing high heels as available ankle range is used up by excess plantar-flexion. Lumbosacral fusion makes the wearing of high heels close to impossible. Likewise, high heels produce vertical pelvic oscillation, maybe a goal in itself? The wife of a famous spine surgeon had a lumbosacral fusion after injury in a plane crash. She asked, “Why is it I can't wear high heels anymore?” Answer, “You're married. You don't need them anymore.” No. It didn't go over well. The long explanation followed, which you just suffered through.

An obvious reason to prefer measuring distance & lengths in STATURES [height or arm-span] is that we can measure real functional change over time regardless of age and current size. Another plus is that those horrible “Normal” [2 std dev]

graphic envelopes of ‘normal’ taken from populations by AGE – melt away. Walking is about pendulums. We don't measure pendulums nor metronomes by their age. We want to know the distance from apex to center of mass. Stats from mixed populations muddy everything as so many body types in a population 'norm' would imply that there is wide tolerance for deviation in metronomes and pendulums. There is not. A normal comfortable stride length for an adult is 75% of stature [how far center of mass travels]. Those color bars on the floor are showing how far center of mass went projected onto the floor onto a foot-floor contact point which helps visualize how much of that foot travel actually made it to body progression.

The stature wheel also has great utility in following side to side transfer. It is made on point. Trailing heel rises before the leading opposite side heel has touched ground.

A circle is equally described by it's radius or diameter . We use the diameter when the entire stature is in play. So, a full gait cycle of two steps is measured in statures from the wheel diameter (full stature). One step (either side) is measured using the radius of that circle (half diameter). So normal stride (2 steps) = 75% of stature. One step (either side) is 75% of the radius or half stature. So easy!! A mild slowing might get down to about 65%. A pressured walk might get to 85% stature.

If a man walks with a left step length of half of his right step length, say, a thousand steps... he is called what? He is called dead. That statement has half his body departing from the other half. Correct step lengths are from center of mass to center of mass during that step. We like to draw it on the ground as that makes the efficiency of that step more obviously visible. A step-to gait has equal step lengths of the feet , but almost all progression of the body is from one leg only, it claims new ground, the other leg just catches up. Have you any idea how many published articles screw this up? And it leads to wrong conclusions.

Here are the 5 built-in wheels with fixed radii, and turning velocity driven by inertia through the linkages. Most of the lower leg movements in walking are NOT pulled there by muscles set up to do what they are named to do. Knee flexors do not flex the knee, they temper (dampen & deflect) knee extension. Hamstrings do not extend the hip nor flex the knee. They dampen ongoing hip flexion and end the inertial knee extension. This reverse, energy bouncing, muscle use is called eccentric, elongating as they activate . Extensors control flexion INERTIA. They deflect motion.

POLAR GRAPHS Periodic data can be (& often is) polar graphed in engineering. The knee curves from three conditions are seen on the left with their polar graphs on right. The polar graphs colors mark out equal time segments. The 'harmonics' that are active in each data set are easily seen in polar graph format. Also notice that an ellipse is a circle of two centers. Hip and knee cooperating can generate functional elliptical paths and do. The knee graph has changes that come from the hip (toe on ground) , rarely from the knee, from the heel and forefoot by ground reaction on the linkages. Looking at the standard graphs on the left gives us little clue as to what is contributing what to what. Polar graphs have each harmonic quite obvious in contribution size and when active.

Concentric Isometric Eccentric In walking, only the Iliopsoas is concentric , meaning that it shortens when active. Nearly all the power of walking is from this one concentric muscle which is not actually in the leg but in the body. Having huge multi-segment vascularity, it contributes to body heat. Nothing wasted. Only the briefest beginning of swing phase is “concentric”. Nearly all of the energy of efficient walking that comes from the iliopsoas is from a very brief oomph. /\__________________ Think of a mother pushing her child in a swing seat. It goes away and returns as a pendulum. Her next push is minimal needing only what air resistance and swivel drag took away, not much. Mother pushes swing concentrically. The Iliopsoas pulls it concentrically. Same deal.

The stance leg behaves like a Joe Palooka punching object (Joe stand on the floor, bottom weighted, and rights itself after being punched). That down to up return must time itself to the opposite side swinging double pendulum (which not chaotic as it is bounded by damping and energy transfer mechanisms).

