Reciprocal interactions between cells and extracellular matrix during remodeling of tissue constructs

Cells remodel extracellular matrix during tissue development and wound healing. Similar processes occur when cells compress and stiffen collagen gels. An important task for cell biologists, biophysicists, and tissue engineers is to guide these remodeling processes to produce tissue constructs that mimic the structure and mechanical properties of natural tissues. This requires an understanding of the mechanisms by which this remodeling occurs. Quantitative measurements of the contractile force developed by cells and the extent of compression and stiffening of the matrix describe the results of the remodeling processes. Not only do forces exerted by cells influence the structure of the matrix but also external forces exerted on the matrix can modulate the structure and orientation of the cells. The mechanisms of these processes remain largely unknown, but recent studies of the regulation of myosin-dependent contractile force and of cell protrusion driven by actin polymerization provide clues about the regulation of cellular functions during remodeling.     

Strain history and TGF-β1 induce urinary bladder wall smooth muscle remodeling and elastogenesis

Mechanical cues that trigger pathological remodeling in smooth muscle tissues remain largely unknown and are thought to be pivotal triggers for strain-induced remodeling. Thus, an understanding of the effects mechanical stimulation is important to elucidate underlying mechanisms of disease states and in the development of methods for smooth muscle tissue regeneration. For example, the urinary bladder wall (UBW) adaptation to spinal cord injury (SCI) includes extensive hypertrophy as well as increased collagen and elastin, all of which profoundly alter its mechanical response. In addition, the pro-fibrotic growth factor TGF-β1 is upregulated in pathologies of other smooth muscle tissues and may contribute to pathological remodeling outcomes. In the present study, we utilized an ex vivo organ culture system to investigate the response of UBW tissue under various strain-based mechanical stimuli and exogenous TGF-β1 to assess extracellular matrix (ECM) synthesis, mechanical responses, and bladder smooth muscle cell (BSMC) phenotype. Results indicated that a 0.5-Hz strain frequency triangular waveform stimulation at 15% strain resulted in fibrillar elastin production, collagen turnover, and a more compliant ECM. Further, this stretch regime induced changes in cell phenotype while the addition of TGF-β1 altered this phenotype. This phenotypic shift was further confirmed by passive strip biomechanical testing, whereby the bladder groups treated with TGF-β1 were more compliant than all other groups. TGF-β1 increased soluble collagen production in the cultured bladders. Overall, the 0.5-Hz strain-induced remodeling caused increased compliance due to elastogenesis, similar to that seen in early SCI bladders. Thus, organ culture of bladder strips can be used as an experimental model to examine ECM remodeling and cellular phenotypic shift and potentially elucidate BMSCs ability to produce fibrillar elastin using mechanical stretch either alone or in combination with growth factors.     

A physically motivated constitutive model for cell-mediated compaction and collagen remodeling in soft tissues

Collagen is the main load-bearing component of many soft tissues and has a large influence on the mechanical behavior of tissues when exposed to mechanical loading. Therefore, it is important to increase our understanding of collagen remodeling in soft tissues to understand the mechanisms behind pathologies and to control the development of the collagen network in engineered tissues. In the present study, a constitutive model was developed by coupling a recently developed model describing the orientation and contractile stresses exerted by cells in response to mechanical stimuli to physically motivated collagen remodeling laws. In addition, cell-mediated contraction of the collagen fibers was included as a mechanism for tissue compaction. The model appeared to be successful in predicting a range of experimental observations, which are (1) the change in transition stretch of periosteum after remodeling at different applied stretches, (2) the compaction and alignment of collagen fibers in tissue-engineered strips, (3) the fiber alignment in cruciform gels with different arm widths, and (4) the alignment of collagen fibers in engineered vascular grafts. Moreover, by changing the boundary conditions, the model was able to predict a helical architecture in the vascular graft without assuming the presence of two helical fiber families a priori. Ultimately, this model may help to increase our understanding of collagen remodeling in physiological and pathological conditions, and it may provide a tool for determining the optimal experimental conditions for obtaining native-like collagen architectures in engineered tissues.     

