BME/ME 456 Biomechanics
Mechanically Mediated Bone Adaptation
I. Overview
As we saw in the section on bone structure function, bone mechanical properties depend significantly on bone tissue structure. We also outlined a feedback loop as to how bone structure and subsequent properties "filter" mechanical load to bone cells which could then act on the information to alter bone structure. This diagram is repeated below:
In this section, we describe theories about how cells can sense mechanical stimulus and how cells respond to different levels of mechanical stimulus. We will take a historical view of theories about mechanically mediated bone adaptation.
II. Review of Physiologic Adaptation Processes
We quickly review physiologic adaptation processes. It is important to keep these adaptation processes in mind when examining mechanically mediated bone adaptation theories. The three major methods of bone adaptation are given below:
1. Osteogenesis
a.
Bone formed on soft tissue
b. Occurs
during embryonic development, early stages of growth, and during healing
c. Two
major subclassifications: intramembranous ossification and endochondral ossification
d. Intramembranous:
bone formed on soft fibrous tissue
e. Endochondral:
bone formed on cartilage
f. Osteoblasts
derived from mesenchymal cells act indepdendent of osteoclasts
g. Potential
to create large amounts of bone
2. Modeling
a.
Bone formed on existing bone tissue
b. Occurs
during growth, and during healing
c. Osteoblasts
and osteoclasts act independently at different sites
d. Potential
to create or resorb large amounts of bone
3. Remodeling
a.
Bone both resorbed and formed at the same site
b. Occurs
from growth through death.
c. The
only normal physiologic mechanism for chaning bone in adult skeleton
d. At
best leads to maintenance of bone; however as we age leads to net loss of bone
III. Mechanically Mediated Bone Adaptation Theories (1865 - 1920)
Theories of how mechanical stimulus affected bone adaptation begin in earnest about the time the American Civil War was ending. In 1867, a German anatomist Von Meyer received a grant from the Prussian government to study skeletal posture. As part of this grant, Von Meyer studied trabecular orientation in the proximal femur. While presenting these results at a scientific meeting, a Swiss engineer named Culmann noticed that Von Meyer's trabecular drawings bore a striking resemblance to principal stress lines Culmann had determined for a crane. The trabecular drawings and crane principal stress lines are shown below:
Upon conferring (an example of the interdisciplinary nature of biomedical engineering in the 1800's!), they postulated what became know as the trajectorial theory of trabecular bone structure. Details are outlined below:
Von Meyer publishes drawing of trabecular structure, 1867
Culmann notes similarities to principal stress lines in curved crane
Culmann & Von Meyer postulated trajectorial theory of trabecular bone: Trabeculae
are oriented along principal
Note at this point no attempt is made to state that the creation of trabecular structure is influenced by mechanical stimulus, only that trabecular structure seems to coincide with principal stress directions.
A contemporary of Von Meyer and Culmann, Julius Wolff a German anatomist, took there theory one step farther. Wolff postulated not only that trabeculae were aligned with principal stress directions, but that the orientation of trabeculae could change if there was a change in mechanical stress directions. This became the first indication that bone structure could respond to alterations in stress. Wolff based his theories on the evidence of trabecular structure post-fracture as shown below:
You can see that it looks as though trabecular patterns have changed in response to what must be altred loading. Wolff also suggested that bone adapted optimally to changes in stress, seeking to minimize mass to carry load. This ties the idea of optimization to bone adaptation, a theme that continues to this day. The observations of Wolff can be summarized:
Wolff was a German Anatomist who is credited with general theory of bone
adaptation known as Wolff's Law: 1870-1894
Suggested that bone obtained maximum mechanical efficiency with minimum mass
-> optimal
Bone structure could adapt in response to changing Mechanical Environment
Based on these ideas, Wolff generated the famous postulate that is named after him as Wolff's law:
"Every change in the form and the function of a bone or of their function alone is followed by certain definite changes in their internal architecture, and equally definite secondary alterations in their external confirmation, in accordance with mathematical laws"
At this point, we now have ideas that bone trabeculae are aligned along principal stress directions and that bone is adapted according to alterations of stress. However, we do not have any tie in as to the mechanism of how bone is adapted with respect to mechanical stimulus. This idea was postulated by Wilhem Roux, a German surgeon, who suggested that cells within the bone could sense and respond to mechanical stress at their level. This is really the basis of modern theories of adaptation. Roux's ideas are summarized below:
