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The anisotropic collagen architecture of an engineered cardiovascular tissue has a major impact on its in vivo mechanical performance. This evolving collagen architecture is determined by initial scaffold microstructure and mechanical loading. Here, we developed and validated a theoretical and computational microscale model to quantitatively understand the interplay between scaffold architecture and mechanical loading on collagen synthesis and degradation. Using input from experimental studies, we hypothesize that both the microstructure of the scaffold and the loading conditions influence collagen turnover. The evaluation of the mechanical and topological properties of in vitro engineered constructs reveals that the formation of extracellular matrix layers on top of the scaffold surface influences the mechanical anisotropy on the construct. Results show that the microscale model can successfully capture the collagen arrangement between the fibers of an electrospun scaffold under static and cyclic loading conditions. Contact guidance by the scaffold, and not applied load, dominates the collagen architecture. Therefore, when the collagen grows inside the pores of the scaffold, pronounced scaffold anisotropy guarantees the development of a construct that mimics the mechanical anisotropy of the native cardiovascular tissue.

Collagen provides cardiovascular tissues with the ability to withstand haemodynamic loads. A similar network is essential to obtain in tissue-engineered (TE) samples of the same nature. Yet, the mechanism of collagen orientation is not fully understood. Typically collagen remodelling is linked to mechanical loading. However, TE constructs also show an oriented collagen network when developed under static culture. Experiments under these conditions also indicate that the tissue gradually compacts due to contractile stresses developed in the α-actin fibres of the cells. Therefore, it is hypothesised that cellular contractile stresses are responsible for collagen orientation. A model describing the cellular α-actin turnover and the stresses developed by them is integrated in a structural constitutive model describing the mechanical behaviour of collagen fibres. Results show that the model can successfully capture the sample compaction, tissue stress generation and its heterogeneous collagen arrangement.

Accurate material models and associated parameters of atherosclerotic plaques are crucial for reliable biomechanical plaque prediction models. These biomechanical models have the potential to increase our understanding of plaque progression and failure, possibly improving risk assessment of plaque rupture, which is the main cause of ischaemic strokes and myocardial infarction. However, experimental biomechanical data on atherosclerotic plaque tissue is scarce and shows a high variability. In addition, most of the biomechanical models assume isotropic behaviour of plaque tissue, which is a general over-simplification. This review discusses the past and the current literature that focus on mechanical properties of plaque derived from compression experiments, using unconfined compression, micro-indentation or nano-indentation. Results will be discussed and the techniques will be mutually compared. Thereafter, an in-house developed indentation method combined with an inverse finite element method is introduced, allowing analysis of the local anisotropic mechanical properties of atherosclerotic plaques. The advantages and limitations of this method will be evaluated and compared to other methods reported in literature.

Electrospinning has proven to be a promising method to produce scaffolds for tissue engineering despite the frequently encountered limitations in 3-dimensional tissue formation due to a lack of cell infiltration. To fully unlock the potential of electrospun scaffolds for tissue engineering, the void space within the fibrous network needs to be increased substantially and in a controlled manner. Low-temperature electrospinning (LTE) increases the fiber to fiber distance by embedding ice particles as void spacers during fiber deposition. Scaffold porosities up to 99.5% can be reached and in line with the increase in void space, the mechanical properties of the scaffolds shift towards the range for native biological tissue. While both the physiological mechanical properties and high porosity were promising for tissue engineering applications, control of the porosity in three dimensions was still limited when using LTE methods. Based on a range of LTE spun scaffolds made of poly(lactic acid) and poly(ε-caprolactone), we found that changing the ratio between the rate of ice crystal formation and polymer fiber deposition only had a small effect on the 3D-porosity of the final scaffold architecture. Varying the fiber stiffness, however, offers considerable control over the scaffold void space.

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. © 2013 Springer-Verlag Berlin Heidelberg.

