Weickenmeie, J.; Saez, P.; Butler, C.; Young, P.G.; Gorily, A.; Kuhl, E. Journal of elasticity Vol. 129, num. 1-2, p. 197-212 DOI: 10.1007/s10659-016-9606-1 Data de publicació: 2017-12 Article en revista
Brain swelling is a serious condition associated with an accumulation of fluid inside the brain caused by trauma, stroke, infection, or tumors. It increases the pressure inside the skull and reduces blood and oxygen supply. To relieve the intracranial pressure, neurosurgeons remove part of the skull and allow the swollen brain to bulge outward, a procedure that is widely known as decompressive craniectomy. Decompressive craniectomy has been preformed for more than a century; yet, its e¿ects on the swollen brain remain poorly understood. Here we characterize the deformation, strain, and stretch in bulging brains using the nonlinear field theories of mechanics. Our study shows that even small swelling volumes of 28 and 56ml induce maximum principal strains in excess of 30%. For radially outward-pointing axons, we observed maximal normal stretches of 1.3 deep inside the bulge and maximal shear stretches of 1.3 around the craniectomy edge. While the stretch magnitude varies with opening site and swelling site, our study suggests that the locations of maximum stretch are universally shared amongst all bulging brains. Our model can inform neurosurgeons and rationalize the shape and position of the skull opening, with the overall goal to reduce brain damage and improve the structural and functional outcomes of decompressive craniectomy.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10659-016-9606-1
Fingertips wrinkle due to long exposure to water. The biological reason for this morphological change is unclear and still not fully understood. There are two main hypotheses for the underlying mechanism of fingertip wrinkling: the ‘shrink’ model (in which the wrinkling is driven by the contraction of the lower layers of skin, associated with the shrinking of the underlying vasculature), and the ‘swell’ model (in which the wrinkling is driven by the swelling of the upper layers of the skin, associated with osmosis). In reality, contraction of the lower layers of the skin and swelling of the upper layers will happen simultaneously. However, the relative importance of these two mechanisms to drive fingertip wrinkling also remains unclear. Simulating the swelling in the upper layers of skin alone, which is associated with neurological disorders, we found that wrinkles appeared above an increase of volume of ˜10%.˜10%. Therefore, the upper layers can not exceed this swelling level in order to not contradict in vivo observations in patients with such neurological disorders. Simulating the contraction of the lower layers of the skin alone, we found that the volume have to decrease a ˜20%˜20% to observe wrinkles. Furthermore, we found that the combined effect of both mechanisms leads to pronounced wrinkles even at low levels of swelling and contraction when individually they do not. This latter results indicates that the collaborative effect of both hypothesis are needed to induce wrinkles in the fingertips. Our results demonstrate how models from continuum mechanics can be successfully applied to testing hypotheses for the mechanisms that underly fingertip wrinkling, and how these effects can be quantified.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10439-016-1764-6
Mechanical forces transmitted through specific molecular bonds drive biological function, and their understanding and control hold an uncharted potential in oncology, regenerative medicine and biomaterial design. However, this potential has not been realised, because it requires developing and integrating disparate technologies to measure and manipulate mechanical and adhesive properties from the nanometre to the metre scale. We propose to address this challenge by building an interdisciplinary research community with the aim of understanding and controlling cellular mechanics from the molecular to the organism scale. At the nanometric molecular level, we will develop cellular microenvironments enabled by peptidomimetics of cell-cell and cell-matrix ligands, with defined mechanical and adhesive properties that we will dynamically control in time and space trough photo-activation. The properties under force of the molecular bonds involved will be characterized using single-molecule atomic force microscopy and magnetic tweezers. At the cell-to-organ scale, we will combine controlled microenvironments and interfering strategies with the development of techniques to measure and control mechanical forces and adhesion in cells and tissues, and to evaluate their biological response. At the organism scale, we will establish how cellular mechanics can be controlled, by targeting specific adhesive interactions, to impair or abrogate breast tumour progression in a mouse model. At all stages and scales of the project, we will integrate experimental data with multi-scale computational modelling to establish the rules driving biological response to mechanics and adhesion. With this approach, we aim to develop specific therapeutic approaches beyond the current paradigm in breast cancer treatment. Beyond breast cancer, the general principles targeted by our technology will have high applicability in oncology, regenerative medicine and biomaterials.