Roux, a German surgeon, suggests in 1881 that cell activity is modulated
by mechanical stress
Apposition and resorption by cells determines change in bone structure
Cell based apposition and resorption regulated by value of local stress
Finally in this period of study, an American anatomist at Johns Hopkins University named Koch performs a stress analysis of the proximal femur and compares shear stress to density and trabecular directions with principal stress directions. He confirms Wolff's findings and further notes that bone density is highest in areas of highest shear stress. This work also builds evidence that bone is an optimal structure. A summary of Koch's findings:
Koch, American Anatomist Johns Hopkins 1917, performed strength of materials
analysis for proximal femur
Confirms trajectorial theory, trabeculae along principal stress
Suggests that bone density should be highest in areas of highest shear stress
Again suggests bone attains maximum strength with minimum material
Thus, at the end of 1920, we have theories in place that are the foundation of modern bone adaptation theories. These include the idea that trabeculae are aligned along principal stress directions, bone density is highest in areas of highest shear stress, bone adapts to mechanical loads placed upon it in an optimal manner and bone cells within the bone matrix can respond to local stress and adapt tissue correspondingly. The last point is important because it is still the basis of many current research projects. The important points are:
Trabecular orientation aligned with principal stresses
Density highest in areas of highest shear stress
Bone structure can be adapted to change in load
Bone cells may be regulated by local stress
Results show no direct relation of stress to cell activity; Relationship of
bone structure to mechanics derived without regard to physiological mechanisms
III. Bone Adaptation 1920-1970: General Relationships of Mechanics to Bone Physiology
Up through the 1930's, we have much theory and observational evidence about mechanically mediated bone adaptation, but no direct experimental evidence to support these theories. The first such evidence was generated by Glucksman working in the Strangeways laboratories at Cambridge in the late 1930's and early 1940's. Glucksman developed organ cultures of chick emybro limbs and arranged them so that when they grew they were constrained and developed bending loads. He notes that areas in which he thought high tensile loads were applied corresponded to areas of increased ossification. A summary of Glucksman's results:
A. Glucksman, performed experiments on tissue undergoing intramembranous
ossification in vitro, Cambridge, 1938-1941
Arranged ossifying tissues so that as they grew different amounts of tensile
stress developed
Tensile stresses promoted increased ossification of fibrous tissue
Histological structure of ossifying tissue aligned along principal tensile
stresses
At this point, although we now have experimental evidence that altered stresses can affect tissue generation, we lack knowledge in two areas: 1) we don't know the physiologic mechanisms by which bone structure is altered 2) we don't have a good way to quantify the alteration in mechanical stresses.
Major advances in the first area, physiologic mechanisms of bone adaptation, did not come until the 1960's when an orthopaedic surgeon at Henry Ford Hospital in Detroit Michigan, Harold Frost, investigated physiologic mechanisms by which bone structure is altered. He basically layed the foundation for our current understanding of physiologic adaptation mechanisms. It was Frost who first theorized differences between remodeling and modeling (resisted at first, but widely accepted today) and also who theorized that the adolescent skeleton could adapt differently to mechanical stimuli than the adult skeleton. Frosts contributions:
Determined in 1966 that bone could be adapted by either modeling or remodeling
mechanisms
Determined that osteoblast and osteoclast activity were coupled during remodeling,
no net gain of bone
Suggested that the relationship between strains and bone mass was different
in growing (modeling) and mature (remodeling)
Thus, at the end of the 1970's we have some experimental evidence that alterations in mechanical stress and strain can also cellular generation of bone tissue structure. We also have evidence that bone structure may be altered by a few different mechanisms, that could tightly goven the amount of bone tissue structure that may be altered. The next decade saw a flurry of experimental work that enhanced our understanding of bone adaptation.
IV. Bone Adapation: 1970 - 1984 Experimental Study of Mechanically Mediated Bone Adaptation
One of the earliest studies of mechanically mediated bone adaptation in a living systems was published by Chamay and Tschantz in 1972. They found the following:
Chamay and Tschantz (1972) performed osteotomy of radius in dogs.
