Increase your Stature with Plastic Deformation

 Recently, someone asked if it was possible to grow taller while running with ankle weights and natural height growth recently posted about tensile stress for height growth.  The goal for tensile stress for height growth is to induce enough stress in the bone to induce plastic deformation in the bone to make it longer. The point at which this occurs is the yield stress. Cortical bone is the limiting factor for this to occur.  Ultimate stress is the point where the bone breaks.  According to this engineering page, the ultimate stress for bone is 133MPa whereas the yield stress is 115MPa.  It would be hard to generate this kind of stress in the bone but it's possible that there may be some residual strain that occurs at the nanometer level.  Can we generate enough residual strain via tensile forces on the bone to eventually reach the plastic deformation range?  According to LOAD TRANSFER ACROSS THE PELVIC BONE DURING NORMAL WALKING, 20-67MPa stresses were generated in the hip bone during walking.  So it's conceivable that a tensile force of 115MPa could be generated by a physiological loading regime. I couldn't find how much tensile stress is generated by running.

Plastic deformation refers to residual strain whereas elastic strain refers to strain that has no residual strain.  So a potential treatment would involve using say a tensile strain mechanism to stretch the bone to such a degree that it retains some of the stretch after the load is removed.

Plastic deformation seems to take a high level of strain to occur.

Orientation dependence of progressive post-yield behavior of human cortical bone in compression.

"[We] determine the effect of loading direction on the evolution of post-yield behavior of bone using a progressive loading protocol. To do so, cylindrical compressive bone samples were prepared each in the longitudinal, circumferential and radial directions, from the mid-shaft of cadaveric femurs procured from eight middle-aged male donors (51.5 ± 3.3 years old). These specimens were tested in compression in a progressive loading scheme. The elastic modulus, yield stress, and energy dissipation were significantly greater in the longitudinal direction than in the transverse (circumferential and radial) directions. However, no significant differences were observed in the yield strain as well as in the successive plastic strain with respect to the increasing applied strain among the three orientations. The initiation and progression of plastic strain are independent of loading orientations, thus implying that the underlying mechanism of plastic behavior of bone in compression is similar in all the orientations."

Therefore we can see what loads are required in other orientations like compressive loading and use those some loads to induce tensile strain to such a degree as to induce plastic strain.

"the post-yield behavior of bone is associated with an exponential decay of elastic modulus (microdamage accumulation), linear plastic deformation, and an acute saturation of viscous behavior of the tissue"

Cooperation of length scales and orientations in the deformation of bovine bone.

"Combined wide angle X-ray diffraction and small angle X-ray scattering were used together with in situ tensile testing to investigate the deformation and failure mechanisms of bovine cortical bone at three material levels: (1) the atomic level, corresponding to the mineral crystal phase; (2) the nano level, corresponding to the collagen fibrils; (3) the macroscopic level.  Deformation was linear at all three levels up to a strain of 0.2% in the longitudinal tensile direction. At this critical strain a sudden 50% decrease in the fibrillar and mineral strains was observed.  The presence of partial local damage leads to inhomogeneous strain distributions within the probed gauge volume. This gives rise to diffraction peak broadening in the mineral phase, as well as strain relaxation at the nanoscale. Above the critical strain the longitudinally oriented strains below the nanoscale remained constant at a reduced level until failure. The lateral orientation of the nanostructures toughens the bone, while a higher material level dominated the subsequent deformation process, either by sliding between the lamellar layers or by the growth of microcracks. The bone has compressive residual stress in the crystal phase."

"At low stresses the bone behaves linear elastically with stiffness primarily coming from the mineral phase. Physiological loading generally falls in this elastic region. The mineral phase that provides rigidity is proposed to carry the load, while the soft matrix transfers the load to neighboring mineral crystals by shear. Yielding is known to be the start of damage, when strain reaches a critical level and starts initiating crack formation. In the post-yield region cortical bone experiences large plastic deformation while absorbing large amounts of energy prior to fracture"

"The post-yield deformation involves a combination of slippage at cement lines, which reduces strain energy and slows down crack propagation by deflecting the crack path, and discontinuity of microcracks, that greatly reduces the stress intensity at the crack tip. At the nanoscopic level, breaking of sacrificial bonds at the fibrillar level dissipates energy, while long mineral platelets delocalize the crack-tip deformation"<-maybe inducing other forms of slippage of cement lines will also permanently make the bone grow longer without the high levels of tensile strain required for plastic strain.

" Upon tensile loading the gap zones between the fibrils were stretched and the change in the dimensions of the gap zones is a measure of fibrillar strain."



"Fracture surface of the bone captured by an optical camera during tensile testing."<-So the stretching did induce microfractures in such a way as to kind of lengthen the bone.

How tough is bone? Application of elastic-plastic fracture mechanics to bone.