Endothelial cells (ECs) play a significant role in modulating arterial functions [1,2]. ECs are the interface between vessel wall and blood flow, and perform tasks such as the regulation of permeability and the sensing of fluid forces acting on the vessels’ walls. ECs have shown contrasting effects between laminar shear flow with a definite direction the “disturbed” shear seen at arterial branch points. Evidences suggest that wall shear stress (WSS) is capable of (1) changing the morphology and orientation of ECs via a cytoskeleton filaments remodeling and (2) stimulating the ECs to produce several chemical factors. ECs subjected to a laminar flow and high WSS tend to elongate and align in the direction of flow and expression of genes that may protect ECs from inflammation and the development of atherosclerotic plaques. In areas of low and oscillatory WSS, ECs lack organization of the cytoskeleton, intercellular junctional proteins and a unique pattern of ECs gene expression predisposing these arterial regions to atherosclerotic lesion. Despite increasing efforts in the experimental characterization of the ECs remodeling, the computational approach has not gained such an attention. In this work we study the morphological change of ECs within a realistic hemodynamic environment. For such an aim, we adopted a remodeling model for the ECs based on the reorientation of individual cytoskeleton filaments to describe the EC cell shape due to different flow features. A wide amount of flow features is obtained from CFD simulations of 46 patient specific geometries of carotid bifurcation (Fig. 1) , allowing the study of the relationship between near-wall fluid features and ECs morphology consistently with experimental observations found in literature . The impact of different variables such as the oscillatory shear index (OSI), the time average wall shear stresses (TAWSS) and fluctuations of the mean wall shear stress orientation on ECs shape is explored.
Waffenschmidt, T., T.; Cilla, M.; Saez, P.; Pérez, M.; Menzel, A.; Peña, E. Journal of biomechanics Vol. 49, num. 12, p. 2390-2397 DOI: 10.1016/j.jbiomech.2016.01.043 Data de publicació: 2016-08-16 Article en revista
The goal of this work consists in a quantitative analysis and constitutive modelling of ageing processes associated to plaque formation in mice arteries. Reliable information on the characteristic evolution of pressure–stretch curves due to the ageing effects is extracted from previous inflation test experiments. Furthermore, characteristic age-dependent material parameters are identified on the basis of a continuum-mechanics-based parameter optimisation technique. The results indicate that the aorta-stiffness of the healthy control mice remains basically constant irrespective of the diet-time and age. In contrast, significant differences exist within the material response and in consequence within the material parameters between the and the control mice as well as for the different locations over the aorta which is underlined by our experimental observations. With regard to the temporal evolution of the material parameters, we observe that the material parameters for the mice aortas exhibit a saturation-type increase with respect to age.
Myocardial infarction, commonly known as heart attack, is caused by reduced blood supply and damages the heart muscle because of a lack of oxygen. Myocardial infarction initiates a cascade of biochemical and mechanical events. In the early stages, cardiomyocytes death, wall thinning, collagen degradation, and ventricular dilation are the immediate consequences of myocardial infarction. In the later stages, collagenous scar formation in the infarcted zone and hypertrophy of the non-infarcted zone are auto-regulatory mechanisms to partly correct for these events. Here we propose a computational model for the short-term adaptation after myocardial infarction using the continuum theory of multiplicative growth. Our model captures the effects of cell death initiating wall thinning, and collagen degradation initiating ventricular dilation. Our simulations agree well with clinical observations in early myocardial infarction. They represent a first step toward simulating the progression of myocardial infarction with the ultimate goal to predict the propensity toward heart failure as a function of infarct intensity, location, and size.
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Computer Methods in Biomechanics and Biomedical Engineering on October, 2016, available online at: http://www.tandfonline.com/10.1080/10255842.2015.1105965
Computational continuum mechanics have been used for a long time to deal with the mechanics of materials. During the last decades researches have been using many of the theoretical models and numerical approaches of classical materials to deal with biological tissue which, in many senses, are a much more sophisticated material. We aim to review the last achievements of continuum models and numerical approaches on adaptation processes in biological tissues. In this review, we are looking, in particular, at growth in terms of changes of density and/or volume as, e.g., in collagen remodeling, wound healing, arterial thickening, etc. Furthermore, we point out some of the most relevant limitations of the current state-of-the-art in terms of these well established computational continuum models. In connection with these limitations, we will finish by discussing the trend lines of future work in the field of modeling biological adaptation, focusing on the computational approaches and mechanics that could overcome the current drawbacks. We would also like to attract the attention of all those researchers in classical materials (metal, alloys, composites, etc), to point out how similar the continuum and computational models between our fields are. We hope we can motivate them for getting their expertize in this challenging field of research.