At 9 weeks, significant hypertrophy with 60% to 100% increase in cortical
thickness
Noted several cases of fatigue fracture
Carter estimated strains were between 5000 and 7000 mstrain; suggested hypertrophy
due to damage
Thus, although Chamay and Tschantz found significant bone adaptation, there is evidence that the loads they generated by the osteotomy were pathologic, that is much higher than normal skeletal loads.
The next key experiment in this area was performed by Dennis Carter when he was at the Mass General hospital in Boston. Carter basically performed the inverse experiment of Chamay and Tschantz. He osteomized the ulna in the canine instead of the radius. In addition, Carter performed more rigorous quantification of both the altered mechanics and the bone adaptation. He strain gauged the remaining radius to measure cortical surface strains. He also used tetracycline labeling to quantify the rate of mineralization. What Carter found was quite interesting. Despite a doubling of strains, from 600 to 1500 microstrain, he noticed NO significant alteration of bone structure. This lead Carter to postulate the existence of a "lazy" zone for bone adaptation. Basically a range of strains in the adult skeleton for which no significant adaptation occured. A summary of Carters results:
Carter and co-workers performed osteotomy of ulna in Canines (1981)
Measured strains in control and experimental limbs cortex with strain gauge
Found strain increased from 600 mstrain to 1500 mstrain after osteotomy
No significant change in bone geometry or deposition of mineral after 8 weeks
A series of pioneering works by Clint Rubin and Lance Lanyon led to similar conclusions as those of Carter. Rubin and Lanyon strain gauged the cortical surfaces of many species of animals. Despite the differences in species and bone, they found a remarkably narrow range of peak strains under various activities, basically from 2000 to 3000 microstrain. Their results indicated that adult bone seem to exist within a homeostatic range of strains, perhaps Carter's lazy zone. Their results:
Rubin and Lanyon (1982) compiled strains measured on the cortex of different
animals during normal activity
Bone Activity Principal Strain (mstrain)
Horse radius Trotting -2800 (-.28%)
Dog radius Trotting -2400
Goose humerus Flying -2800
Sheep femur Trotting -2200
Pig radius Trotting -2400
Fish hypural Swimming -3000
Monkey mandible Biting -2200
Rubin and Lanyon also performed a series of experiments in turkey ulna in which they surgically isolated the turkey ulna and applied controlled bending loads. In this case, the could control not only the strain magnitude on the bone, but also the number of cycles of load to which they bone was subjected. What they found was that as few as 4 cycles of load per day were enough to maintain bone, and that above 1800 cycles of load per day did not stimulate significantly altered bone adaptation. A summary of the turkey ulna results:
Rubin and Lanyon (1984) also performed a procedure to isolate the turkey
ulna and impose controlled dynamic bending strains on the isolated ulna
Found that dynamic strains are necessary to maintain bone; Static load led
to bone resorption
4 cycles of load per day was sufficient to maintain bone; 36 to 1800 cycles
per day produced no response
Finally at this point Frost weighed in with his treatise the Intermediary Organization of the Skeleton. He postulated a different adaptational response for adolescent and adult skeleton. Basically he said that the adolescent skeleton was much more sensitive to mechanical stimulus because it had mechanisms of modeling and remodeling. Since the adult skeleton could only remodel, its bone structure was much less senstive to mechanical stimulus. Strains above 4000 to 5000 microstrain Frost believed would cause damage in any skeleton and lead to a pathologic adaptation response involving both modeling and remodeling. A graph depicting his ideas (very similar to Carter's idea of a lazy zone) are shown below:
Thus, by almost the mid 1980's there has been significant refinement on theories of mechanically mediated bone adaptation. For one, we know that the type of adaptation mechanisms present basically constrains the type of bone adaptation we see in response to mechanical stimulus. Second, we see that in adult bone there is a range of homeostatic strains in which bone likes to exist. Frost believes that one reason that bone mass is lost is that the process of aging or disease resets the setpoints of strain sensitivity that bone cells possess. In other words, if a normal bone cell sees 2000 microstrain has a strain to maintiain bone, a cell in a disease process may see this strain as too low to maintain bone structure and thus lead to a loss of bone structure. While a number of experiments have progressed to this day, their results are further clouded by the fact that to control loads in the skeleton, we must typically surgically alter the skeleton. This in itself will alter the adaptational response, giving a mix of osteogenesis, modeling and remodeling. Hollister et al. (1996) found that this wound healing response due to surgical intervention may be much stronger than the affect of mechanical stimulus.