Stem cell-based growth, regeneration, and remodeling of the planarian intestine

Although some animals are capable of regenerating organs, the mechanisms by which this is achieved are poorly understood. In planarians, pluripotent somatic stem cells called neoblasts supply new cells for growth, replenish tissues in response to cellular turnover, and regenerate tissues after injury. For most tissues and organs, however, the spatiotemporal dynamics of stem cell differentiation and the fate of tissue that existed prior to injury have not been characterized systematically. Utilizing in vivo imaging and bromodeoxyuridine pulse-chase experiments, we have analyzed growth and regeneration of the planarian intestine, the organ responsible for digestion and nutrient distribution. During growth, we observe that new gut branches are added along the entire anteroposterior axis. We find that new enterocytes differentiate throughout the intestine rather than in specific growth zones, suggesting that branching morphogenesis is achieved primarily by remodeling of differentiated intestinal tissues. During regeneration, we also demonstrate a previously unappreciated degree of intestinal remodeling, in which pre-existing posterior gut tissue contributes extensively to the newly formed anterior gut, and vice versa. By contrast to growing animals, differentiation of new intestinal cells occurs at preferential locations, including within newly generated tissue (the blastema), and along pre-existing intestinal branches undergoing remodeling. Our results indicate that growth and regeneration of the planarian intestine are achieved by co-ordinated differentiation of stem cells and the remodeling of pre-existing tissues. Elucidation of the mechanisms by which these processes are integrated will be critical for understanding organogenesis in a post-embryonic context.     

Micro-Mechanical Characterization of Lung Tissue Using Atomic Force Microscopy

Matrix stiffness strongly influences growth, differentiation and function of adherent cells^1-3. On the macro scale the stiffness of tissues and organs within the human body span several orders of magnitude⁴. Much less is known about how stiffness varies spatially within tissues, and what the scope and spatial scale of stiffness changes are in disease processes that result in tissue remodeling. To better understand how changes in matrix stiffness contribute to cellular physiology in health and disease, measurements of tissue stiffness obtained at a spatial scale relevant to resident cells are needed. This is particularly true for the lung, a highly compliant and elastic tissue in which matrix remodeling is a prominent feature in diseases such as asthma, emphysema, hypertension and fibrosis. To characterize the local mechanical environment of lung parenchyma at a spatial scale relevant to resident cells, we have developed methods to directly measure the local elastic properties of fresh murine lung tissue using atomic force microscopy (AFM) microindentation. With appropriate choice of AFM indentor, cantilever, and indentation depth, these methods allow measurements of local tissue shear modulus in parallel with phase contrast and fluorescence imaging of the region of interest. Systematic sampling of tissue strips provides maps of tissue mechanical properties that reveal local spatial variations in shear modulus. Correlations between mechanical properties and underlying anatomical and pathological features illustrate how stiffness varies with matrix deposition in fibrosis. These methods can be extended to other soft tissues and disease processes to reveal how local tissue mechanical properties vary across space and disease progression.     

Gene therapy for tissue regeneration

Tissue repair and regeneration are the normal biological responses of many different tissues in the body to injury. During the healing process, profound changes occur in cell composition and extracellular matrix (ECM) formation. Fibroblasts and equivalent reparative cells migrate to the wounded area and subsequently proliferate. These cells and reparative cells from the surrounding tissue are responsible for the rapid repair which results in tissue regeneration. Growth factors, one of which is transforming growth factor-beta (TGF-beta), stimulate fibroblasts and smooth muscle cells to proliferate and synthesize ECM proteins. This process of early repair provides a rapid way to restore new tissue and mechanical integrity. This early tissue repair process is normally followed by involution, which requires the production and activation of proteases, tissue maturation and remodeling, reorganization and finally regeneration. Alternately, failure to replace the critical components of the ECM, including elastin and basement membrane, results in abnormal regeneration of the epithelial cell layer. Although remodeling should occur during healing, provisional repair may be followed by excessive synthesis and deposition of collagen, which results in irreversible fibrosis and scarring. This excessive fibrosis which occurs in aberrant healing is at least in part mediated by persistent TGF-beta. Because of the central role of collagen in the wound healing process, the pharmacological control of collagen synthesis has been of paramount importance as a possible way to abrogate aberrant healing and prevent irreversible fibrosis. Fibrosis is an abnormal response to tissue injury.     