The final publication is available at Springer via http://dx.doi.org/10.1007/s11831-014-9142-8
Background Mechanical characteristics of vascular tissue may play a role in different arterial pathologies, which, amongst others, requires robust constitutive descriptions to capture the vessel wall’s anisotropic and non-linear properties.Specifically, the complex 3D network of collagen and its interaction with other structural elements has a dominating effect of arterial properties at higher stress levels.The aim of this study is to collect quantitative collagen organization as well as mechanical properties to facilitate structural constitutive models for the porcine carotid artery.This helps the understanding of the mechanics of swine carotid arteries, being a standard in clinical hypothesis testing, in endovascular preclinical trials for example. Method Porcine common carotid arteries (n = 10) were harvested and used to (i) characterize the collagen fiber organization with polarized light microscopy, and (ii) the biaxial mechanical properties by inflation testing.The collagen organization was quantified by the Bingham orientation density function (ODF), which in turn was integrated in a structural constitutive model of the vessel wall.A one-layered and thick-walled model was used to estimate mechanical constitutive parameters by least-square fitting the recorded in vitro inflation test results.Finally, uniaxial data published elsewhere were used to validate the mean collagen organization described by the Bingham ODF. Results Thick collagen fibers, i.e.the most mechanically relevant structure, in the common carotid artery are dispersed around the circumferential direction.In addition, almost all samples showed two distinct families of collagen fibers at different elevation, but not azimuthal, angles.Collagen fiber organization could be accurately represented by the Bingham ODF (¿1,2,3=[13.5,0.0,25.2] and ¿1,2,3=[14.7,0.0,26.6]; average error of about 5%), and their integration into a structural constitutive model captured the inflation characteristics of individual carotid artery samples.Specifically, only four mechanical parameters were required to reasonably (average error from 14% to 38%) cover the experimental data over a wide range of axial and circumferential stretches.However, it was critical to account for fibrilar links between thick collagen fibers.Finally, the mean Bingham ODF provide also good approximation to uniaxial experimental data. Conclusions The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, the collagen fiber orientations measured from polarized light microscopy, alone, seem to be insufficient structural information. Alternatively, a larger dispersion of collagen fiber orientations, that is likely to arise from analyzing larger wall sections, could have had a similar effect, i.e. could have avoided coupling amongst thick collagen fibers.
Endothelial cells are key units in the regulatory biological process of blood vessels. They represent an interface to transmit variations on the fluid dynamic changes. They are able to adapt its cytoskeleton, by means of microtubules reorientation and F-actin reorganization, due to new mechanical environments. Moreover, they are responsible for initiating a huge cascade of biological processes, such as the release of endothelins (ET-1), in charge of the constriction of the vessel and growth factors such as TGF-ß and PDGF. Although a huge efforts have been made in the experimental characterization and description of these two issues the computational modeling has not gained such an attention. In this work we study the 3D remodeling of endothelial cells based on the main features of blood flow. In particular we study how different oscillatory shear index and the time average wall shear stresses modify the endothelial cell shape. We found our model fitted the experimental works presented before in in vitro studies. We also include our model within a computational fluid dynamics simulation of a carotid artery to evaluate endothelial cell shape index which is a key predictor of atheroma plaque formation. Moreover, our approach can be coupled with models of collagen and smooth muscle cell growth, where remodeling and the associated release of chemical substance are involved.
Saez, P.; Peña, E.; Tarbell, J.; Martínez, M. The International Journal for Numerical Methods in Biomedical Engineering Vol. 31, num. 2, p. 1-25 DOI: 10.1002/cnm.2705 Data de publicació: 2015-02 Article en revista
t is well known that biological tissues adapt their properties because of different mechanical and chemical stimuli. The goal of this work is to study the collagen turnover in the arterial tissue of hypertensive patients through a coupled computational mechano-chemical model. Although it has been widely studied experimen- tally, computational models dealing with the mechano-chemical approach are not. The present approach can be extended easily to study other aspects of bone remodeling or collagen degradation in heart diseases. The model can be divided into three different stages. First, we study the smooth muscle cell synthesis of differ- ent biological substances due to over-stretching during hypertension. Next, we study the mass-transport of these substances along the arterial wall. The last step is to compute the turnover of collagen based on the amount of these substances in the arterial wall which interact with each other to modify the turnover rate of collagen. We simulate this process in a finite element model of a real human carotid artery. The final results show the well-known stiffening of the arterial wall due to the increase in the collagen content.
