A pinboard by
Tommaso Ristori

PhD candidate, Technical University of Eindhoven


Predicting and understanding cellular forces and (re)orientation in response to different stimuli

Our body is populated by trillions of cells that constantly remodel and respond to the stimuli of their surroundings. For example, cells are known to change their orientation in response to the mechanical stimuli caused by blood flow and the topographical stimuli provided by collagen fibers, the most abundant protein in our bodies. Mostly along their main direction, cells exert traction forces that can influence the biomechanics and functionality of tissues in our bodies. For instance, excessive cellular forces can lead to unwanted retraction and opening of heart valves, fundamental structures that ensure the unidirectionality of the blood circulation. Predicting and understanding cellular forces and (re)orientation is therefore of paramount importance.

In this context, computational simulations are very useful because of their predictive potential and versatility in testing different hypotheses. During my PhD I have developed unique computational models for the prediction and explanation of the remodeling and (re)orientation of cells in response to a wide range of mechanical and topographical stimuli. For the first time, these computational models could predict cellular forces and (re)orientation both in two- and three-dimensional environments. Overall, the computational simulations suggest that many feedback mechanisms contribute to the responses of cells to the stimuli coming from their surroundings.

In a subsequent study, I have coupled the models for cellular (re)orientation with a mathematical model for collagen remodeling. These coupled computational models were adopted to investigate cellular and collagen remodeling in native heart valves. Investigating collagen remodeling in such tissues is particularly important, because collagen fibers are their main load-bearing constituent, and collagen fiber organization strongly influences the heart valve functionality.

Strikingly, the computational simulations could successfully predict and explain the fundamental contribution of cells for the organization of collagen fibers in native heart valves. This computational approach is not only useful to understand native heart valves, but it also provides useful information for the improvement of current therapies for heart valve diseases, and the advancement of the growing field of regenerative medicine. Furthermore, it is also applicable to a wide range of other tissues, such as arteries and tendons.


A kinematic model of stretch-induced stress fiber turnover and reorientation.

Abstract: A kinetic model based on constrained mixture theory was developed to describe the reorganization of actin stress fibers in adherent cells in response to diverse patterns of mechanical stretch. The model was based on reports that stress fibers are pre-extended at a "homeostatic" level under normal, non-perturbed conditions, and that perturbations in stress fiber length destabilize stress fibers. In response to a step change in matrix stretch, the model predicts that stress fibers are initially stretched in registry with the matrix, but that these overly stretched fibers are gradually replaced by new fibers assembled with the homeostatic level of stretch in the new configuration of the matrix. In contrast, average fiber stretch is chronically perturbed from the homeostatic level when the cells are subjected to cyclic equibiaxial stretch. The model was able to describe experimentally measured time courses of stress fiber reorientation perpendicular to the direction of cyclic uniaxial stretch, as well as the lack of alignment in response to equibiaxial stretch. The model also accurately described the relationship between stretch magnitude and the extent of stress fiber alignment in endothelial cells subjected to cyclic uniaxial stretch. Further, in the case of cyclic simple elongation with transverse matrix contraction, stress fibers orient in the direction of least perturbation in stretch. In summary, the model predicts that the rate of stretch-induced stress fiber disassembly determines the rate of alignment, and that stress fibers tend to orient toward the direction of minimum matrix stretch where the rate of stress fiber turnover is a minimum.

Pub.: 26 Dec '08, Pinned: 29 Oct '17

Cell-mediated retraction versus hemodynamic loading - A delicate balance in tissue-engineered heart valves.

Abstract: Preclinical studies of tissue-engineered heart valves (TEHVs) showed retraction of the heart valve leaflets as major failure of function mechanism. This retraction is caused by both passive and active cell stress and passive matrix stress. Cell-mediated retraction induces leaflet shortening that may be counteracted by the hemodynamic loading of the leaflets during diastole. To get insight into this stress balance, the amount and duration of stress generation in engineered heart valve tissue and the stress imposed by physiological hemodynamic loading are quantified via an experimental and a computational approach, respectively. Stress generation by cells was measured using an earlier described in vitro model system, mimicking the culture process of TEHVs. The stress imposed by the blood pressure during diastole on a valve leaflet was determined using finite element modeling. Results show that for both pulmonary and systemic pressure, the stress imposed on the TEHV leaflets is comparable to the stress generated in the leaflets. As the stresses are of similar magnitude, it is likely that the imposed stress cannot counteract the generated stress, in particular when taking into account that hemodynamic loading is only imposed during diastole. This study provides a rational explanation for the retraction found in preclinical studies of TEHVs and represents an important step towards understanding the retraction process seen in TEHVs by a combined experimental and computational approach.

Pub.: 26 Nov '13, Pinned: 29 Oct '17

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

Abstract: 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.

Pub.: 29 Dec '13, Pinned: 29 Oct '17

Computational and experimental investigation of local stress fiber orientation in uniaxially and biaxially constrained microtissues.