Assessing the mechanical energy costs of various tissue reshaping mechanisms

Early-stage embryos must reshape the tissues of which they are made into organs and other life-sustaining structures; and if non-mammalian embryos fail to complete these tasks before the energy provided by their yolk runs out, they die. The aim of this study is to use a cell-level computational model to investigate the energetic cost of a variety of mechanisms that can drive an in-plane reshaping pattern known as convergent extension—a motif in which a tissue narrows in one in-plane direction and expands in another. Mechanisms considered include oriented lamellipodia, directed mitosis, stress fibers, and anisotropic external tension. Both isolated patches of tissue and actively contracting tissues that deform adjacent passive areas are considered. The cell-level finite element model used here assumes that the cell membrane and its associated proteins generate a net tension γ along each cell–cell interface and that the cytoplasm and its embedded networks and structures have an effective viscosity?μ. Work costs are based exclusively on mechanical considerations such as edge lengths and tensions, and because a traditional mechanical efficiency cannot be calculated, mechanisms are compared on the basis of the work they must do to the tissue to cause a specified rate of in-plane reshaping. Although the model contains a number of simplifications compared to real embryonic tissues, it is able to show that the work requirements for tissue reshaping by mitoses and by lamellipodia are of the same order. Lamellipodia are energetically most effective when their tensions are approximately twice as large as the interfacial tensions in the surrounding cells. The model also shows that stress fibers or other direct stretch or compression mechanisms are at least five times more efficient for tissue reshaping than are mitoses or lamellipodia and that the work needed to deform a typical cellular tissue is more than thirty times greater than if it did not contain cell boundaries. Collectively, these findings indicate that common tissue reshaping mechanisms have mechanical efficiencies of less than one percent and that mechanical efficiency is not the primary determinant of which mechanism(s) an embryo uses to reshape its tissues.     

Hard tissue remodeling using biofabricated coralline biomaterials

Biotechnical and biomedical approaches were combined in an attempt to identify potential uses of biofabricated marine carbonate materials in biomedical applications, particularly as biomatrices for remodeling bone and cartilage tissue. After grafting, it is desirable for bone ingrowth to proceed as quickly as possible because the strength of the implanted region depends on a good mechanical bond forming between the implant and surrounding regions in the body. Ingrowth can take place as a result of growth of tissue and cells into the implanted porous material, or it may be promoted by transplanting cells seeded onto such a material. The rate at which ingrowth occurs is dependent on many factors, including pore size and the interconnectivity of the implanted structure. In vivo graftings into osteochondral defects demonstrated that our biofabricated porous material is highly biocompatible with cartilage and bone tissue. The biofabricated matrix was well incorporated into the biphasic osteochondral area. Resorption was followed by bone and cartilage formation, and after 4 months, the biomaterial had been replaced by new tissue. Ossification was induced and enhanced without introduction of additional factors. We believe that this is the first time that such biofabricated materials have been used for biomedical purposes. In face of the obvious environmental disadvantages of harvesting from limited natural resources, we propose the use of bioengineered coralline and other materials such as those cultured by our group under field and laboratory conditions as a possible biomatrix for hard tissue remodeling.     

Equibiaxial cyclic stretch stimulates fibroblasts to rapidly remodel fibrin

Understanding the effects of the mechanical environment on wound healing is critical for developing more effective treatments to reduce scar formation and contracture. The aim of this study was to investigate the effects of dynamic mechanical stretch on cell-mediated early wound remodeling independent of matrix alignment which obscures more subtle remodeling mechanisms. Cyclic equibiaxial stretch (16% stretch at 0.2 Hz) was applied to fibroblast-populated fibrin gel in vitro wound models for eight days. Compaction, density, tensile strength, and collagen content were quantified as functional measures of remodeling. Stretched samples were approximately ten times stronger, eight-fold more dense, and eight times thinner than statically cultured samples. These changes were accompanied by a 15% increase in net collagen but no significant differences in cell number or viability. When collagen crosslinking was inhibited in stretched samples, the extensibility increased and the strength decreased. The apparent weakening was due to a reduction in compaction rather than a decrease in ability of the tissue to withstand tensile forces. Interestingly, inhibiting collagen crosslinking had no measurable effects on the statically cultured samples. These results indicate that amplified cell-mediated compaction and even a slight addition in collagen content play substantial roles in mechanically induced wound strengthening. These findings increase our understanding of how mechanical forces guide the healing response in skin, and the methods employed in this study may also prove valuable tools for investigating stretch-induced remodeling of other planar connective tissues and for creating mechanically robust engineered tissues.     