This is the peer reviewed version of the following article: Saez, P., Peña, E., Tarbell, J., Martínez, M. Computational model of collagen turnover in carotid arteries during hypertension. "International journal for numerical methods in biomedical engineering - Online", Febrer 2015, vol. 31, núm. 2, p. 1-25, which has been published in final form at https://doi.org/10.1002/cnm.2705. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-013-0959-z
The objective of this work is to develop a remodeling model for biological matter coupling two different processes in a 3D framework: reorientation of the preferential direction of a given fibered structure and reorientation of the fibrils or filaments that make up such a structure. This work uses the microsphere-based approach to take into account the micro mechanics involved in biological fibered structures regarding both their passive behavior and the reorientation of their micro constituents. Moreover, the macro behavior of the material as a whole is obtained by means of homogenizing the underlying micro response. We associate the orientation space of the integration directions to the physical space of micro-fibrils. To approximate the directional distribution of the fibrils within each fiber bundle, a Bingham probability orientation density function is introduced into the Helmholtz energy function. With all these assumptions, the problem is studied from an energetic point of view, describing the dissipation inherent to remodeling processes, and the evolution equations for both reorientations (change in preferential direction of the network and change in shape of the fibril distribution) re obtained. The model is included in a finite element code which allows computing different geometries and boundary value problems. This results in a complete methodology for characterizing the reorientation evolution of different fibered biological structures, such as cells. Our results show remodeling of fibered structures in two different scales, presenting a qualitatively good agreement with experimental findings in cell mechanics. Hierarchical structures align in the direction of the maximum principal direction of the considered stimulus and narrow in the perpendicular direction. The dissipation rates follows predictable trends although there are no experimental findings to date for comparison. The incorporation of metabolic processes and an insight into cell-oriented mechano-sensing processes can help to overcome the limitations involved.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10439-014-0995-7
Saez, P.; Pena, E.; Doblaré, M.; Martínez, M.A. International journal of solids and structures Vol. 50, num. 14-15, p. 2353-2370 DOI: 10.1016/j.ijsolstr.2013.03.029 Data de publicació: 2013 Article en revista
Remodeling and other evolving processes such as growth or morphogenesis are key factors in the evolution of biological tissue in response to both external and internal epigenetic stimuli. Based on the description of these processes provided by Taber, 1995 and Humphrey et al., 2002 for three important adaptation processes, remodeling, morphogenesis and growth (positive and negative), we shall consider the latter as the increase/decrease of mass via the increase/decrease of the number or size of cells, leading to a change in the volume of the organ. The work of Rodriguez et al. (1994) used the concept of natural configuration previously introduced by Skalak et al. (1982) to formulate volumetric growth. Later, Humphrey et al. (2002) proposed a constrained-mixture theory where changes in the density and mass of different constituents were taken into account. Many other works about biological growth have been presented in recent years, see e.g. Imatani and Maugin, 2002, Garikipati et al., 2004, Gleason and Humphrey, 2004, Menzel, 2004, Amar et al., 2005, Ganghoffer et al., 2005, Ateshian, 2007, Goriely et al., 2007, Kuhl et al., 2007, Ganghoffer, 2010a, Ganghoffer, 2010b and Goktepe et al., 2010. Morphogenesis is associated to changes in the structure shape (Taber, 1995 and Taber, 2009) while remodeling denotes changes in the tissue microstructure via the reorganization of the existing constituents or the synthesis of new ones with negligible volume change. All these processes involve changes in material properties. Although remodeling and growth can, and usually do, occur simultaneously, there are some cases where these processes develop in a decoupled way. For example, Stopak and Harris (1982) reported some experimental results showing remodeling driven by fibroblasts, with no volume growth. We will assume this scenario in this contribution, focusing exclusively on remodeling processes and on the reorientation of fibered biological structures.
