of Journal Biomechanics 35 (2002) 401414
ESB Keynote LectureFDublin 2000
Why mechanobiology? A survey article
Marjolein C.H. van der Meulena,b, Rik Huiskesc,*
Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA Department of Biomedical Mechanics and Materials, The Hospital for Special Surgery, New York, NY 10021, USA c Department of Biomedical Engineering, Eindhoven University of Technology, Wh 4.131, PO Box 513, 5600 MB Eindhoven, Netherlands
b a
Accepted 5 September 2001
Abstract The central paradigm of skeletal mechanobiology is that mechanical forces modulate morphological and structural tness of the skeletal tissuesFbone, cartilage, ligament and tendon. Traditionally, skeletal biomechanics has focussed on how these tissues perform the structural and locomotory functions of the vertebrate skeleton. In mechanobiology the central question is how these same load-bearing tissues are produced, maintained and adapted by cells as an active response to biophysical stimuli in their environment. The idea that form follows function is not new, but we now believe that the scientic community has the knowledge and tools to prove, understand and use functional adaptation to benet medicine and human health. In this Survey Article the philosophy and progress of skeletal mechanobiology are discussed. The revival of this science, with roots dating back to the 19th Century, is now driven by new developments in cellular, molecular and computational technologies. These developments are still in an early stage of application, but if modern mechanobiology fullls the promises of its ambitions, the results will bring great benets to tissue engineering and to the treatment and prevention of skeletal conditions such as congenital deformities, osteoporosis, osteoarthritis and bone fractures. r 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Tissue dierentiation; Bone adaptation; Computer simulation; Tissue engineering; Bone diseases
1. Introduction Skeletal growth and development is an intricately choreographed process involving many cell and tissue types (Fig. 1). During growth in the embryo, the long bones initially form as mesenchymal condensations which chondrify to become cartilaginous anlagen. As development progresses, the cartilage cellsFchondrocytesFhypertrophy and their extracellular matrix mineralizes, forming the primary ossication center. The chondrocytes die by apoptosis and the mineralized cartilage is modeled to bone by the coordinated activity of bone forming cells, osteoblasts, and bone resorbing cells, osteoclasts. Osteoblasts that continue to produce extracellular matrix and become trapped within the matrix develop into mature bone cells, osteocytes. The cycle of chondrocyte hypertrophy, extracellular miner*Corresponding author. Tel.: [phone]; fax: [phone]. E-mail address: [e-mail] (R. Huiskes).
alization, chondrocyte apoptosis and bone modeling proceeds spatially from the mid-diaphysis towards the epiphyses. As the primary center progresses axially, in some bones a secondary center forms, which mineralizes through the same endochondral process. The growth plate is where the two growth fronts meet. Longitudinal growth at the growth plate occurs through chondrocyte division and hypertrophy, and continues until skeletal maturity. Concurrently, radial diaphyseal growth occurs through direct apposition of bone by osteoblasts on the periosteal surface and resorption by osteoclasts on the endosteal surface. In parallel with the formation of the mineralized skeleton, layers of cartilage at the joint surfaces develop into articular cartilage and brous anlagen develop into tendons and ligaments. Joints form at the interzones between the cartilage anlagen. The premise of mechanobiology is that these biological processes are regulated by signals to cells generated by mechanical loading, a concept dating back to Roux (1881). The relevant questions include how external and
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Development of bone
A
B
C Embryonic
D
E Postnatal
F
Fig. 1. Schematic illustration of the development of long bones from embryonic to mature (gures not to scale). (A) Cartilaginous anlage with chondrocytes; (B) Chondrocytes in the center swell; (C) Cartilage mineralization occurs around hypertrophic chondrocytes, proliferating attened cells develop; (D) Blood vessels penetrate the tissue, mineralized tissue is resorbed, bone formation takes place, and longitudinal growth commences; (E) Secondary ossication centers develop and growth plates remain in between; (F) The bone is mature, the growth plates are closed; courtesy of Dr. E. Tanck (2001).