A computational model of intussusceptive microvascular growth and remodeling

Non-sprouting angiogenesis, also known as intussusceptive angiogenesis (IA), is an important modality of blood vessel morphogenesis in growing tissues. We present a novel computational framework for simulation of IA to answer some of the questions concerning the underlying mechanisms of the remodeling process. The model relies on mechanical interactions between blood and tissue, includes the structural maturation of the vessel wall, and is controlled by stimulating or inhibiting chemical agents. The model provides a simple explanation for the formation of microvessels and bifurcations from capillaries via IA, allowing for both maintenance and avoidance of shunt vessels. Detailed hemodynamic and transport properties for oxygen, metabolites or growth factors can be predicted. The model is an in silico framework for testing certain conceptual ideas about the mechanisms of intussusceptive growth and remodeling, in particular those related to mechanical and transport phenomena.     

Molecular and Mesoscale Mechanisms of Osteogenesis Imperfecta Disease in Collagen Fibrils

Osteogenesis imperfecta (OI) is a genetic disorder in collagen characterized by mechanically weakened tendon, fragile bones, skeletal deformities, and in severe cases, prenatal death. Although many studies have attempted to associate specific mutation types with phenotypic severity, the molecular and mesoscale mechanisms by which a single point mutation influences the mechanical behavior of tissues at multiple length scales remain unknown. We show by a hierarchy of full atomistic and mesoscale simulation that OI mutations severely compromise the mechanical properties of collagenous tissues at multiple scales, from single molecules to collagen fibrils. Mutations that lead to the most severe OI phenotype correlate with the strongest effects, leading to weakened intermolecular adhesion, increased intermolecular spacing, reduced stiffness, as well as a reduced failure strength of collagen fibrils. We find that these molecular-level changes lead to an alteration of the stress distribution in mutated collagen fibrils, causing the formation of stress concentrations that induce material failure via intermolecular slip. We believe that our findings provide insight into the microscopic mechanisms of this disease and lead to explanations of characteristic OI tissue features such as reduced mechanical strength and a lower cross-link density. Our study explains how single point mutations can control the breakdown of tissue at much larger length scales, a question of great relevance for a broad class of genetic diseases.     

Computational determination of the critical microcrack size that causes a remodeling response in a trabecula: a feasibility study

Bone is a living tissue, which undergoes continuous renewal to repair local defects. Two separate processes, adaptation and remodeling, are involved when a defect appears. The defect produces stress concentrations that provoke regional adaptation, and is gradually repaired, first by resorption and then by deposition of new bone. Using a mathematical formulation of the adaptation mechanism in trabeculae of cancellous bone, we hypothesize that in some cases, where a microcrack is small enough relative to the dimensions of the trabecula, the adaptation response of the whole trabecula may be sufficient to regain homeostatic mechanical conditions (with no need for a remodeling process). The simulation results showed that for trabeculae with nominal length of 900 microm and nominal thickness of 80-800 microm, a microcrack with minimal length of 48 microm and minimal depth of 13% of the trabecula's thickness was required to initiate a remodeling process. A longer (100 microm) but shallower (depth of 7% of the trabecula's thickness) crack also triggered remodeling. These computational results support our hypothesis that when a microcrack small enough relative to the dimensions of the trabecula occurs, adaptation of the whole trabecula may be sufficient to regain homeostatic mechanical conditions with no need for a local remodeling process.     

Biomechanics of the lung parenchyma: critical roles of collagen and mechanical forces.

The biomechanical properties of connective tissues play fundamental roles in how mechanical interactions of the body with its environment produce physical forces at the cellular level. It is now recognized that mechanical interactions between cells and the extracellular matrix (ECM) have major regulatory effects on cellular physiology and cell-cycle kinetics that can lead to the reorganization and remodeling of the ECM. The connective tissues are composed of cells and the ECM, which includes water and a variety of biological macromolecules. The macromolecules that are most important in determining the mechanical properties of these tissues are collagen, elastin, and proteoglycans. Among these macromolecules, the most abundant and perhaps most critical for structural integrity is collagen. In this review, we examine how mechanical forces affect the physiological functioning of the lung parenchyma, with special emphasis on the role of collagen. First, we overview the composition of the connective tissue of the lung and their complex structural organization. We then describe how mechanical properties of the parenchyma arise from its composition as well as from the architectural organization of the connective tissue. We argue that, because collagen is the most important load-bearing component of the parenchymal connective tissue, it is also critical in determining the homeostasis and cellular responses to injury. Finally, we overview the interactions between the parenchymal collagen network and cellular remodeling and speculate how mechanotransduction might contribute to disease propagation and the development of small- and large-scale heterogeneities with implications to impaired lung function in emphysema.     