It is well known that biological tissue remodels itself when driven by a given stimulus, e.g. mechanical loads such as an increase in blood pressure, or changes in the chemical environment that control the signaling processes and the overall evolution of the tissue. Biological remodeling can occur in any kind of biological tissue. In particular, the study of collagen as the most important substance to be remodeled, in all its types (preferentially
Saez, P.; Alastrué, V.; Pena, E.; Doblaré, M.; Martínez, M.A. Biomechanics and modeling in mechanobiology Vol. 11, num. 5, p. 595-608 DOI: 10.1007/s10237-011-0336-9 Data de publicació: 2012-05 Article en revista
An anisotropic damage model for soft fibered tissue is presented in this paper, using a multi-scale scheme and focusing on the directionally dependent behavior of these materials. For this purpose, a micro-structural or, more precisely, a microsphere-based approach is used to model the contribution of the fibers. The link between micro-structural contribution and macroscopic response is achieved by means of computational homogenization, involving numerical integration over the surface of the unit sphere. In order to deal with the distribution of the fibrils within the fiber, a von Mises probability function is incorporated, and the mechanical (phenomenological) behavior of the fibrils is defined by an exponential-type model. We will restrict ourselves to affine deformations of the network, neglecting any cross-link between fibrils and sliding between fibers and the surrounding ground matrix. Damage in the fiber bundles is introduced through a thermodynamic formulation, which is directly included in the hyperelastic model. When the fibers are stretched far from their natural state, they become damaged. The damage increases gradually due to the progressive failure of the fibrils that make up such a structure. This model has been implemented in a finite element code, and different boundary value problems are solved and discussed herein in order to test the model features. Finally, a clinical application with the material behavior obtained from actual experimental data is also presented.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10237-011-0336-9
We present a theoretical and computational model for collagen turnover in soft biological tissues. Driven by alterations in the mechanical environment, collagen fiber bundles may undergo important chronic changes, characterized primarily by alterations in collagen synthesis and degradation rates. In particular, hypertension triggers an increase in tropocollagen synthesis and a decrease in collagen degradation, which lead to the well-documented overall increase in collagen content. These changes are the result of a cascade of events, initiated mainly by the endothelial and smooth muscle cells. Here, we represent these events collectively in terms of two internal variables, the concentration of growth factor TGF-$\beta$ and tissue inhibitors of metalloproteinases TIMP. The upregulation of TGF-$\beta$ increases the collagen density. The upregulation of TIMP also increases the collagen density through decreasing matrix metalloproteinase MMP. We establish a mathematical theory for mechanically-induced collagen turnover and introduce a computational algorithm for its robust and efficient solution. We demonstrate that our model can accurately predict the experimentally observed collagen increase in response to hypertension reported in literature. Ultimately, the model can serve as a valuable tool to predict the chronic adaptation of collagen content to restore the homeostatic equilibrium state in vessels with arbitrary micro-structure and geometry.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-012-0613-y
Evolutionary processes in biological tissue, such as adaptation or remodeling, represent an enterprising area of research. In this paper, we present a multiscale model for the remodeling of fibered structures, such as bundles of collagen fibrils. With this aim, we introduce a von Mises statistical distribution function to account for the directional dispersion of the fibrils, and we remodel the underlying fibrils by changing their orientation. To numerically compute this process, we make use of the microsphere approach, which provides a useful multiscale tool for homogenizing the microstructure behavior, related to the fibrils of the bundle, in the macroscale of the problem. The results show how the fibrils respond to the stimulus by reorientation of their structure. This process leads to a stiffer material eventually reaching a stationary state. These results are in agreement with those reported in the literature, and they characterize the adaptation of biological tissue to external stimuli.
Constitutive models for arterial tissue have been an active research field during the last years. The main micro-constituents of blood vessels are different types of cells and the extra-cellular matrix formed by an isotropic high water content ground substance and a network composed of elastin and collagen fibres. Usually the arterial tissue has been modelled as a hyperelastic material within the framework of continuum mechanics, whereas inclusion of structural tensors into constitutive laws is the most widely used technique to introduce the anisotropy induced by the fibres. Though the different existing fibre bundles present a clear preferential direction, the dispersion inherent to biological tissue advices using of constitutive models including representative structural information associated to the spatial probabilistic distribution of the fibres. Lately, microsphere-based models have demonstrated to be a powerful tool to incorporate this information. The fibre dispersion is incorporated by means of an Orientation Density Function (ODF) that weights the contribution of each fibre in each direction of the micro-sphere. In previous works the rotationally symmetric von Mises ODF was successfully applied to the modelling of blood vessels. In this study, the inclusion of the Bingham ODF into microsphere-based model is analysed. This ODF exhibits some advantages with respect to the von Mises one, like a greater versatility and a comparable response to simple tension and equibiaxial tension tests.
En este trabajo se presenta un modelo de daño para material biológico fibrado según un comportamiento micro-estructural. Se han utilizado modelos de daño para describir el ablandamiento de tejidos blandos bajo la aplicación de grandes deformaciones. Para caracterizar la contribución y distribución de las fibras que estos materiales poseen, se ha utilizado una aproximación micro-estructural. La matriz del material se caracteriza a través de una función densidad de energía de tipo Neo-Hookiano, mientras que las fibras se caracterizan mediante
leyes fenomenológicas de tipo exponencial. El paso de la contribución micro-estructural al comportamiento macroscópico se realiza a través de una integración numérica sobre la superficie una esfera unitaria.