A multiscale modeling framework for studying the mechanobiology of sarcopenic obesity.

An inactive sedentary lifestyle is a common risk factor contributing to sarcopenic obesity. At the cell scale, sustained mechanical deformations of the plasma membrane (PM) in adipocytes, characterizing chronic static loading in weight-bearing tissues during prolonged sitting or lying, were found to promote adipogenesis. Taking a mechanobiological perspective, we correlated here the macroscale mechanical deformations of weight-bearing adipose tissues (subcutaneous and intramuscular) with mechanical strains developing in the PMs of differentiating adipocytes. An innovative multiscale modeling framework for adipose tissues was developed for this purpose, where the buttocks, adipose tissues, adipocytes and the subcellular components: intracytoplasmic nucleus and lipid droplets as well as the PMs of the cells, were all represented. We found that a positive feedback loop very likely exists and is involved in the onset and progression of sarcopenic obesity, as follows. Adipogenesis in statically deformed adipocytes results in gaining more macroscopic subcutaneous and intramuscular fat mass, which then increases fat deformations macroscopically and microscopically, and hence triggers additional adipogenesis, and so on. Our present study is highly relevant in research of sarcopenic obesity and other adipose-related diseases such as diabetes, since mechanical distortion of adipocytes promotes adipogenesis and fat gain at the different dimensional scales.

Contoured Foam Cushions Cannot Provide Long-term Protection Against Pressure-Ulcers for Individuals with a Spinal Cord Injury: Modeling Studies.

OBJECTIVE: To determine changes in internal soft-tissue loads in the buttocks of individuals with a spinal cord injury (SCI), who undergo pathoanatomical changes during the first months and years following the occurrence of the SCI, while sitting on a contoured foam cushion (CFC) that has been fitted close to the time of the injury but has not been replaced in subsequent years. DESIGN: Internal tissue loads in variant buttocks anatomies on a CFC were analyzed by means of finite element computer simulations. The pathoanatomical changes that are characteristic to SCI and were simulated here are: increase in fat tissue mass, intramuscular fat infiltration, muscle atrophy, and combinations of these conditions. SETTING: Computational biomechanical modeling. MAIN RESULTS: Simulating the aforementioned pathoanatomical changes consistently resulted in greater mechanical strain and stress magnitudes and more inhomogeneity in the loading state of muscle and fat tissues, with a more profound effect in fat. The simulations further indicated a clear trend of exacerbation in tissue exposure to loads as the pathoanatomical changes progress chronologically and the CFC is not replaced. CONCLUSIONS: A CFC that has been fitted at a time close to the SCI, but has not been replaced in subsequent years, substantially loses its efficacy in protecting patients from developing pressure ulcers and deep tissue injury in particular.

Simulating single cell experiments in mechanical testing of adipocytes.

This study introduces new three-dimensional finite element cell modeling for simulating the structural, large deformation behavior of maturing adipocytes, based on empirically acquired geometrical properties of cultured adipocyte cells. We created models of adipocyte differentiation and maturation, which represented four stages along that process. The modeling focused on two specific and commonly used experimental setups, one involving compression of individual adipocytes and the other stretching of adipocytes. Both are physiological loading regimes for fat tissues and cells in vivo, and both are often employed for testing cell responses to deformations in the context of obesity and pressure ulcer research. In both simulation types, and in all the cell models, external loads induced localized effective Lagrange strains in the plasma membrane that reached maximum values over the lipid droplets (LDs). We also observed that the effective stresses (averaged across the entire cell volume in each model case) increased with cell maturation and varied between cells with different structure and dimensions. This result points to an increase in the effective cell stiffness with maturation, which would have been expected, since the volume of the stiffer LDs increases as adipocytes mature. Overall, the mechanical behavior of an individual cell is influenced not only by the external mechanical loads that are exerted, but also by the cell structure and dimensions, and is fundamental to any interpretation of cell mechanics experiments, and particularly for testing adipocytes.

