The Values For The Magnitudes For The Forces And Loads Needed To Increase Epiphyseal Cartilages Thickness And Human Femur Bone Without Fracture (Important)

While we are usually talking about how it would be possible to distract and pull apart the extremely strong bone tissue for our height increase desires, it might be useful to first see how much of a weight would be required to pull the cartilage of a real growth plate apart.

Let’s see what some other PubMed studies have shown about at least distracting the cartilage in the growth plate for limb lengthening. It would seem that bones are considered brittle materials. For cartilage, they may not be that brittle, but they are also very strong. This means that there is probably a very small range of loading magnitude which will do the plastic deformation before the cartilage of the epiphyseal growth plate develops fractures.

Breaking force of the rabbit growth plate and its application to epiphyseal distraction.

Acta Orthop Scand. 1982 Feb;53(1):13-6.
Breaking force of the rabbit growth plate and its application to epiphyseal distraction.
Noble J, Diamond R, Stirrat CR, Sledge CB.
Abstract

The in vitro breaking forces of the distal femoral growth plates of young rabbits were measured as a background to the design of a bone lengthening method, using epiphyseal distraction. The mean breaking force in 16 femora was 12.98 +/- 3.48 kg and the mean strain was 0.91 +/- 0.33 mm. The mean stress in 10 femora was 14.51 +/- 3.88 kg/cm2. The procedure was repeated, after applying a 1.0 kg dead weight to 6 femora for 24 hours and the breaking force was then 15.01 +/- 4.70 kg, with a mean strain of 0.85 +/- 0.62 mm. A further 8 rabbits then underwent epiphyseal distraction for 2 days in vivo, with 1 or 2 kg forces delivered to two parallel K wires by a pair of spring devices, whereupon the femora were removed and tested as before. The breaking force on the distracted side was now only 8.91 +/- 3.71 kg, compared with 13.99 +/- 3.40 kg on the control side. Although not fractured, these plates had obviously been weakened. The clinical implication of this is discussed.

PMID: 7064671

Clin Orthop Relat Res. 1978 Oct;(136):111-9.
Sledge CB, Noble J.
Abstract

Kirshner wires were placed either side of the right distal femoral epiphysis and a constant tension device applied a distracting force across the plate in rabbits. Growth increase was measured between the wires and found to be about 150% greater than the concurrent normal growth between 2 control (undistracted) wires on the left; such growth increase can occur in the absence of fracturing. The forces required to do this were between 1/5 and 1/10 of those shown to cause fracturing in vitro. The growth increase was shown to be associated with hyperplasia and hypertrophy of the plate, as well as an increased rate of cell division and sulfated polysaccharide synthesis. This was in turn shown to be associated with an increase in new bone formation.

PMID: 729274

Clin Orthop Relat Res. 1990 Jan;(250):61-72.
Kenwright J, Spriggins AJ, Cunningham JL.
Source

Nuffield Orthopaedic Centre, Oxford, England.

Abstract

Axial force applied during epiphyseal distraction has been measured close to skeletal maturity in patients having leg lengthening, in a rabbit model, and in vitro from an amputation specimen. In the patient study, both slow distraction rates and low constant distraction loads were applied. For all the distraction regimens, it was not possible to lengthen the limb significantly without evidence of fracture as demonstrated by a sudden decrease in distraction force. Growth plate failure was observed from 600 to 800 N, these levels being lower than those recorded from the in vitro tests. In the animal study, three distraction regimens (0.13, 0.26, and 0.53 mm/day) were applied across the upper tibial growth plate of New Zealand white rabbits close to skeletal maturity. Distraction was applied and force measured using a strain-gauge dual-frame external fixator. The force-time results revealed two distinct patterns. One pattern, in which the forces rapidly increased to maximum values of approximately 25 N and then suddenly decreased, indicated fracture of the growth plate, which was confirmed histologically. In the other pattern, forces increased steadily throughout distraction, reaching maximum values at the end of distraction of approximately 16 N. Histologic observations indicated hyperplasia of the growth plate without fracture, however, only a small increase in limb length was detectable. Hence, if a significant increase in leg length is required close to skeletal maturity, then fracture of the growth plate must occur.