muscle loads are transferred to the tissues, how the cells sense these loads, and how the signals are translated into the cascade of biochemical reactions to produce cell expression or dierentiation. Ultimately, we want to predict growth and dierentiation in quantitative terms, based on a given force exerted on a given tissue matrix populated by cells. While understanding the mechanobiology of bone development and growth can be relevant for the prevention and treatment of congenital deformities, there is also another motive for its study. The processes of bone development continue in the mature organism during bone regeneration in fracture healing and during skeletal adaptation to implants. These involve tissue dierentiation from granulation through brous connective tissue and cartilage to bone. The dierentiation pathway from granulation tissue to cartilage is a gradual process that can be inuenced over time. Mineralization, on the other hand, is a catastrophic event, occurring almost instantly and irreversibly. This event transforms the mechanical and morphological status of the tissue dramatically and completely, not a single chondrocyte remains afterwards. After ossication, bone dierentiation continues within the tissue. Osteoclasts and osteoblasts now build the characteristic microstructures of cortical or cancellous bone tissue. This process of structural modulation and growth is called modeling (Frost, 1987). Mechanics also modulates the bone modeling process, as evident from the trabecular patterns that line up with external forces, suggesting
an optimized structure of minimal weight and maximal strength (Wol, 1892). After the tissue has matured, bone is continually maintained by osteoclastic resorption and subsequent osteoblastic formation in a process called remodeling (Frost, 1987). One purpose of this process is the removal of microcracks and microdamage (Verborgt et al., 2000), hence the term maintenance. Osteoclasts are believed to be attracted by microcracks, through the apoptosis of osteocytes (Noble et al., 1997). At maturity, bone modeling continues due to variations in physical activity; exercise enhances bone mass, while inactivity reduces it. In the elderly osteoporosis can develop, the etiology of which is also thought to be aected by mechanobiology. And nally, the development of osteoarthritis in the elderly may be related to mechanical loading as well. To understand how a mechanical stimulus produces a biological signal for cells to dierentiate or adapt a tissue, we need to understand the relevant stimuli, the signal transduction pathways and the response processes (Duncan and Turner, 1995). Here, we described some experimental and analytical approaches to address these questions, with examples from work examining skeletal adaptation and dierentiation. As in many sciences, the integration of experimental and analytical models is critical to gaining an understanding of the skeletal response to mechanical factors. Experiments provide insights and measurements, which can then be interpreted within the context of analytical
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frameworks. Analytical simulations permit investigation of possible explanations that require in vivo validation and will suggest further experimental investigations. These investigations are greatly impacted by recent technological advances in imaging, computational mechanics, genetics and molecular biology. The integration of these techniques will provide many important insights into skeletal development and diseases.
2. Experimental mechanobiology Adaptation experiments examining skeletal mechanobiology have been performed for more than a century and have examined the inuence of both increasing and decreasing the habitual loads applied to the skeleton. Yet, despite the multitude of studies that have been completed, there are still many unanswered questions regarding the skeletal response to normal, perturbed and pathological mechanical loading. Some of the diculties arise from the design of experiments, others in the interpretation of data, and many from the inability to compare across dierent species, ages, bones, loading protocols, and so forth. Many of these issues arise from the inherent challenge of in vivo experiments. An introduction to in vivo bone mechanobiology experiments, what is known from these experiments and the open questions are presented below. Emphasis is placed on bone adaptation models due to the greater presence in the literature. However, analogous questions can be posed for skeletal tissue dierentiation and the adaptation of other musculoskeletal tissues in response to mechanical loading. Underlying this discussion is the fundamental goal of understanding skeletal mechanotransduction, which can be considered to consist of a mechanical signal, response pathway and cellular adaptive response. 2.1. Skeletal tissue dierentiation Fracture healing is a natural skeletal tissue dierentiation process. A well-dened temporal-spatial tissue generation and replacement pathway is present normally during secondary fracture healing. Three phases follow bone injury: an initial inammatory phase, a tissue formation phase and nally tissue remodeling. Biophysical stimuli are integral to the healing process. This can already be appreciated by comparing primary fracture healing to secondary healing. Primary healing is completely stable and forms bone directly (Einhorn, 1998). Secondary healing involves lower fragment stability and larger gap sizes and heals through successive tissue formation and replacement (Einhorn, 1998). Experiments have demonstrated a signicant role of mechanical forces in the process of secondary fracture healing. When compared to rigid xation, fractures