Multiscale modeling of tissue-engineered fat: is there a deformation-driven positive feedback loop in adipogenesis?

Mechanotransduction plays a role in adipose tissues by transducing the environmental mechanical signals. It is recognized that dynamic or cyclic mechanical strains suppress adipogenesis, but static strains activate the adipogenic signaling pathways. This phenomenon needs to be investigated further, given its potential use in tissue engineering of fat. We used in vitro cultures as model systems for studying differentiation and function of adipocytes. Additionally, using the finite element method, we developed here sets of multiscale models (MSM), which represent single or multiple adipocytes embedded in scaffolds, stimulated mechanically in a static regime. Based on in vitro adipocyte culture work, these models were employed to study the hypothesis that the loading state of the plasma membrane (PM) in adipocytes is influenced by neighboring cells, which could reflect positive feedback loops of en mass adipose cell differentiation. We demonstrate that under static loading, tensile strains at the PM increase with the stage of cell maturation. Furthermore, when the cell density was sufficient (above 19 cells per 100 µm(3)), progressive differentiation in some of the cells caused higher magnitudes of tensile strains in the PMs of other nearby cells. MSM are currently the only feasible means to correlate continuum (macrolevel) construct deformations to subcellular-level PM stretches in distorted cells. These macro-to-micro mechanobiology relationships, revealed through MSM, point to stimulations that promote the formation of lipid droplet accumulations and the increase of adipogenesis. Such models are a cost-effective useful platform for achieving better understanding of these deformation-driven cell processes toward optimized design of tissue-engineered fat constructs.

Effects of accumulation of lipid droplets on load transfer between and within adipocytes.

Adipogenesis, a process of cell proliferation followed by the accumulation of lipid droplets (LDs), is accompanied by morphological changes in adipocytes, leading to a gradual rise in the structural stiffness of these cells. The increase in cellular structural stiffness can potentially influence the localized deformations of adjacent adipocytes in weight-bearing fat tissues, which, based on previous work, may accelerate intracytoplasmatic lipid production to form even larger and more tightly packed intracellular LDs. This process is based on mechanotransduction phenomena which are hypothesized (again, following empirical studies), to play a critical role in "en mass" adipocyte hypertrophy, and hence are important to characterize through computational modeling. Accordingly, we examined here how maturing adipocytes may affect localized loads acting on adjacent immature cells, using a set of finite element models of adipocytes embedded in an extracellular matrix. The peak strain energy density at the plasma membrane (PM) of the adipocytes, when constructs were externally loaded, was found to depend on the levels of lipid accumulation in the neighboring cells if the external compressive and shear deformations were large enough ([Formula: see text] and [Formula: see text], respectively). The mechanosignaling transduces through the PM and could therefore affect intracellular pathways to produce more lipid contents. Our results support the theory of deformation-induced differentiation in adipocytes. The findings are thus relevant in the context of a sedentary lifestyle, in which sustained deformations of weight-bearing adipose tissues may activate a positive feedback loop that promotes the "en mass" differentiation of cells, which subsequently increases the total mass of living fat tissues.

Adipocyte stiffness increases with accumulation of lipid droplets.

Adipogenesis and increase in fat tissue mass are mechanosensitive processes and hence should be influenced by the mechanical properties of adipocytes. We evaluated subcellular effective stiffnesses of adipocytes using atomic force microscopy (AFM) and interferometric phase microscopy (IPM), and we verified the empirical results using finite element (FE) simulations. In the AFM studies, we found that the mean ratio of stiffnesses of the lipid droplets (LDs) over the nucleus was 0.83 ± 0.14, from which we further evaluated the ratios of LDs over cytoplasm stiffness, as being in the range of 2.5 to 8.3. These stiffness ratios, indicating that LDs are stiffer than cytoplasm, were verified by means of FE modeling, which simulated the AFM experiments, and provided good agreement between empirical and model-predicted structural behavior. In the IPM studies, we found that LDs mechanically distort their intracellular environment, which again indicated that LDs are mechanically stiffer than the surrounding cytoplasm. Combining these empirical and simulation data together, we provide in this study evidence that adipocytes stiffen with differentiation as a result of accumulation of LDs. Our results are relevant to research of adipose-related diseases, particularly overweight and obesity, from a mechanobiology and cellular mechanics perspectives.