PMID: 2293946

Analysis & Interpretation

I have looked over my old post “Long Bone Tensile Strength, Loading Capacity, Compression Strength” and looked over the values which I had found back then. It seems that the values found for the bones were from a doctor from many decades ago taking the leg bones of already slaughtered cows and doing the tensile testing on them.

What we can gain in information from the old post is that the tensile strength in bones seem to be from collagenous fibers. However the collagenous fibers are more elastic than say the mineral calcium derived compressive strength. I note that one of the most basic elements that form the extracellular matrix of cartilage is Collagen Type 2. The stuff that is supposedly giving human long bones their strength in the tensile fashion is the exact same material as the element that makes up the majority of the cartilage in the growth plates.

Does this means that if we figure out what is the tensile loading capacity of the growth plate cartilage, we will be able to figure out the real tensile strength of human bone?

So cartilage might have around the same level of tensile strength as bones, but we have not ever really been able to figure out just how much of the overall material’s intrinsice resistance to the strain induced by tensile loading can be contributed to the calcium minerals.

So what does the results say from the abstract of these 3 PubMed studies?

From study #1, the testing was done on rabbit growth plate cartilage, is the results are not that easily translated into human growth plate cartilage values much less human bone tissue deformation values. The distal femoral growth plates were tested. The average magnitude of the force where the growth plate would “break” (whatever that means) was around 13 plus or minus 3.5 KG. The average real difference seen in the growth plate was around 0.90 plus or minus 0.33 mm. The average stress was around 14.50 plus or minus 3.90 kg. If the same growth plates had just 1 kg of a load was added on them for 24 hours, the average breaking force increased to 15 plus or minus 4.7 kgs. However after just the smallest epiphyseal distraction, the average force load needed dropped to 8.90 plus or minus 3.70 kg compared to the concurrent controlled growth plates which averaged around 14.0 plus or minus 3.4 kgs. For this study, the researchers didn’t see any type of fracturing but the growth plates were definitely weakened by just the smallest of distraction on the growth plate.

From study #2, two kirshner wires wrapped around the growth plate of the rabbits were pulled in opposite directions to simulate a tensile force in the axial direction. The tension force was constant and increased at a steady linear rate. The result is that the growth of the growth plates did increase by 150% which means that the growth plates increased in the thickness or rate of longitudinal increase by 2.5 X of the normal rates. It seems that the value of the tensile loading/ tension forces needed to push the growth rates up to this level is 10-20% of the amount of force needed to cause fracturing if the femur of the rabbits was instead removed from the rabbits body and done in vitro. The cause of the increase is determined to be from hyperplasia and hypertrophy

It seems that study #3 is the one that really reveals to us just how feasible is the idea of even trying out cartilage distraction would be for our endeavor let alone bone distraction. The results are not good. when the distraction forces are applied on just the cartilage when the rabbit or human reaches close to skeletal maturity shows that “…it was not possible to lengthen the limb significantly without evidence of fracture as demonstrated by a sudden decrease in distraction force”

The fact is that when we get close to the point where we loss the cartilage completely, it seems that any type of plastic deformation of even the cartilage seems to disappear, possibly due to the fact that the growth plate thickness becomes too small due to thinning and the creeping nature of the calcification layer moving upwards. The point where the distraction drops dramatically aka the point where fractures show up is around the 600-800 Newtons mark. This converts to around 135-180 lbs in american units. It seems that this is done in the body of the rabbit. However if the femur is taken out and have the tension testing done in vitro, the value of the breaking point is decrease. This is significant since most height increase seekers wish for something non-invasive. We would have to be able to stretch out the bones in vivo. With the cartilage testing from this study, it seems to suggest that cartilage stretching in vivo have higher values.