V. Theories of Bone Adaptation (1985 to present): Numerical Simulations
Another approach to the study of mechanically mediated bone adaptation is the use of computational simulations. If you recall Wolff's law, he postulated that we could write a mathematical formula that could relate changes in bone structure to changes in mechanical stimulus. We can write this law generically as:
In other words, the change in bone structure should be some function of the change in mechanical stimulus and the underlying physiologic mechanisms. Beginning in the mid-1970's, mathematical theories of bone adaptation were developed to predict changes in bone shape and density based on strain, stress or strain energy density. These are based on the generic equations above, but generally derive a time rate of change of some measure of bone structure to a stress or strain state. These algorithms have achieved some success in predicting normal bone architecture. However, as with experiments they do not give us the complete story. We review the concepts next.
One of the first fundamental theories of bone remodeling was proposed by Cowin in 1976. This theory was based on general continuum mechanics principles. The computational implementation of the theory using finite element modeling was done by Hart and colleagues in 1983. The basic equation underlying the theory is:
where e is a measure of bone structure (typically bone density), a, Aij, and Bijkl are remodeling tensors that must be determined experimentally, and eij is the strain. Note that the remodeling tensors depend on the current bone structure. It is also theoretically possible that the remodeling tensors could incorporate the state of the skeleton, ie whether modeling or remodeling was possible. To predict changes in bone structure using adaptation simulations, we must incorporate equations we have already discussed, namely structure-function relationships and the elasticity equations. We must iterate among the three 1) remodeling equation to obtain structure from stress/strain, 2) structure function relationship to obtain stiffness from structure and 3) elasticity equations to solve for stress and strain based on stiffness. Using a specially written finite element code and the above equation, Hart reached the following conclusions:
Cowin proposed idea of adaptive elasticity 1976; Hart performed computational
implementation in 1983
Separates surface and external remodeling
Rate of Change of bone volume fraction related to strain
Tensors A,B must be determined by experiment
Constants difficult to determine; Qualitative results good, Rigorous validation
not done
A different approach to predict adaptation was proposed by Fyhrie in 1986. In this case, he postulated that bone was a self-optimizing material, adapting its orientation and density in response to its stress/strain state. The optimization statement posed by Fyhrie was:
where r is bone density, q
is bone orientation, s is bone stress and Q is a
measure of a remodeling goal for bone. By assuming a structure function relationship
of the form: 
,
Fyhrie was able to show the following relationship between bone density and
stress:
where F is a matrix of constants, r is bone density, Qmax is a measure of the bone remodeling goal, and B is the coeffient from the structure function relationship. Using the above relationships for different matrices F, Fyhrie was able to predict bone density distributions in the femoral head similar to observed distributions:
A third remodeling algorithm proposed by Huiskes et al., derived from Cowin's model, included the idea of a lazy or homeostatic zone. A graph of their structure strain energy relationship is shown below:
This graph is represented mathematically as:
The above equations mimic Frosts idea of adaptation in the adult skeleton. Above a certain level of strain or in this case strain energy density, we see an increase in bone mass, probably due to modeling from stress fractures. Below a certain threshold we see excessive remodeling of bone. In between these levels we see a maintainence of bone structure. To implement the above equation numerically, we use Euler forward differencing for the time derivative to obtain:
The above equations show that bone density is incrementally changed based on the current density, the current strain energy density, and a remodeling constant K. Again, the remodeling constant incorporates affects of physiology, disease state, etc on bone structural changes.
The ability to relate bone structural changes to stress state adds new mathematical descriptions to our feedback loop between mechanical loads, bone structure, and bone cells:
V. Summary
Here is our current state of knowledge in bone adaptation theory:
State of bone (growth,healing,mature) determines its ability to respond to
mechanical strain
Mature bone may seek to exist within limited strain range
Resulting structure (from growth) shows attributes of efficient or optimized
structure -> fully stressed/strained?
Computational models have the ability to predict qualitatively correct bone
structure distribution Bone cells can respond directly to mechanical strain
Here are areas for future work:
1. Strain measured on cortical surface or computed by single level solid continuum
models is not the same as that experienced by cells due to hierarchical bone
structure
2. Specific relationships between strain and adaptation for different states
of bone response have not been clearly delineated
3. Nature of loads on bone are difficult to determine, but are necessary to fully understand mechanics/adaptation