The mechanics of hyaluronic acid/adipic acid dihydrazide hydrogel: towards developing a vessel for delivery of preadipocytes to native tissues.

Promising treatment approaches in repairing tissue defects include implementation of regenerative medicine strategies, particularly delivery of preadipocytes to sites where adipose tissue damage needs to be repaired or where fat needs to be generated. In this study, we suggest that the injectable hyaluronic acid/adipic acid dihydrazide (HA/ADH) hydrogel may be an adipose-tissue-like material in terms of biological compatibility as well as mechanical behavior. First, we show that the hydrogel enables and supports growth, proliferation and differentiation of 3T3-L1 preadipocytes. Second, given that adipose tissue is a weight-bearing biological structure, we investigate the large deformation mechanical behavior of the hydrogel with and without embedded preadipocytes, by performing confined and unconfined compression tests and then calibrating a strain energy density (SED) function to the results. Four test groups were examined: (1) Hydrogel specimens right after the preparation without cells, (2) and (3) 3-days-cultured hydrogel specimens with and without cells, respectively, and (4) 6-days-cultured hydrogel specimens with cells. A one-term Ogden SED was found to adequately describe the hyperelastic behavior of the hydrogel specimens in all experimental groups. Importantly, we found that the mechanical properties of the hydrogel, when subjected to compression, are in good agreement with those of native adipose tissue, with the better fit occurring 3-6 days after preparation of the hydrogel. Third, computational finite element studies of the mechanical (stress-strain) behavior of the HA/ADH hydrogel when containing mature adipocytes indicated that the stiffnesses of the constructs were mildly affected by the presence of the adipocytes. Hence, we conclude that injectable HA/ADH hydrogel may serve as a vessel for protecting preadipocytes during, and at a short-term after delivery to native tissues, e.g. in research towards regenerative medicine in tissue reconstructions.

A new technique for studying directional cell migration in a hydrogel-based three-dimensional matrix for tissue engineering model systems.

Cell migration has a key role in biological processes, e.g. malignancy, wound healing, immune response and morphogenesis. Studying migration and factors that influence it is beneficial, e.g. for developing drugs to suppress metastasis, heal wounds faster or enhance the response to infection. Though the majority of the literature describes two-dimensional (2D) migration studies in culture dishes, a more realistic approach is to study migration in three-dimensional (3D) constructs. However, simple-to-implement, straight-forward standardized quantitative techniques for analysis of migration rates of cell colonies in 3D are still required in the field. Here, we describe a new model system for quantifying directional migration of colonies in a hyaluronic acid (oxi-HA) and adipic acid dihydrazide (ADH) hydrogel-based 3D matrix. We further demonstrate that our previously reported image processing technique for measuring migration in 2D (Topman et al., 2011, 2012) is extendable for analyzing the rates of migration of cells that directionally migrate in the hydrogel and are fluorescently stained with a 4',6-diamidino-2-phenylindole (DAPI) nuclear stain. Together, the present experimental setup and image processing algorithm provide a standard test bench for measuring migration rates in a fully automated, robust assay which is useful for high-throughput screening in large-scale drug evaluations, where effects on migration in a 3D matrix are sought.

Deformations, mechanical strains and stresses across the different hierarchical scales in weight-bearing soft tissues.