However there is some good results which suggest that the values we need to get distraction may not be that high. If we increase the loading magnitude at a much faster rate at just the 25 Newtons point, the growth plate cartilage will distract meaning that fractures will occur. The other option is to increase the load at a slower rate, but the results show that the cartilage had very little lengthening although there was no fractures in the cartilage, being only up to 16 Newtons.

The conclusion made by the researcher I feel is most revealing in that they state “Hence, if a significant increase in leg length is required close to skeletal maturity, then fracture of the growth plate must occur.”

Implications For Height Increase:

The biggest considerations we have to make about the results in the study and the ability to translate the results for human height increase applications are…

  • The studies were most performed on small laboratory rabbits, specifically New Zealand white rabbits.
  • In addition, the rabbits were also young, indicating that they might have had much more cartilage than one who was closer to bone maturity. We as human are not that young, and most of us don’t have growth plates anymore. 
  • The studies were done to see what are the values when the cartilage will distract and/or fracture, not for bones. This means that we have to account for the difference in different tissue types, and that may not be possible to do accurately without some serious “guesstimation”

The values were are finding are 13-15 KGs, 600-800 Newtons, and 25 Newtons if there is a sudden jerking motion done. So for what situations do these load values work in?

  • 13-15 kgs – To to induce cartilage fracture or distraction for young new zealand lab rabbits
  • 600-800 Newtons (135-180 lbs) – To induce fracture in the cartilage of old or adult new zealand lab rabbits that are about to reach full bone maturity.
  • 25 Newtons (5.6  lbs ) – To induce fracture in the cartilage of old or adult new zealand lab rabbits that are about to reach bone maturity through a very fast, quick increase in the tensile force loading aka a sudden jerk or “tug” on the long bone cartilage area. 

This shows that even for rabbits who are young with a lot of cartilage in their growth plate, the needed amount of load to get growth plate increased growth has to be as high as 30-35 lbs of force. For the ages rabbits who still have a little bit of cartilage left, the value increases to 135-180 lbs, and the researchers say that plastic deformation is not possible, but fractures has to occur.

Now, let’s remember that we are talking about RABBITS, NOT HUMANS. The human bone is at least around 10 times wider which means that the overall cross-sectional area of human long bones, minus the cavity from the intermedullary cavity, is around 50-100 more in area.

In addition, we are talking about rabbits with cartilage, and we want to translate these values to humans without cartilage!!

So let’s try to do a level by magnitude calculation.

  • Young rabbits with a lot of cartilage: 35 lbs
  • Older rabbits with very little cartilage and close to full cartilage ossification: 180 lbs

I had stated earlier from older posts that the main reason that human bones have their compressive strength is due to the calcium mineralization in the bone matrix and that the tensile strength is from the collagenous material.

So if the calcium minerals were removed from the huma bone, would the “bone” still have the same value of tensile strength? I mean, it is said that the tensile strength is from collagenous tissue.

I guess is that it would not.

Cartilage is also made from the same collageneous material.

I would guess that while the calcium minerals are not as dominant in being the real contributors to the bone strength in the tensile direction as the compressive direction, they still make up around a large percentage of the bone’s tensile strength. I would guess the calcium is 60-80% of the cause for high tensile strength too.

So we have to multiple the value of 180 lb by 5X. to get 900 lb. I really do think that it requires 900 lbs of force to cause fracture in the long bone of rabbits without cartilage. 

I am guessing the human femur bone is usually around 3 cms wide. The rabbit femur I would guess is maybe half a cm wide, 0.5 cms.

If we did an area difference between human femur and rabbit femur calculationg, assuming that the cavity in the middle of the femur is around 1/3rd the length.