subjected to cyclic loading after initial healing demonstrate signicantly greater increases in stiness and produce larger calluses (Goodship and Kenwright, 1985). Cyclic compression produces stronger, but more compliant, healing fractures than static compression (Panjabi et al., 1979). Excessive strains inhibit the normal healing process, producing less bone tissue and more initial inammatory tissue (Augat et al., 1998). However, growth factors and other chemical stimuli likely play a more critical regulatory role than mechanical stimuli, confounding these purely mechanobiological models. Understanding the interaction between growth factor expression and mechanical stimuli may provide signicant insights into the healing process. Computer models and simulations can aid our understanding of these fracture experiments (Blenman ! et al., 1989; Bailon-Plaza and van der Meulen, 2001; Lacroix et al., 2000). Distraction osteogenesis is a similar process to fracture healing and can also be used to study tissue dierentiation (Carter et al., 1998; Tay et al., 1998). In vivo experiments have been used to examine both tissue dierentiation and adaptation to altered loading, with the majority of experiments examining tissue remodeling in response to mechanical stimuli. Skeletal tissue dierentiation experiments are complex to design; however, historically many natural examples have been cited (Pauwels, 1941; Wol, 1892). The most common experimental design is a device that isolates or controls the mechanical stimuli and then examines the tissues that form (Goodman et al., 1994; Guldberg et al., 1997a; Sballe et al., 1992; Tagil and Aspenberg, 1999). When empty chambers are implanted into skeletal sites, new tissue forms often in a process similar to fracture healing. Bone can be formed both through intramembranous formation (Guldberg et al., 1997a) and endochondral ossication (de Rooij et al., 2001). Often brous tissue forms within the chambers under particular loading protocols (Goodman et al., 1994). Once the process for a given model is established, cellular and tissue dierentiation can be examined in the absence of loading or with the application of controlled micromotion or loads in the device. These experiments demonstrated the sensitivity of dierentiating tissues to the mechanical stimuli in their environment. With loading, dierent tissues form (de Rooij et al., 2001) and the morphology of the tissues also diers (Guldberg et al., 1997a). While the intent is a simple loading situation, this is dicult to realize in these in vivo devices due to complex boundary conditions, tissue interfaces and nonlinear behavior of the tissues, in addition to the continually evolving nature of these conditions. Again, mechanical-hypothesis-based theories can help explain and interpret these tissue dierentiation models, as discussed below (Yuan et al., 2000; Prendergast et al., 1997; Giori et al., 1995)
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2.2. Bone functional adaptation Bone adaptation to mechanical stimuli has been studied extensively using in vivo models. This subject is a subset of the broader examination of cell and tissue dierentiation and may be a more straightforward problem as a starting point for our understanding, because only a single tissue is under consideration, bone. Bone adaptation has been studied using a wide variety of experimental models. Approaches used to increase loading include exercise, osteotomy and devices to apply controlled loading (Biewener and Bertram, 1993; Churches and Howlett, 1982). Decreased loading was achieved by casting, neurectomy, hindlimb suspension and space ight (Morey-Holten et al., 1996; Uhtho and Jaworksi, 1978; Vico et al., 2001). Several common concepts emerge from the past century of in vivo experimentation. We know that bone adaptation occurs in response to cyclic, not static, loading. The outcome is mainly changes in cortical bone quantity, not bone quality. Cancellous adaptation is less well characterized but has similar responses that are present as changes in the tissue apparent density. In general, demonstrating a denitive increase in bone mass or strength is more dicult than demonstrating a loss. Increased properties are also harder to achieve with physiological than nonphysiological loading conditions. Finally, we know that the adaptive response is generally greater in growing than mature animals, but growth may confound the results. While these qualitative observations generally hold true, precise quantitative predictions of the skeletal response to mechanical stimuli are often desirable and currently impossible. Much of our inability to predict adaptation arises from experimental logistics: until recently, most skeletal functional adaptation experiments could not identify the driving feature of the mechanical stimulus nor the contributing elements of the response pathway (Duncan and Turner, 1995). For example, when the loading environment is altered by exercise and a skeletal eect is observed, does the response result from the increased applied forces, the increased numbers of loading cycles, the increased loading rates, another exercise-induced parameter, or a combination of these and other factors? Can one design an exercise study to distinguish these features of the stimulus? Increasing bone mass and strength with in vivo physiological loading such as exercise is notoriously dicult. Exercise studies have produced contradictory results: running chickens at one speed was shown to increase cortical area and moments of inertia (Biewener et al., 1986), while running for a longer duration at a similar intensity suppressed bone growth and reduced strength over a similar experimental period (Matsuda et al., 1986). Dierences from one skeletal site to the next within the same animal were also found in these
studies (Li et al., 1991). Whether these dierences were caused by dierences in the local mechanical environment or by fundamentally dierent adaptive responses is unknown. Answering these questions experimentally is dicult because the in vivo loads cannot be measured directly. In adult animals, physiological exercise generally produced bone hypertrophy or no response. The absence of a response may indicate that the exercise protocol did not suciently elevate the loads above habitual levels. These unknowns all point towards the need for a better understanding of the applied mechanical loads. To better address the mechanical stimulus underlying bone adaptation, noninvasive experimental models have been developed recently, which control the stimulus applied to the cortical diaphysis (Gross et al., 2000; Mosley et al., 1997; Torrance et al., 1994; Turner et al., 1991). The two most common, currently, are the ulnar compression model of Lanyon and coworkers (Fig. 2) and the tibial four-point bending approach developed at Creighton by Turner and colleagues. The ulnar compression model likely creates more physiological stresses and strains within the bone and has load application points that are farther from the point of interest than the tibial four-point bending model. Both models were initially developed for the rat and have been modied for the mouse (Akhter et al., 1998; Fritton et al., 2001). Neither model requires surgery as previous controlled loading models often did (Churches and Howlett, 1982; Hert et al., 1969; Rubin and Lanyon, 1984). In both systems, dynamic loads are applied and the load magnitude, rate, number of cycles and duration are well controlled. These noninvasive models, combined with increased computing power, higher resolution
Fig. 2. The ulnar compression model (from Mosley and Lanyon, 1998).