Sustained internal tissue loads (deformations, mechanical strains and stresses) which develop during immobile weight-bearing postures such as while in bed or in a chair were identified as a fundamental cause for the onset and progression of pressure ulcers (PUs), particularly of the deep tissue injury (DTI) type. The sustained loading may compromise tissue viability either directly, by geometrically distorting cells, or indirectly, by distorting the vasculature or lymphatic networks or, at the micro-scale, by distorting cellular organelles involved in regulating transport, e.g. the plasma membrane, since transport-control-mechanisms are essential for adequate biological function of cells. In this article we provide a comprehensive, rigorous review of the up-to-date published computational-modeling-work as well as relevant experimental studies concerning tissue deformations, strains and stresses across the different hierarchical scales: tissue-scale [cm], meso-scale [mm] and cell-scale [µm]. Viability of tissues exposed to sustained loading should be investigated in all dimensional scales, from the macro to micro, in order to provide complete understanding of the etiology of PUs and DTIs and in particular, for identifying individuals for whom and conditions at which the susceptibility to these injuries might be greater. Emerging relevant bioengineering methods of computer simulation such as multiscale and multiphysics modeling will undoubtedly contribute to the aetiological research in this field in the near future.

The influence of mechanical stretching on mitosis, growth, and adipose conversion in adipocyte cultures.

The mechanotransduction of adipocytes is not well characterized in the literature. In this study, we employ stochastic modeling fitted to experiments for characterizing the influence of mechanical stretching delivered to adipocyte monolayers on the probabilities of commitment to the adipocyte lineage, mitosis, and growth after mitosis in 3T3-L1 adipocytes. We found that the probability of a cell to become committed to the adipocyte lineage in a single division when cultured on an elastic substrate was 0.025, which was indistinguishable between cultures that were radially stretched (to 12% strain) and control cultures. The probability of undergoing mitosis however was different between the groups, being 0.4 in the stretched cultures and 0.6 in the controls. The probability of growing after mitosis was affected by the stretching as well and was 0.9 and 0.8 in the stretched and control groups, respectively. We conclude that static stretching of the substrate of adipocyte cultures influences the mitotic potential of the cells as well as the growth potential post-mitosis. The present work provides better understanding of the mechanotransduction of adipocytes and in particular quantify how stretching influences the likelihood of cell proliferation and differentiation and, consequently, adipogenesis in the adipocyte cultures.

Static mechanical stretching accelerates lipid production in 3T3-L1 adipocytes by activating the MEK signaling pathway.

Understanding mechanotransduction in adipocytes is important for research of obesity and related diseases. We cultured 3T3-L1 preadipocytes on elastic substrata and applied static tensile strains of 12% to the substrata while inducing differentiation. Using an image processing method, we monitored lipid production for a period of 3-4 wk. The ratio of %-lipid area per field of view (FOV) in the stretched over nonstretched cultures was significantly greater than unity (P < 0.05), reaching ∼1.8 on average starting from experimental day ∼10. The superior coverage of the FOV by lipids in the stretched cultures was due to significantly greater sizes of lipid droplets (LDs) with respect to nonstretched cultures, starting from experimental day ∼10 (P < 0.05), and due to significantly more LDs per cell between days ∼10 and ∼17 (P < 0.05). The statically stretched cells also differentiated significantly faster than the nonstretched cells within the first ∼10 days (P < 0.05). Adding peroxisome proliferator-activated receptor-γ (PPARγ) antagonist did not change these trends, as the %-lipid area per FOV in the stretched cultures that received this treatment was still significantly greater than in the nonstretched cultures without the PPARγ antagonist (14.44 ± 1.96% vs. 10.21 ± 3%; P < 0.05). Hence, the accelerated adipogenesis in the stretched cultures was not mediated through PPARγ. Nonetheless, inhibiting the MEK/MAPK signaling pathway reduced the extent of adipogenesis in the stretched cultures (13.53 ± 5.63%), bringing it to the baseline level of the nonstretched cultures without the MEK inhibitor (10.21 ± 3.07%). Our results hence demonstrate that differentiation of adipocytes can be enhanced by sustained stretching, which activates the MEK signaling pathway.