  • For Rabbits: so 0.5 cm = 5 mm so radius 2.5 mm –> remove the 1/3rd in the middle of the femur to get a value of Area= 2.5^2*pi – 0.83^2*pi = 6.24*pi mm^2
  • For Adult Human Male: I assume diameter of human femur at 3 cm in thickness. 3 cm is 30 mm so radius is half, at 15 mm –>remove the 1/3rd in the middle of the femur to get a value of Area = 15^2*pi – 5^2*pi = 200*pi mm^2 

If I am to assume that my guess that 900 lb of force is needed to distract an adult rabbit’s femur bone to induce any type of elongation, whether through fracture or plastic deformation, then I have to somehow be able to extrapolate that already guessed value to a value for humans that is even further from hard data.

Calculation Style #1: Value for needed tensile force to elongate or “stretch” an adult human male’s femur bone 

Since the human bone is 6 times as wide as a rabbits bone, 3 cm in comparison to just 0.5 cms, the needed tensile load would be 36 times as much, since to calculate area, we have to square everything, and that would have to be applied to tensile force loading on bone. Sot the value for calculation style #1 is 36*900 = 32400 lbs of force needed.

Calculation Style #2: Value for needed tensile force to elongate or “stretch” an adult human male’s femur bone 

If we instead assume that strength is determined in terms of discrete quantities of area of bone, then he relative difference aka ratio of the human bone area to the rabbit bone area is the multiplicative factor we need. The values are human/rabbits = 200/6.24 = 32

So the value needed from Calculation Style #2 for adult human femur bones is 32*900 = 28800 lbs of force needed.

Previously, I had stated that the values of the breaking point of the human long bone was around 120-150 MPa which was found from Wikipedia and some very old studies done in the 19th century by amateur medical researchers. 150 MPA is around 21750 psi. Psi is pound per square inch. If we then multiple the area of the average adult male human femur bone, at around 3 cms thick, we get  

in terms of calculations, when the 3 cms is converted to inches, and then the area of the cortical bone is calculated, it is…

((1.18110236/2)^2-(1.18110236/6)^2)*pi = 0.9739 inches^2 = so the adult bone for tensile strength needs around 21750 pounds of tensile force to pull the bone apart. 

Conclusion: 

From the values found on a study looking at the breaking point of cartilage in lab rabbit legs, we reach 3 different values for how much tensile force would be needed to cause the bone lengthening in adult humans, 32000 lbs, 29,000 lbs, and 21,000 lbs, but all of them showing that the human bone can withstand more than an 2 – 5 elephants standing on a scale pulling the human bone apart.

It would seem that there is no hope in hell that height increase seekers would ever be able to even find a machine that can create that much tensile force.

However that might be something that I did not include from the results of the 3 studies. The fact is that when the cartilage of the rabbit experienced really fast increases in tensile load aka a “strong tug or pull”, the break point of the cartilage was just 25 Newtons, which is much smaller than the 600-800 Newtons needed if the tensile force was increased gradually. The ratio of 800/25 is 32.

If could be that if we took the value of the lowest value we have found or calculated, at 21,000 lbs and divided it by 32, it suggest that with just around 660 lb of tensile loading, maybe the human femur bone might be able to deform and elongate if we gave the bone a really strong, and really fast jerk or tug.

As an after thought to this post, I am not against the idea of pulling bone longitudinally for plastic deformation it since the idea can not be completely disapproved yet. If anyone can give me a single study or article which shows that bone itself can deform in the longitudinal direction, I would look into it further.

4 thoughts on “The Values For The Magnitudes For The Forces And Loads Needed To Increase Epiphyseal Cartilages Thickness And Human Femur Bone Without Fracture (Important)

  1. Pingback: The Concept Of Youngs Modulus, Stress, And Strain Explained For The Application Of Bone Tensile Loading Or Bone Stretching (Important) | Natural Height Growth

  2. Pingback: A Method To Distract Bone Slowly Using Magnetic Fields, Metal Implants, And Acidic Solution | Natural Height Growth

  3. Hans Feng

    I think you should take alternating stress into consideration, which may damage things far under the yield stress of a material, and what you mentioned before is clearly constant force. Just some advice!

    Reply

Leave a Reply

Your email address will not be published. Required fields are marked *