Progression of thanatophagy in cadaver brain and heart tissues

Autophagy is an evolutionarily conserved catabolic process for maintaining cellular homeostasis during both normal and stress conditions. Metabolic reprogramming in tissues of dead bodies is inevitable due to chronic ischemia and nutrient deprivation, which are well-known features that stimulate autophagy. Currently, it is not fully elucidated whether postmortem autophagy, also known as thanatophagy, occurs in dead bodies is a function of the time of death. In this study, we tested the hypothesis that thanatophagy would increase in proportion to time elapsed since death for tissues collected from cadavers. Brain and heart tissue from corpses at different time intervals after death were analyzed by Western blot. Densitometry analysis demonstrated that thanatophagy occurred in a manner that was dependent on the time of death. The autophagy-associated proteins, LC3 II, p62, Beclin-1 and Atg7, increased in a time-dependent manner in heart tissues. A potent inducer of autophagy, BNIP3, decreased in the heart tissues as time of death increased, whereas the protein levels increased in brain tissues. However, there was no expression of BNIP3 at extended postmortem intervals in both brain and heart samples. Collectively, the present study demonstrates for the first time that thanatophagy occurs in brain and heart tissues of cadavers in a time-dependent manner. Further, our data suggest that cerebral thanatophagy may occur in a Beclin-1- independent manner. This unprecedented study provides potential insight into thanatophagy as a novel method for the estimation of the time of death in criminal investigationsAbstract: Autophagy is an evolutionarily conserved catabolic process for maintaining cellular homeostasis during both normal and stress conditions. Metabolic reprogramming in tissues of dead bodies is inevitable due to chronic ischemia and nutrient deprivation, which are well-known features that stimulate autophagy. Currently, it is not fully elucidated whether postmortem autophagy, also known as thanatophagy, occurs in dead bodies is a function of the time of death. In this study, we tested the hypothesis that thanatophagy would increase in proportion to time elapsed since death for tissues collected from cadavers. Brain and heart tissue from corpses at different time intervals after death were analyzed by Western blot. Densitometry analysis demonstrated that thanatophagy occurred in a manner that was dependent on the time of death. The autophagy-associated proteins, LC3 II, p62, Beclin-1 and Atg7, increased in a time-dependent manner in heart tissues. A potent inducer of autophagy, BNIP3, decreased in the heart tissues as time of death increased, whereas the protein levels increased in brain tissues. However, there was no expression of BNIP3 at extended postmortem intervals in both brain and heart samples. Collectively, the present study demonstrates for the first time that thanatophagy occurs in brain and heart tissues of cadavers in a time-dependent manner. Further, our data suggest that cerebral thanatophagy may occur in a Beclin-1- independent manner. This unprecedented study provides potential insight into thanatophagy as a novel method for the estimation of the time of death in criminal investigations     

Impact of left ventricular assist device (LVAD) support on the cardiac reverse remodeling process

With improved technology and expanding indications for use, left ventricular assist devices (LVADs) are assuming a greater role in the care of patients with end-stage heart failure. Following LVAD implantation with the intention of bridge to transplant, it became evident that some patients exhibit substantial recovery of ventricular function. This prompted explantation of some devices in lieu of transplantation, the so-called bridge-to-recovery (BTR) therapy. However, clinical outcomes following these experiences are not always successful. Patients treated in this fashion have often progressed rapidly back to heart failure. Special knowledge has emerged from studies of hearts supported by LVADs that provides insights into the basic mechanisms of ventricular remodeling and possible limits of ventricular recovery. In general, it was these studies that spawned the concept of reverse remodeling now recognized as an important goal of many heart failure treatments. Important examples of myocardial and/or ventricular properties that do not regress towards normal during LVAD support include abnormal extracellular matrix metabolism, increased tissue angiotensin levels, myocardial stiffening and partial recovery of gene expression involved with metabolism. Nevertheless, studies of LVAD-heart interactions have led to the understanding that although we once considered the end-stage failing heart of patients near death to be irreversibly diseased, an unprecedented degree of myocardial recovery is possible, when given sufficient mechanical unloading and restoration of more normal neurohormonal milieu. Evidence supporting and unsupporting the notion of reverse remodeling and clinical implications of this process will be reviewed.     