Large, but not small sustained tensile strains stimulate adipogenesis in culture.

Understanding the mechanoresponsiveness of adipocytes and the characteristics of the mechanical stimuli that regulate adipogenesis is critically important in establishing knowledge in regard to the long-term effects of a sedentary lifestyle (or immobility in extreme medical conditions) as well as concerning obesity and related diseases. In this study we subjected 3T3-L1 preadipocytes cultured on elastic substrata to different levels of static equiaxial tensile strains within the physiological range, up to substrate tensile strain (STS) of 12%, while inducing differentiation in the cultures. Based on prior work which revealed that adipogenesis is accelerated in cultures subjected to STS of 12% by activating the mitogen-activated protein kinase kinase signaling pathway, we were specifically interested in identifying the STS levels which trigger this process. We hence monitored the production and accumulation of lipid droplets (LDs) using a non-destructive, image-processing-based method that we have previously developed, for a period of 4 weeks. The experimental data demonstrated accelerated adipogenesis in the cultures subjected to STS levels of 6%, 9%, and 12% with respect to cultures subjected to STS of 3% and (non-stretched) control cultures. This accelerated adipogenic response to the large sustained STS manifested in significantly larger numbers and greater sizes of LDs in the cultures that were stretched to large STS levels (p < 0.05), starting at approximately day 14 following induction of differentiation. Hence, indeed, there appears to be a certain tensile strain threshold, or domain-which is found within the physiological range-above which the responsiveness of adipocytes to sustained static stretching increases and is manifested in accelerated adipogenesis.

Mechanotransduction in adipocytes.

Obesity is widely recognized as a major public health problem due to its strong association with a number of serious chronic diseases including hyperlipidemia, hypertension, type II diabetes and coronary atherosclerotic heart disease. During the development of obesity, the positive energy balance involves recruitment of new adipocytes from preadipocytes in adipose tissue, which have proliferated and differentiated. Given that cells in adipose tissues are physiologically exposed to compound mechanical loading: tensile, compressive and shear strains/stresses, which are caused by bodyweight loads as well as by weight-bearing, it is important to determine whether the adipose conversion process is influenced by mechanical stimulations. In this article we provide a comprehensive review of the experimental studies addressing mechanotransduction in adipocytes, as well as of mathematical and computational models that are useful for studying mechanotransduction in adipocytes or for quantifying the responsiveness of adipocytes to different types of mechanical loading. The new understanding that adipogenesis is influenced by mechanical stimulations has the potential to open new and important research paths, driven by mechanotransduction, to explore mechanisms as well as treatment approaches in obesity and related conditions.

Stochastic modeling of adipogenesis in 3T3-L1 cultures to determine probabilities of events in the cell's life cycle.

3T3-L1 preadipocytes are often being used in research of adipose-related diseases such as obesity, insulin resistance, and hyperlipidemia. We developed a stochastic model that simulated differentiation of four 3T3-L1 culture conditions distinct by the insulin concentration in the differentiation medium (2.5, 5, 7.5, or 10 µg/mL). The model simulated culture behavior and the accumulation of lipid droplets in the maturing cells from the day of induction of differentiation through 28 days after that. The cellular processes including cell adhesion, mitosis, growing after undergoing mitosis, commitment to the adipocyte lineage, and apoptosis were referred to as stochastic events in the modeling. By minimizing the error between our model and experimental results, we found that the probability for becoming committed to the adipocyte lineage in a single division and the probability for growing after undergoing mitosis were 0.02 and 0.8, respectively, regardless of the insulin concentration. The probability for undergoing mitosis was equal to 0.2 and 0.4 in cultures that had insulin concentrations of 2.5 and 5-10 µg/mL in the differentiation medium, respectively; hence the insulin concentration affected the probability for mitosis in the 3T3-L1 cells. The model and resulted probabilities now allow quantitative and visual predictions of adipogenesis in 3T3-L1 cultures, toward computational design of cell culturing protocols.