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imaging and new molecular and genetic techniques enable systematic evaluation of loading parameters to understand the nature of the osteogenic stimuli and pathways. For the cortical diaphysis, stimulus characteristics that induce bone modeling are becoming evident. The applied strain rates and magnitudes need to be high (Mosley et al., 1997; Mosley and Lanyon, 1998), the strain rate contributes to the morphology of the bone formed (Turner et al., 1994), distinct, temporally separated loading episodes are required, not just increased numbers of loading cycles (Robling et al., 2000), and gender and genetic background inuence the nature of the response (Akhter et al., 1998; Pedersen et al., 1999). Similar questions need to be examined in cancellous bone, a site of more clinical relevance than the cortical diaphyses. Applying controlled loading to cancellous bone is more dicult than to the cortical diaphyses. Trabecular bone adaptation models include direct stimulation of the site of interest as well as in encapsulating bone chambers (Chambers et al., 1993; Goldstein et al., 1991, 1997b; Guldberg et al., 1997b; Hollister et al., 1996; Lamerigts et al., 2000; Morgan et al., 2001). Nearly all models require surgical intervention at the trabecular site; the rat-tail vertebra model is an exception, since only the adjoining vertebral bodies are operated on. Systematic application of dynamic loading needs to be performed to address the same questions posed above for cortical bone. For example, the rodent ulna model can presumably be extended also to examine cancellous bone, and perhaps also the response of the cartilage in the growth plate to mechanical loading. Compared to questions about the nature of the stimulus, even less is known regarding the transduction of osteogenic signals to stimulate bone formation or resorption. This pathway is hard to delineate, particularly when using in vivo models. However, recent molecular advances allow examination of whether individual genes and molecules contribute to the adaptation pathways. The mouse provides a unique opportunity to examine genetic factors through manipulation of murine embryonic stem cells and because signicant portions of the genome have been characterized (Clark and Rowe, 1996). Transgenic technology has led to the creation of both knockout and transgenic animals, either missing or over-expressing genes, and previously recorded natural mutations can now be identied. One can now directly determine whether a given protein is important to skeletal adaptation by removing it. Transgenic technology allows the role of potential regulatory factors (Erlebacher and Derynck, 1996), cell surface receptors (Zimmerman et al., 2000) and matrix constituents (Khillan et al., 1991) to be examined. Increasingly, mouse genetic studies are demonstrating extreme redundancy within the genome under normal
conditions; simply characterizing the normal phenotype may be unrevealing or insucient. However, manipulating the system by changing the applied loads can require cellular/tissue adaptation above and beyond normal development and can demonstrate signicant phenotypic eects. Examples include the osteopontin-knockout mouse and the bone morphogenetic protein-5 decient short ear mouse. The former has no obvious phenotype, but does not lose bone when subjected to hindlimb suspension (Ishijima et al., 2001). The phenotype of the latter is an overall reduced body size and these mice respond to increased loads more slowly than heterozygous controls (Mikic et al., 1996; van der Meulen, 1999). Unfortunately, developing transgenic or knockout mice and examining all the potential regulatory factors will consume many research careers. However, further strengths of these genetic models will become evident when we start to examine genetic control of skeletal responses by not only expression but also linkage analyses (Beamer et al., 2001; Klein et al., 2001; Yershov et al., 2001). In summary, many questions remain regarding the role of mechanics in the formation and adaptation of skeletal tissues. For functional adaptation, we need to be able to globally describe the adaptive response for dierent skeletal sites and ages, for example. To do so will require understanding the nature of an osteogenic mechanical stimulus and characterizing the molecular pathway that this stimulus activates. More generally, in skeletal tissue formation these same questions apply, focused on the mechanical stimuli that induce cell and tissue dierentiation. Answering these questions will require carefully controlled experiments with wellcharacterized mechanical environments. When designing and interpreting experiments, consideration must be given to contributing factors, including the type of model (in vitro or in vivo), species, type of loading (physiological or invasive), the nature of loading (tension/compression, cyclic/static, controlled/natural, etc.) and level of analysis (cell, organ or tissue level). The discussion here has focused on in vivo models with an emphasis on controlled applied loading. A similar discussion could be presented for in vitro experiments, which are used to answer similar questions, and subject to dierent limitations.
3. Computational mechanobiology The purpose of computational mechanobiology is to determine the quantitative rules that govern the eects of mechanical loading on tissue dierentiation, growth, adaptation and maintenance by trial-and-error. From a mechanics point of view, the task is considered a boundary value problem, whereby the boundary loads of a domain are translated into local mechanical
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variables within the domain, depending on the geometry and mechanical properties of its materials. Such problems are usually solved with nite element analysis (FEA). The biological side of the computation is based on the premise that local mechanical variables stimulate cell expression to regulate matrix composition, density or structure. These two parts of the problem are combined in a computer simulation model. Modeling considerations include force application at the boundary, force transmission through the tissue matrix, mechanosensation by cells, mechanotransduction by the cells, cell gene expression, and transformation of extracellular matrix characteristics. These processes must be represented in variables, parameters and mathematical relationships. Some of these are known, or can be measured (e.g. morphology, mechanical tissue properties, external loading characteristics), but others cannot. So how are these unknowns dealt with in the computations? There is a dierence between the output of a computation and the output of a problem to be solved. For example, the local mechanical variables that might stimulate the cells are usually not known and neither are the mathematical relationships between a given stimulus value and its eect on local cell expression and matrix adaptation. Potential stimuli include strain, uid ow, strain rate and strain energy. Although these unknowns must be entered into the computer simulation, they also represent precisely the quantitative rules that we are trying to determine. Computational mechanobiologists hypothesize a potential rule and determine if the outcome of this hypothesis produces realistic tissue structures and morphologies, hence trial-and-error. If the results correspond well, they might be an explanation for the mechanism being modeled. This method of research is common practiceFand productiveFin physics, less common in biology (Huiskes, 1995); although theoretical biology is based on this type of approach. Computer simulation has recently been cited as the third method of science, after logic and experimentation (Kelly, 1998). Below we give some examples from skeletal development, repair, maintenance and adaptation, particularly to demonstrate the general approach, its limitations and its progress in recent years. 3.1. Tissue dierentiation Tissue dierentiation occurs in bone development and regeneration, fracture healing and adaptation to skeletal implants. In 1941, Pauwels proposed a theoretical framework in which the eects of mechanical forces on tissue dierentiation pathways occur through mechanical deformation of the tissues. The local deformations in a tissue can be described by a strain tensor, which has rst and second invariants representing the