In tissue-engineered (TE) heart valves, cell-mediated processes cause tissue compaction during culture and leaflet retraction at time of implantation. We have quantified and correlated stress generation, compaction, retraction, and tissue quality during a prolonged culture period of 8 weeks. Polyglycolic acid /poly-4-hydroxybutyrate strips were seeded with vascular-derived cells and cultured for 4-8 weeks. Compaction in width, generated force, and stress was measured during culture. Retraction in length, generated force, and stress was measured after release of constraints at weeks 4, 6, and 8. Further, the amount of DNA, glycosaminoglycans (GAGs), collagen, and collagen cross-links was assessed. During culture, compaction and force generation increased to, respectively, 63.9% +/- 0.8% and 43.7 +/- 4.3mN at week 4, after which they remained stable. Stress generation reached 27.7 +/- 3.2 kPa at week 4, after which it decreased to similar to 8.5 kPa. At release of constraints, tissue retraction was 44.0% +/- 3.7% at week 4 and decreased to 29.2% +/- 2.8% and 26.1% +/- 2.2% at, respectively, 6 and 8 weeks. Generated force (8-16mN) was lower at week 6 than at weeks 4 and 8. Generated stress decreased from 11.8 +/- 0.9 kPa at week 4 to 1.4 +/- 0.3 and 2.4 +/- 0.4 kPa at, respectively, weeks 6 and 8. The amount of GAGs increased at weeks 6 and 8 compared to week 4 and correlated to the reduced stress and retraction. In summary, prolonged culture resulted in decreased stress generation and retraction, likely as a result of the increased amount of GAGs. These results demonstrate the potential of prolonged tissue culture in developing functional, nonretracting, TE heart valves.

Deep tissue injury (DTI) is a severe form of pressure ulcer where tissue damage starts in deep tissues underneath intact skin. Tissue deformation may play an important role in the aetiology, which can be investigated using an experimental–numerical approach. Recently, an animal-specific finite element model has been developed to simulate experiments in which muscle tissue was compressed with an indenter. In this study, the material behaviour and boundary conditions were adapted to improve the agreement between model and experiment and to investigate the influence of these adaptations on the predicted strain distribution. The use of a highly nonlinear material law and including friction between the indenter and the muscle both improved the quality of the model and considerably influenced the estimated strain distribution. With the improved model, the required sample size to detect significant differences between loading conditions can be diminished, which is clearly relevant in experiments involving animals.

Microneedle arrays have been developed to deliver a range of biomolecules including vaccines into the skin. These microneedles have been designed with a wide range of geometries and arrangements within an array. However, little is known about the effect of the geometry on the potency of the induced immune response. The aim of this study was to develop a computational model to predict the optimal design of the microneedles and their arrangement within an array. The three-dimensional finite element model described the diffusion and kinetics in the skin following antigen delivery with a microneedle array. The results revealed an optimum distance between microneedles based on the number of activated antigen presenting cells, which was assumed to be related to the induced immune response. This optimum depends on the delivered dose. In addition, the microneedle length affects the number of cells that will be involved in either the epidermis or dermis. By contrast, the radius at the base of the microneedle and release rate only minimally influenced the number of cells that were activated. The model revealed the importance of various geometric parameters to enhance the induced immune response. The model can be developed further to determine the optimal design of an array by adjusting its various parameters to a specific situation.

Electrospinning is a promising technology to produce scaffolds for cardiovascular tissue engineering. Each electrospun scaffold is characterized by a complex micro-scale structure that is responsible for its macroscopic mechanical behavior. In this study, we focus on the development and the validation of a computational micro-scale model that takes into account the structural features of the electrospun material, and is suitable for studying the multi-scale scaffold mechanics. We show that the computational tool developed is able to describe and predict the mechanical behavior of electrospun scaffolds characterized by different microstructures. Moreover, we explore the global mechanical properties of valve-shaped scaffolds with different microstructural features, and compare the deformation of these scaffolds when submitted to diastolic pressures with a tissue engineered and a native valve. It is shown that a pronounced degree of anisotropy is necessary to reproduce the deformation patterns observed in the native heart valve.