The knee flexion at heel strike is without any flexor help. The knee extensors tighten to slow the inertial driven knee flexion. This knee flexion is eccentric to the knee extensors which lengthen despite their activation.

Knee flexors are getting a free ride.

Inman found that at midstance the supple ankle freezes solid. The normal ankle joint is not mobile at the key moment of its function. The calf muscles while they are elongating, slow then freeze forward shin motion. The forward inertia of the body keeps on coming as the weight

centered on the heel shifts to midfoot then to forefoot rollover. Keeping stiff at the ankle causes the heel to rise as that body keeps on coming. The heel rise pushes up on the forward body path (90 deg = tangential nudge from below) which keeps the trajectory above from dipping down. What did the heel do? Cushioned the landing. SACH – there it is. Cushion Heel, CH Inertia extends the swinging lower leg (no knee extensors here). The hip extensor/knee flexor hamstrings elongate as they tense to slow the extension of the knee &flexion of the hip. That thigh/foot/shin deceleration kinetic energy gets transferred by the hamstring transmitting that tug to the pelvis. So the hamstring is using hip extension during flexion and also using knee

flexion during extension. This is like billiards. Things deflect the energy and seldom add to it (iliopsoas only in hip flexion does that). Concentric muscle action costs the most energy. Cross bow fires. Eccentri c muscle action (being externally elongated while active) gets a free setting of the muscle to max. Setting cross bow to fire later. Isometric is between the other two in energy using some energy to not elongate by external pull.

The lengths of the limb segments create varied wheel sizes that together can solve center of mass trajectory to ground variations. Gears all of one size only allow one outcome. Varied sizes are required to solve change. Hmm. What sizes require the fewest gears to handle the common issues? And can we not compromise speed as there are nasty beasts out there with big teeth. Cocontraction sets up large wheels with isometric properties in the components.

Immediately, the Fibonacci series came to mind. It is all over the place and artists have been using it with 1:1.618 calipers since medieval times. It's close, but not quite … wait lengths??? No. ? Periods?

Centers of mass of each segment matter. The metronome rod length does not change when you move the weight up & down, but the period changes with the position of the sliding weight. The speed varies with the distance to center of mass, not the bar length. Interesting. The CoM lengths to pivot point, plotted are indeed even closer to the 1.618 ratio. The amplitude (wheel radius) & period (wheel revolution speed) have a Fibonacci progression. What is it about THAT ratio that is so compelling to nature? Two things (related). It is probably THE most reenter ant ratio. That is, when you scale up the thing it can self fit with the least shortage or extra waste than other ratios. Whatever rule or calculation or mechanism you used to operate the first set will work to run the second … & third & so on. Things generated tend to not tax the part that generated them. A computer model using Fibonacci weight distributions (aside from segment lengths) comes pretty close to actual human curve plots. Cool. But clinically, do we only see Fibonacci combinations to solve functional problems? NO! Beware of cute relationships. Fibonacci legs may look nice but not when half eaten by wolves. Energy conservation is a great general skill, but running very fast, able to jump a crevasse may be more likely to allow you to procreate your winning style. Nature does not put all our eggs in one basket. We won’t cover it, but walking in deep water has its own features. The very savvy therapists use that to get movement coordination otherwise hard to elicit or convey verbally. Speed runners hyper-flex the knee (heel on buttock). Why? It shortens the pendulum to assist a faster hip flexion delaying knee extension to the last moment. So much more. But, no. Time to move on.

What if that neat and wildly efficient pattern generating mechanism is goober-ed? Inman's prosthetic oriented studies did not study gait in neurologically impaired cases. Also the ground stresses (think stump ouch) were very important. The swing mechanics did not pursue so many things we see in neurologically altered gait. Simple question: What do people do when they can't do the thing they normally do? Easy answer: Something else. Like what?

Whatever gets it done. These SOLUTIONS to the energy impasses are described as ABNORMALITIES . Nooooooooooooooooooooooooo. Yup. Outside normal range graphs need a chisel. And blame bone lengths – lever arms – they show on x-rays and levers come in types. Ooooooooooooooo. No joke. There are people still quoting this nonsense and going after lever arms with monstrous bone cutting and rotating to eliminate the solutions that kids have found around their muscle drag impediments.

The girl above is walking with zero knee flexion/extension in stance phase. She is also toe walking . There is obvious medial rotation crouch (upper right insert image).