dilatational and distortional strain components. The rst invariant represents a change in volume (as caused by dilatational or hydrostatic stress), the second a change in shape (as caused by distortional or shear stress). Pauwels proposed that the combination of these variables determines the dierentiation pathway from the mesenchymal origin to brous, bro-cartilaginous or cartilaginous tissue. Endochondral bone formation would be stimulated in areas of low distortional and high dilatational strain (Prendergast and van der Meulen, 2001).1 Pauwels theory was based on clinical observation and logic, but he did not have the capacity to measure or calculate the tissue strains or stresses accurately. In the following discussion we will show how the application and evolution of FEA has aected our thoughts about Pauwels ideas, and how computational mechanobiology is gradually maturing. Carter and colleagues tested Pauwels theory relative to endochondral bone formation using FEA. Endochondral ossication was dened by the peak cyclic hydrostatic stress (D) and the peak cyclic octahedral shear stress (S), combined in an osteogenic index I, as I S kD; summed over a number of loading cycles; k is an empirical constant. High values of the index were hypothesized to stimulate ossication; no specic threshold value was specied. Note that S is always positive, but D can both be positive (tension) or negative (compression). This tissue dierentiation rule was tested with an FEA model of a developing joint to determine whether this approach could predict the emergence of secondary ossication centers (Carter and Wong, 1988). High values of the osteogenic index were found in the cartilage precisely where osteogenesis occurs during in vivo skeletal development. Comparing the results with biological examples, the most predictive values for the constant k were determined at 0:3pkp1:0 (Fig. 3). Similarly successful predictions of endochondral ossication sites were performed for other skeletal sites, for bone regeneration in fracture healing and for healing around orthopaedic implants (Carter et al., 1998; Carter ! and Beaupre, 2001; Giori et al., 1995). A vital issue for mechanobiological FEA models is to what extent they can be simplied without loosing their potential to obtain meaningful results. On the one hand, simplicity is dictated by contemporary computational technology, and on the other it depends on the
1 The inclusion of enchondral ossication in a theoretical framework for skeletal dierentiation pathways is not entirely justied, as mineralization and bone modeling are very dierent kinds of processes, which actually terminate dierentiation. Mineralized tissue cannot dedierentiate, only resorb; or rather be resorbed. However, mineralization occurs when particular conditions in cartilage are met and the creation of those conditions can be seen as a part of the dierentiation pathway.
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Fig. 3. The distributions of the osteogenic index as computed in the cartilaginous part of developing bone with a 2-D FEA model, using 3 dierent values for the empirical constant k (Carter and Wong, 1988). Ossication is predicted where the index is high (from Carter, 1987).
hypothesis to be tested. In that sense a model takes for granted the matter in dispute, or begs the question, because its assumptions determine its answers. One can only make conclusions about phenomena accounted for in the model, not about what is omitted or assumed not to contribute. This is equally true for experimental models of course. The above FE analyses of the cartilage in the models assumed homogeneity, isotropy and linear elasticity; while in reality the tissue is multi-phasic, nonlinear and highly structured at many levels of scale. Hydrostatic pressure and octahedral stress in biphasic tissues seemed to be well captured by single-phasic linear elastic FEA, provided that the permeability is low, as is the case in cartilage (Mow et al., 1980; Tanck et al., 2000; Yuan et al., 2000). Hence, relative to the hypothesis the authors wanted to test, the conclusions about the predictive quality of the osteogenic index may not have been any dierent had they described the cartilage as biphasic. But, although the proposed denition of the osteogenic index produces realistic results, another choice for other mechanical variables, or an alternative mathematical rule, might produce equal or potentially even better results. One important consideration is uid ow in cartilage. There are several reasons that interstitial uid ow could be a more realistic mechanical variable for feedback information to the cells during tissue dierentiation than hydrostatic pressure. Flow is known to stimulate anabolic cell expressions during in vitro testing (Jacobs et al., 1998). The hydrostatic stress, computed in linear-elastic FEA models, is believed to be indicative of the interstitial uid pressure in vivo. However, biphasic
analyses of bone ossication suggested that the true uid pressure in the tissue might be sensitive to the solid matrix compressibility, another poorly understood parameter (Tanck et al., 1999). Based on a comparative analysis of experimental tissue mineralization studies (Burger et al., 1991) with biphasic FEA, the hypothesis that hydrostatic stress was a modulating variable was refuted (Tanck et al., 2000). In a biphasic analysis of a tissue dierentiation experiment around a moving piston in the femoral condyles of dogs (Sballe et al., 1992), Prendergast and Huiskes (1996), Prendergast and colleagues (1997) found that local tissue uid pressure does not change as the tissue dierentiates. Yuan et al. (2000) came to a similar conclusion from a biphasic analysis of soft-tissue membranes under tibial knee implants, comparing results to those of an earlier linearelastic analysis of the same problem (Giori et al., 1995). Prendergast and Huiskes (1996), Prendergast et al. (1997) also found that the stresses on cells are not only generated by the tissue matrix, but also to a large extent by the drag forces from interstitial uid ow. This conclusion indicates the need for dynamically loaded, biphasic models, because these eects cannot be examined with static or linear elastic ones. Interstitial uid ow and pressure need to be investigated as potential signaling variables in the simulations. Improvements in computer capacity