"bone contains a high volumetric percentage of organics and water that makes it behave nonlinearly before fracture. We applied elastic-plastic fracture mechanics to study bone's fracture toughness. The J integral, a parameter that estimates both the energies consumed in the elastic and plastic deformations, was used to quantify the total energy spent before bone fracture. Twenty cortical bone specimens were cut from the mid-diaphysis of bovine femurs. Ten of them were prepared to undergo transverse fracture and the other 10 were prepared to undergo longitudinal fracture. The specimens were prepared following the apparatus suggested in ASTM E1820 and tested in distilled water at 37 degrees C. The average J integral of the transverse-fractured specimens was found to be 6.6 kPa m, which is 187% greater than that of longitudinal-fractured specimens (2.3 kPa m). The energy spent in the plastic deformation of the longitudinal-fractured and transverse-fractured bovine specimens was found to be 3.6-4.1 times the energy spent in the elastic deformation. The toughness of bone estimated using the J integral is much greater than the toughness measured using the critical stress intensity factor."

"bone contains water that can affect the properties of collagen"

"60% of water was bonded to collagen [in dog bones]"

Mechanisms of short crack growth at constant stress in bone.

"Slow, stable crack growth occurred at a rate and angle which were dependent on the orientation of the sample: tests were conducted with the loading axis both parallel and perpendicular to the longitudinal axis of the bone. All cracks showed intermittent growth in which periods of relatively rapid propagation alternated with periods of temporary crack arrest or relatively slow growth. In some cases crack arrest could be clearly linked to microstructural features such as osteons or Volkmann's canals, which acted as barriers to crack growth. Crack-opening displacement increased over time during the arrest periods. The growth of small cracks in bone at constant stress, [involves] microstructural barriers, time-dependent deformation of material near the crack tip and strain-controlled propagation."

Progressive post-yield behavior of human cortical bone in shear.

" the shear modulus of bone decreased with respect to the applied strain, but the rate of degradation was about 50% less than those previously observed in compression and tension tests. In addition, a quasi-linear relationship between the plastic and applied strains was observed in shear mode, which is similar to those previously reported in tension and compression tests. However, the viscous responses of bone (i.e. relaxation time constants and stress magnitude) demonstrated slight differences in shear compared with those observed in tension and compression tests."

"After a preload of 10 N in compression, each specimen was loaded using the cyclic loading protocol. In each cycle, the specimens were loaded under the displacement control with a rate of 0.005 mm/s, held at the displacement level for 120 s, unloaded to 25 N, and held at the 25 N for 120 s. The dwelling time (120 s) was determined through pilot studies to ensure that the specimens reach to a quasi-equilibrium condition"

"The shear yield strain and yield stress of the bone specimens were 0.88 ± 0.18% and 35.7 ± 9.88 MPa, respectively"<-These were bones from 80 year olds though.

" the yield strain in shear observed in this study was about 0.88 ± 0.18% (N = 6), which is higher than those in compression (0.71 ± 0.07%, N = 8) and in tension (0.39 ± 0.03%, N = 8) "

Traumatic plastic deformation of the tibia: case report and literature review.

" a 10-year-old girl who, after falling down a slope, came to a sudden stop when her right foot hit a rock. This resulted in a fracture of the fibula and bowing of the tibia."

"Plastic deformation refers to the deformation of a bone, without fracture of its cortices, that persists once the deforming force has been removed. It has been reported most commonly in the forearm, with 58 of a review of 74 cases involving the forearm."

Mechanical and morphological aspects of experimental overload and fatigue in bone

"long bone fatigue is produced in 30 pairs of dog ulnas by applying opposing forces at both extremities thereby causing a strain. On a force-deformation curve the force axis indicates a zone of load, an intermediate zone of fatigue and a zone of overload; the deformation axis shows an elastic zone and a plastic zone"

"the plastic phase is short for dense cortical bone" 

Guided growth: recent advances in a deep-rooted concept.

"Guiding growth by harnessing the ability of growing bone to undergo plastic deformation is one of the oldest orthopaedic principles."

"Bracing for adolescent idiopathic scoliosis does not influence vertebral development."

Damage accumulation in vertebral trabecular bone depends on loading mode and direction.

"251 cylindrical samples (8×18-25mm) were obtained from 50 male and 54 female fresh frozen human vertebrae (T1-L3) of 65 (21-94) years. Vertebrae were randomly assigned to three groups cranial-caudal, anterior-posterior and latero-lateral. Specimens were mechanically loaded in compression, tension or torsion in five load steps at a strain rate of 0.2%/s. Three conditioning cycles were driven per load step. Stress-strain curves were reconstructed from the force-displacement or from the moment-twist angle curves. Damage accumulated from 0 to 86% in compression, from 0 to 76% in tension and from 0 to 86% in torsion through the five load steps. Residual strains accumulated from 0 to -0.008mm/mm in compression, 0 to 0.006mm/mm in tension and 0 to 0.026rad/rad in torsion. Significantly less damage but not residual strains accumulated in transverse directions."