Abstract: The orientation of cells and associated F-actin stress fibers is essential for proper tissue functioning. We have previously developed a computational model that qualitatively describes stress fiber orientation in response to a range of mechanical stimuli. In this paper, the aim is to quantitatively validate the model in a static, heterogeneous environment. The stress fiber orientation in uniaxially and biaxially constrained microscale tissues was investigated using a recently developed experimental system. Computed and experimental stress fiber orientations were compared, while accounting for changes in orientation with location in the tissue. This allowed for validation of the model, and additionally, it showed how sensitive the stress fiber orientation in the experimental system is to the location where it is measured, i.e., the heterogeneity of the stress fiber orientation. Computed and experimental stress fiber orientations showed good quantitative agreement in most regions. A strong local alignment near the locations where boundary conditions were enforced was observed for both uniaxially and biaxially constrained tissues. Excepting these regions, in biaxially constrained tissues, no preferred orientation was found and the distribution was independent of location. The stress fiber orientation in uniaxially constrained tissues was more heterogeneous, and stress fibers mainly oriented in the constrained direction or along the free edge. These results indicate that the stress fiber orientation in these constrained microtissues is mainly determined by the local mechanical environment, as hypothesized in our model, and also that the model is a valid tool to predict stress fiber orientation in heterogeneously loaded tissues.

Pub.: 25 Jan '14, Pinned: 29 Oct '17

A computational analysis of cell-mediated compaction and collagen remodeling in tissue-engineered heart valves

Abstract: One of the most critical problems in heart valve tissue engineering is the progressive development of valvular insufficiency due to leaflet retraction. Understanding the underlying mechanisms of this process is crucial for developing tissue-engineered heart valves (TEHVs) that maintain their functionality in the long term. In the present study, we adopted a computational approach to predict the remodeling process in TEHVs subjected to dynamic pulmonary and aortic pressure conditions, and to assess the risk of valvular insufficiency. In addition, we investigated the importance of the intrinsic cell contractility on the final outcome of the remodeling process. For valves implanted in the aortic position, the model predictions suggest that valvular insufficiency is not likely to occur as the blood pressure is high enough to prevent the development of leaflet retraction. In addition, the collagen network was always predicted to remodel towards a circumferentially aligned network, which is corresponding to the native situation. In contrast, for valves implanted in the pulmonary position, our model predicted that there is a high risk for the development of valvular insufficiency, unless the cell contractility is very low. Conversely, the development of a circumferential collagen network was only predicted at these pressure conditions when cell contractility was high. Overall, these results, therefore, suggest that tissue remodeling at aortic pressure conditions is much more stable and favorable compared to tissue remodeling at pulmonary pressure conditions.

Pub.: 19 Oct '15, Pinned: 25 Oct '17

Free energy analysis of cell spreading.

Abstract: In this study we present a steady-state adaptation of the thermodynamically motivated stress fiber (SF) model of Vigliotti et al. (2015). We implement this steady-state formulation in a non-local finite element setting where we also consider global conservation of the total number of cytoskeletal proteins within the cell, global conservation of the number of binding integrins on the cell membrane, and adhesion limiting ligand density on the substrate surface. We present a number of simulations of cell spreading in which we consider a limited subset of the possible deformed spread-states assumed by the cell in order to examine the hypothesis that free energy minimization drives the process of cell spreading. Simulations suggest that cell spreading can be viewed as a competition between (i) decreasing cytoskeletal free energy due to strain induced assembly of cytoskeletal proteins into contractile SFs, and (ii) increasing elastic free energy due to stretching of the mechanically passive components of the cell. The computed minimum free energy spread area is shown to be lower for a cell on a compliant substrate than on a rigid substrate. Furthermore, a low substrate ligand density is found to limit cell spreading. The predicted dependence of cell spread area on substrate stiffness and ligand density is in agreement with the experiments of Engler et al. (2003). We also simulate the experiments of Théry et al. (2006), whereby initially circular cells deform and adhere to "V-shaped" and "Y-shaped" ligand patches. Analysis of a number of different spread states reveals that deformed configurations with the lowest free energy exhibit a SF distribution that corresponds to experimental observations, i.e. a high concentration of highly aligned SFs occurs along free edges, with lower SF concentrations in the interior of the cell. In summary, the results of this study suggest that cell spreading is driven by free energy minimization based on a competition between decreasing cytoskeletal free energy and increasing passive elastic free energy.

Pub.: 25 Jun '17, Pinned: 25 Oct '17

Computational model predicts cell orientation in response to a range of mechanical stimuli.

Abstract: To build anisotropic, mechanically functioning tissue, it is essential to understand how cells orient in response to mechanical stimuli. Therefore, a computational model was developed which predicts cell orientation, based on the actin stress fiber distribution inside the cell. In the model, the stress fiber distribution evolves dynamically according to the following: (1) Stress fibers contain polymerized actin. The total amount of depolymerized plus polymerized actin is constant. (2) Stress fibers apply tension to their environment. This active tension is maximal when strain rate and absolute strain are zero and reduces with increasing shortening rate and absolute strain. (3) A high active fiber stress in a direction leads to a large amount of fibers in this direction. (4) The cell is attached to a substrate; all fiber stresses are homogenized into a total cell stress, which is in equilibrium with substrate stress. This model predicts that on a substrate of anisotropic stiffness, fibers align in the stiffest direction. Under cyclic strain when the cellular environment is so stiff that no compaction occurs (1 MPa), the model predicts strain avoidance, which is more pronounced with increasing strain frequency or amplitude. Under cyclic strain when the cellular environment is so soft that cells can compact it (10 kPa), the model predicts a preference for the cyclically strained compared to the compacting direction. These model predictions all agree with experimental evidence. For the first time, a computational model predicts cell orientation in response to this range of mechanical stimuli using a single set of parameters.

Pub.: 28 May '13, Pinned: 25 Oct '17