now enable FEA computer simulations in a dynamic sense, as opposed to the earlier computer analyses. In the latter case the mechanical variables are computed for a particular initial conguration and predict a steady state, nal homeostatic conguration. The result is determined from the initial conditions, but the process is not simulated over time. The results of Carter and associates ! (Carter and Beaupre, 2001) relative to the prediction of ossication areas are quite realistic. However, these analyses cannot predict the progression of ossication based on a single set of initial conditions. To simulate the time-varying mineralization process, the evolution of the tissue material properties must also be simulated with time. The process of ossication itself aects the load transfer in the cartilaginous parts while time transpires (Claes and Heigele, 1999; Gardner et al., 2000; Lerner et al., 1998; Prendergast et al., 1997; Stevens et al., 1999). Another advantage of timedependent simulations is the ability to incorporate dynamic loading, including both uctuating loads at a particular instant and overall variation in load over time. Based on the above considerations, and the studies of Prendergast and Huiskes (1996), Prendergast et al. (1997), an alternative rule was proposed for dierentiation from loose connective tissue to cartilage or bone. This was tested in dynamic, biphasic computer simulations as a mechano-regulation index, deciding which tissue phenotype would prevail as an eect of mechan-
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ical stimulation. For that purpose a mechano-regulation index (M) was formulated as (Huiskes et al., 1997) gn M ; ab where g dimensionless is the maximal distortional (or octahedral shear) strain, v (mm/s) the interstitial uidow velocity, a 0:0375 and b 3 (mm/s). Based on experimental data (Sballe et al., 1992), it was proposed that where M > 3; brous tissue would prevail (characterized by a modulus of 2.0 MPa and a permeability of 1.0 1014 m4 N/ s), where 1pMp3; cartilage would prevail (modulus 10.0, permeability 5.0 1015) and where Mo1; bone would form (modulus 4590, permeability 3.7 1013). This theory has two empirical thresholds which determine when transitions in the tissue type occur, and two empirical constants a and b which are, however, interdependent. In this model the value b=a plays a similar role as k in the osteogenic index. The rule was tested in a mechano-regulatory computer simulation, using the FEA model of the Sballe experiment discussed above (Huiskes et al., 1997). Iteratively, cyclic loading was applied to the piston and the tissue modulus and permeability were adjusted locally per iteration, in accordance with the distribution of the mechano-regulation index in the gap tissue, until dierentiation converged to a nal tissue phenotype (Fig. 4). Using this approach, the dierentiation of gap-tissue phenotype from brous connective to cartilage to bone could be predicted, simulating the experiment (Sballe et al., 1992). In the earlier analysis of this experiment the ingrowth process successful
Finite was Element Model Implant Loading Conditions
New Tissue Phenotype Mechanical Characteristics
Mechano-Regulation Diagram
FIBROUS FIBRO CARTILAGE
PIS
TON
GAP
BONE
BONE
Strain
Tissue Strain Fluid-Solid Velocity
Fig. 4. The regulatory scheme used in the computer simulation. The strain and uid-velocity distributions are calculated in the FEA model. Based on the transition criteria, illustrated in a phase diagram representing the dierentiation rule, tissue phenotype characteristics are updated in every iteration. The simulation is continued until no more change occurs and homeostasis is reached (from Huiskes et al., 1997).
because the piston displacement was force controlled (Prendergast et al., 1997). Force control reduces the excursion of the piston when the tissue gets stier, allowing the tissue to control its dierentiation stimulus. To test this conclusion, simulations of motion control were performed using the maximal total excursion as in the force-controlled experiment, regardless of the force required. While the tissue ossied fully in the forcecontrolled simulation, motion control produced a largely bro-cartilaginous tissue, with only a few islands of bone (Fig. 5). This lack of ingrowth under large displacements is also seen around loose orthopedic implants. These results demonstrate the importance of temporal simulation for the questions posed. In both the forcecontrolled and motion-controlled simulations of tissue ingrowth the dierentiation patterns predicted after the rst iterations were identical, because both the force and excursion of the piston were equal (Fig. 5). Therefore, in an analysis based on the rst iteration only, the same outcome would have been predicted for both cases. The same regulatory model was used to simulate tissue dierentiation in fracture healing, using the same values for the empirical constants and tissue characteristics (Lacroix et al., 2000). In these simulations the dierentiation pathways were also not monotonic, again demonstrating the importance of simulation over analyses based on the initial conditions only. While this simulation model captures the dynamic aspects of the system and accounts for the timedependent properties of the tissues, limitations are present as well. The uid pressure and ow velocity can be evaluated, but osmotic eects and chargeddensity ows in the tissue, for example, are not accounted for (Mow et al., 1999). Hence, this model also begs the question. Similar to the linear elastic, homeostatic models, the relevant mechanical variables are evaluated at a macroscopic (homogenized) continuum level and cannot describe what individual cells experience. Cells exist at a much lower scale, surrounded by a quite irregular micro-morphology. These models are mechanistic with respect to uid ow, but very crude and approximate with regard to the cellular environment (Wang et al., 2001). But, as stated earlier, from a scientic point of view, these models could still produce realistic hypotheses, because the importance of these details is unknown. The physiological cellular mechanisms are not understood, so the appropriateness of macroscopic or microscopic formulations is unknown. Perhaps the extracellular matrix acts as a lter for the local environment, making a continuum model equally appropriate. To capture every detail of the system from cells to whole organs, we may need to build FEA models of whole bones with renement to the cellular level, including the cascade of biochemical reactions in and around the cells, but current computer
Fluid Velocity
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Fig. 5. Graphs illustrating the phenotypical stages of the gap tissue during the simulation; every dot represents an element. Initially all elements are brous. After the rst iteration two elements were predicted to become bone, a large number to become bro-cartilaginous and the majority to be still brous, based on the strain and uid velocity history computed. This rst phase developed identical in both the force and motion controlled simulations. In the nal homeostatic stage of the force-controlled simulation all elements turned to bone (Huiskes et al., 1997). In the motioncontrolled simulation, however, the gap tissue was predicted as a nal mixture of brous and bro-cartilaginous, with just a few islands of bone.