Lots of alterations were made to the bone so that may have had effects on physiological loading properties.

"Cortical bone shows qualitatively similar damaging behaviour as trabecular bone"

"substantial damage occurs at the nanometer level "

"Cracks and diffuse damage that accumulate within trabeculae cause reductions in apparent modulus prior to failure of whole trabeculae"<-see above where the scientists stated that cortical bone has similar damaging properites as trabecular bone.


Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue

"Effective tissue modulus and yield strains were calibrated for cadaveric human femoral neck specimens taken from 11 donors, using a combination of apparent-level mechanical testing and specimen-specific, high-resolution, nonlinear finite element modeling. The trabecular tissue properties were then compared to measured elastic modulus and tensile yield strain of human femoral diaphyseal cortical bone specimens obtained from a similar cohort of 34 donors. Cortical tissue properties were obtained by statistically eliminating the effects of vascular porosity. Results indicated that mean elastic modulus was 10% lower (p<0.05) for the trabecular tissue (18.0±2.8 GPa) than for the cortical tissue (19.9±1.8 GPa){so it actually doesn't take that much more stress to induce plastic deformation in the cortical bone than in the trabecular bone(cortical bone is the limiting factor for lengthening)}, and the 0.2% offset tensile yield strain was 15% lower for the trabecular tissue (0.62±0.04% vs. 0.73±0.05%, p<0.001). The tensile–compressive yield strength asymmetry for the trabecular tissue, 0.62 on average, was similar to values reported in the literature for cortical bone. We conclude that while the elastic modulus and yield strains for trabecular tissue are just slightly lower than those of cortical tissue, because of the cumulative effect of these differences, tissue strength is about 25% greater for cortical bone."

The yield modulus is the point where looking for as that is when the bone deforms plastically.

0.2% offset yield stress (MPa) for cortical bone  107.9±12.3

Offset yield means that the extract stress needed is inexact.

107.9 MPa is equal to 107.9N/millimeter^2.  So the larger area over which the force is applied, the less force overall is generated.

Stress Fracture of a Radius Resulting in Malunion: A Case Report

"Stress fractures are the result of repetitive and abnormal stresses on bone and are commonly divided into two basic categories, those due to extrinsic factors that primarily involve the type and intensity of the physical activity and intrinsic factors that are related to the individual's age, weight, and medical conditions that weaken bone strength, such as osteoporosis and osteopenia. Common examples are an enlarged humerus seen in some professional baseball players and an enlarged radius seen in some competitive tennis players.  When stress loading is not gradual and exceeds the elastic range of the bone, plastic deformation occurs.{So by the existence of plastic deformation there must be an alternative to limb lengthening surgery} Stress fractures in the upper extremities are far less common and in two large series accounted for 2.8% to 7.6% of all stress fractures. In adults, they have been reported in the humerus, mainly in baseball pitchers, with 12 cases in one study of injuries in a men's over 30 baseball league. Solitary reports of humeral stress fractures have been reported in other sports as well, including tennis, body building, and weightlifting. Stress fractures also occur in the forearm, more commonly in the ulna than radius, and have been reported following a wide variety of sports activities, including fast-pitch softball, tennis, golf, bowling, and competitive ice-dancing. Most are localized to the diaphysis of the bone that has been shown to have the smallest diameter and the thinnest cortices on computed tomography and is the most vulnerable site for repetitive torque forces that rotation of the radius exerts on the relatively immobile ulna.20 Stress fractures of the radius are exceedingly rare and only six cases have been reported in the English language literature that were confirmed by magnetic resonance imaging (MRI) or radiographs. The first case reported in 1980 involved bilateral fractures in a 23-yearold British naval recruit whose training included "field gun running," that required him and his fellow recruits to straddle a 900-pound gun barrel across their forearms while running through a series of obstacles. The other two cases were unilateral fractures: a 15-year-old high school wrestler whose fracture in the middle third of the diaphysis was confirmed on MRI that showed periosteal bone reaction adjacent to a sclerotic fracture line and a 12-year-old boy who repetitively practiced "wheelies" in which he would lift the front wheel of his bicycle, ride on the rear wheel for a short distance, and then slam the front wheel down on the pavement with all his force. The mechanisms of injury in the other three cases were not from weightbearing activities but from repetitive muscle forces acting on the radius."

"When stress loading is not gradual and exceeds the elastic range of the bone, plastic deformation occurs. Rather than the bone having the opportunity to gradually remodel and hypertrophy, there is bone resorption that at a certain point results in microfractures. The microfractures generally progress to small cortical cracks in the bone and, if the physical activity continues at the same intensity and there is no medical intervention to splint the bone, the result is usually an obvious clinical fracture."

"In children who have not reached skeletal maturity, stresses are more likely to affect the epiphyseal growth plate of a particular bone than the bone itself."