Polarity in Mammalian Epithelial Morphogenesis

Cell polarity is fundamental for the architecture and function of epithelial tissues. Epithelial polarization requires the intervention of several fundamental cell processes, whose integration in space and time is only starting to be elucidated. To understand what governs the building of epithelial tissues during development, it is essential to consider the polarization process in the context of the whole tissue. To this end, the development of three-dimensional organotypic cell culture models has brought new insights into the mechanisms underlying the establishment and maintenance of higher-order epithelial tissue architecture, and in the dynamic remodeling of cell polarity that often occurs during development of epithelial organs. Here we discuss some important aspects of mammalian epithelial morphogenesis, from the establishment of cell polarity to epithelial tissue generation.     

Mechanical and electrical interactions in bone remodeling

The natural remodeling and adaptation of skeletal tissues in response to mechanical loading is a classic example of physical regulation in biology. It is largely because it involves forces that do not seem to fit into the familiar schemes of biochemical controls that bone adaptation mechanisms have intrigued us for at least a century. The effect of electromagnetic fields on organisms is another example of this, and the two have become linked in an attempt to explain bone remodeling (“Yasuda's hypothesis”). This paper re-examines the roles of endogenous and exogenous electromagnetic fields in the response of bone to mechanical forces. A series of experiments is reviewed in which mechanical and electrical stimuli were applied to implants in the medullary canal of rabbit long bones. The results suggest that endogenously generated electrical currents are not required to initiate mechanically stimulated bone formation, but that direct mechanical effects on bone cells is the more likely scenario. Based on this and other evidence from the literature, it is suggested that when exogenous electromagnetic stimuli are applied, bone cells respond by modulating the activity of more primary activators such as hormones, growth factors, cytokines, and mechanical forces. Bioelectromagnetics 18:193–202, 1997. © 1997 Wiley-Liss, Inc.     

Comparative Mechanical Properties and Histology of Bone

Different bone tissues differ in their amounts of porosity,mineralization,reconstruction, and preferred orientation. Allthese have important effects on mechanical properties. Veryporous, cancellous bone is always weaker and morecompliant thancompact bone on a weight for weight basis, yet it occurs inplaceswhere its energyabsorbing ability, or its low density,is advantageous. Bonevaries considerably in its mineralization,and such variations have quite disproportionate effects on mechanicalproperties. These variations can be shown to be adaptive. Inparticular, there must always be a compromise between stiffnessandresistanceto fracture; these two properties run contrary to each other.The reason for secondary remodeling is an unresolved problem,though in a few places the role of such remodeling in changingthe grain of the bone is clearly mechanically adaptive. Themechanical properties of non-mammalian bone are obscure, andas the histology of such bone is often quite different fromthat of mammalian bone, we are no doubt in for some surpriseswhen the mechanical properties ofnonmammalian bone are discovered.     

Interstitial fluid flow in canaliculi as a mechanical stimulus for cancellous bone remodeling: in silico validation

Cancellous bone has a dynamic 3-dimensional architecture of trabeculae, the arrangement of which is continually reorganized via bone remodeling to adapt to the mechanical environment. Osteocytes are currently believed to be the major mechanosensory cells and to regulate osteoclastic bone resorption and osteoblastic bone formation in response to mechanical stimuli. We previously developed a mathematical model of trabecular bone remodeling incorporating the possible mechanisms of cellular mechanosensing and intercellular communication in which we assumed that interstitial fluid flow activates the osteocytes to regulate bone remodeling. While the proposed model has been validated by the simulation of remodeling of a single trabecula, it remains unclear whether it can successfully represent in silico the functional adaptation of cancellous bone with its multiple trabeculae. In the present study, we demonstrated the response of cancellous bone morphology to uniaxial or bending loads using a combination of our remodeling model with the voxel finite element method. In this simulation, cancellous bone with randomly arranged trabeculae remodeled to form a well-organized architecture oriented parallel to the direction of loading, in agreement with the previous simulation results and experimental findings. These results suggested that our mathematical model for trabecular bone remodeling enables us to predict the reorganization of cancellous bone architecture from cellular activities. Furthermore, our remodeling model can represent the phenomenological law of bone transformation toward a locally uniform state of stress or strain at the trabecular level.