capacity still dees that. There is nothing scientically incorrect about the current approaches, however. This discussion relates to the extent a model is mechanistic, i.e. to what detail is the biological cascade of processes, and their biochemical actors, represented or necessary to be represented? In computational mechanobiology mechanistic detail is not a goal by itself; the research question dictates the level of sophistication required. A nal complicating issue for computational models in mechanobiology is the presence of empirical constants, whose values must be determined by comparison to a biological reality. The osteogenic ossication rule ! (Carter and Beaupre, 2001), for example, contains the constant k, which weights the sensitivity of the tissue for hydrostatic stress relative to shear stress in the index. In the mechano-regulation rule (Huiskes et al., 1997; Lacroix et al., 2000) the constant b/a weights the relative sensitivities for ow velocity and strain. In addition, both theories require transitional values for their indexes, which determine when the tissue dierentiates; the ossication rule requires a single value for this purpose and the dierentiation rule requires two. The
values of these constants can only be determined by comparing computational results to similar experiments. If one assumes that the cell mediated processes are independent of cell location, then the empirical constants should have unique values for all dierentiation processes. If the empirical constants must be adjusted per conguration or problem denition, then a theory is not falsiable, and has little predictive power (Prendergast, 2001). Comparing results of several dierent FEA models to evaluate the ossication index to boneformation patterns in ontogenesis, growth-plate orientation, fracture healing, and brous-tissue characteristics around orthopaedic implants, the ossication rule delivered best-tting k-values between 0.0 and 2.0 ! (Carter and Beaupre, 2001; Ribble et al., 2001). As can be seen in Fig. 3, the value of k can have a large eect on the predicted distribution of the osteogenic index. The dierentiation rule was only tested for ingrowth of implants, as shown above, and fracture healing (Lacroix et al., 2000), using the same values for the empirical constants. Much more experimentation will be needed to validate these values.
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Fig. 6. A model to simulate trabecular modeling, remodeling and adaptation governed by strain-energy density rate as produced by external loads, assuming osteocyte mechanosensation and signal transduction to lining cells at the trabecular surface, which stimulates osteoblastic bone formation. Osteoclasts are assumed to remove microcracks in a spatially random way; resorption cavities produce the local strain concentrations attracting osteoblastic repair. An example is shown in which, after 2000 iterations with the FEA model, a homeostatic structure, adapted to magnitude and orientation of the external load, was formed from an arbitrary initial structure (from Huiskes et al., 2000).
Tissue dierentiation encompasses a wide area of scientic eorts, including many computational studies that were not discussed here; relevant ones can be found in the articular cartilage area (Wang et al., 2001). The testing of theories for tissue dierentiation with simulation models has spread to ligaments and tendons (Wren et al., 1998) and development of articular joints (Heegaard et al., 1999). Currently the theories proposed can only be used to predict the past, allowing the formulations to be validated against known experiments or biological realities. Our ultimate objective should be to predict the future. 3.2. Bone adaptation Computer-simulation of bone adaptation is more mature than in the tissue dierentiation area, not in the least because the problems are better dened and concern only bone, as mentioned earlier. For this case the computational studies also started by analysis, with true simulation following more recently. One could say that Wols Law (1892) was already based on the comparison between trabecular morphology and the results of a computational analysis (Huiskes, 2000). The philosophy behind the computer simulation studies in this area is similar to those discussed above for tissue
dierentiation. Hart (2001) recently wrote an excellent historical overview of theories and computational models. Modern developments started with the theory of adaptive elasticity for cortical bone (Cowin and Hegedus, 1976), which was later used for an FEA simulation model by Hart et al. (1984). These studies examined the adaptation of cortical form to external forces. Alternative theories were proposed and used by Huiskes et al. (1987), Mattheck et al. (1998), Prendergast and Taylor (1994) and van der Meulen et al. (1993). Adaptation of (trabecular) bone density was simulated ! by several groups, using dierent isotropic (Beaupre et al., 1990; Carter et al., 1987; Huiskes et al., 1987; Weinans et al., 1992a, b) or anisotropic theories (Hart and Fritton, 1997; Jacobs et al., 1997; Luo et al., 1995). All these trabecular simulation models were phenomenological in nature and simulated the outcome of coordinated osteoclastic and osteoblastic activity as either a net increase or decrease in density. A more mechanistic approach is necessary to represent the true physiology of the adaptation process, which occurs only on trabecular surfaces (Huiskes, 2000). A model to simulate local trabecular adaptation that does allow this surface mechanism to be simulated, and also includes a biological osteocyte mechanosensory and signaling function, was developed by Mullender and Huiskes
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(1995). A model that also includes separate descriptions of osteoclastic resorption and osteoblastic formation, enabling simulation of mechanobiologically modulated growth, adaptation and maintenance (remodeling), illustrated in Fig. 6, was published recently (Huiskes et al., 2000; Ruimerman et al., 2001). Adachi et al. (2001) proposed a phenomenological adaptation model for the trabecular structure using nonuniformity of the local surface stress distribution as the regulatory feedback signal. The models incorporating trabecular morphology have been used only to study adaptation in small cubes of bone. Analyses of whole bone FEA models with renement down to the trabecular level are feasible now (van Rietbergen et al., 1999). However, there is not enough computer capacity yet to use those in iterative simulations to study trabecular adaptation based on a (mechanistic) cell modulation scheme. Future models will need to include both natural boundary conditions at external bone surfaces and rened trabecular architecture.
4. Discussion So why mechanobiology? While the term is the inverse of biomechanics, the denition of biomechanics clearly encompasses the experimental and computational models described here: The science that studies the eects of forces on biological tissues, organs and organisms, in relation to biological and medical problems (ESB, 1978). As a word, however, mechanobiology moves the emphasis from mechanics to biology and to determining the mechanisms behind form follows function. But then what does function follow? In an evolutionary sense, one could consider function to follow form, a strategy that has enabled vertebrates to successfully breed and survive. This then produces yform follows function follows formy Considering this cycle of repetition, one can now distinguish between the two terms: biomechanics focuses on the latter part, whether function follows form, whereas mechanobiology emphasizes the former, whether function determines form. Both experimental and computational studies are critical to advancing our understanding of form and function, and even more important is the integration of models and experiments. Yet we have separated experimental and computational studies in this article, a distinction that reects contemporary science and presumably arises from the cultural roots of both activities. Experimental studies, particularly in vivo models, originated in biology, while computational work is fundamentally based on physics and engineering. To make signicant progress, the objective needs to be the integration of these two types of studies: models
for interpreting experiments and experiments for insights and observation to develop models; yet another circular mechanism! The challenge is to educate scientists who can understand and contribute to both ends of the spectrum and help to eliminate the distinction. Many other elds rely upon this integration. In mechanobiology, however, the interdisciplinary nature of these questions cuts across many additional spectra besides experiments and simulations: in vivo to in vitro, biology to engineering, laboratory to clinic, etc. This not only produces great challenges but also potentially signicant rewards. Beyond the integration within the eld itself, we must ask where mechanobiology ts in a broader scientic and social context. Scientically, mechanobiology is central to unraveling nature versus nurture distinctions. With the sequencing of the human genome complete (Venter et al., 2001) it is now apparent that the genetic code is only the beginning and provides few answers to how form is generated and maintained. The limitations of genomics and proteomics emphasize the importance of understanding the role of environmental inuences, particularly biophysical factors (Stewart, 1998). Scientic interest in form and function is not new, but recent advances in cell and molecular biology allow examination of phenomena that were previously inaccessible. On Earth, gravity is ubiquitous and is likely one of the most pervasive factors in the development of tissues. This particularly holds true for the musculoskeletal system, which plays a central role in vertebrates ability to function in Earths gravitational environment. The potential reward for successful quantitative models and insightful experiments is enormous. The challenge lies in disentangling environmental modulation and genetic predisposition in the skeleton. The conservation of osseous microstructure and morphology speak, to a high degree, of predisposition. Yet, the action of gravity and the resulting mechanical stimuli are also highly conserved, making a case for modulation. Successfully distinguishing adaptation from genetic programming of cell metabolism will be a great mechanobiological feat, requiring intimate interaction between experimental and computational eorts. The potential for mechanobiology to contribute to clinical progress is also promising. Mechanically based diseases such as osteoporosis and osteoarthritis are already areas of intense research activity. In addition, the development of successful synthetic and engineered organs and tissues, tissue engineering, will depend on mechanobiological progress. This is especially true for functional tissue engineering (Butler et al., 2000). Not only is an intimate knowledge of the natural tissues necessary, but controlling and modulating mechanical stimuli will be essential to develop appropriately engineered organs and to integrate and function with
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the host. The realization of this promise will be particularly rewarding.
Acknowledgements This article synthesizes two presentations from the Mechanobiology Symposium of the 12th Conference of the European Society of Biomechanics in Dublin, Ireland, August 2830, 2000. We thank the ESB and the organizing committee for the opportunity to present our work. Funding is acknowledged from the National Institutes of Health (USA) and the Netherlands Foundation for Research (NWO-MW).
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