This study presents an in vitro experimental method to determine shear properties of the epidermis. Shear tests were performed with a parallel plate rheometer on samples of stratum corneum and the viable epidermis. The method was validated on very thin silicon sheets. Preliminary test were performed to determine the linear viscoelastic range, the effect of normal loading on the sample and the time to reach equilibrium after changes of temperature and relative humidity. The study shows that reproducible results can be obtained for the shear properties of epidermis in an in vitro set up. The dynamic shear modulus for stratum corneum roughly ranges from 4 to 12 kPa, decreasing with increasing relative humidity. The values are considerably lower than the shear modulus value based on tensile Young’s moduli in literature, indicating a considerable anisotropic material behavior. Results for the epidermis were of the same order of magnitude, but were less consistent possibly due to a less well-defined tissue composition.

The mechanical properties of soft biological tissues in general and early stage engineered tissues in particular limit the feasibility of conventional tensile tests for their mechanical characterisation. Furthermore, the most important mode in development of deep tissue injury (DTI) is compression. Therefore, an inverse numerical-experimental approach using a finite spherical indentation test is proposed. To demonstrate the feasibility of the approach indentation tests are applied to bio-artificial muscle (BAM) tissue. BAMs are cultured in vitro with (n = 20) or without (n = 12) myoblast cells to quantify the effect of the cells on the passive transverse mechanical properties. Indentation tests are applied up to 80% of the tissue thickness. A non-linear Neo-Hookean constitutive model is fitted to the experimental results for parameter estimation. BAMs with cells demonstrated both stiffer and more non-linear material behaviour than BAMs without cells.

Subcutaneous adipose tissue contributes to the overall mechanical behavior of the skin. Until today, however, no thorough constitutive model is available for this layer of tissue. As a start to the development of such a model, the objective of this study was to measure and describe the linear viscoelastic behavior of subcutaneous adipose tissue. Although large strains occur in vivo, this work only focuses on the linear behavior to show the applicability of the described methods to adipose tissue. Shear experiments are performed on porcine samples on a rotational rheometer using parallel plate geometry. In the linear viscoelastic regime, up to 0.1% strain, the storage and loss modulus showed a frequency- and temperature-dependent behavior. The ratio between the two moduli, the phase angle, did not show any dependency on temperature and frequency. The shear modulus was found to be 7.5 kPa at 10 rad/s and 37 degrees C. Time-temperature superposition was applicable through shifting the shear modulus horizontally. A power-law function model was introduced to describe both the frequency dependent behavior at constant temperature and the stress relaxation behavior. In addition, the effect of snap freezing as a preservation method was analyzed. Histological examination demonstrated possible tissue damage after freezing, but the mechanical properties did not change. Since results were reproducible, it is concluded that the methods we used are most probably suited to explore the non-linear behavior of subcutaneous adipose tissue.

Deep pressure ulcers are caused by sustained mechanical loading and involve skeletal muscle tissue injury. The exact underlying mechanisms are unclear, and the prevalence is high. Our hypothesis is that the aetiology is dominated by cellular deformation (Bouten et al. in Ann Biomed Eng 29:153-163, 2001; Breuls et al. in Ann Biomed Eng 31:1357-1364, 2003; Stekelenburg et al. in J App Physiol 100(6):1946-1954, 2006) and deformation-induced ischaemia. The experimental observation that mechanical compression induced a pattern of interspersed healthy and dead cells in skeletal muscle (Stekelenburg et al. in J App Physiol 100(6):1946-1954, 2006) strongly suggests to take into account the muscle microstructure in studying damage development. The present paper describes a computational model for deformation-induced hypoxic damage in skeletal muscle tissue. Dead cells stop consuming oxygen and are assumed to decrease in stiffness due to loss of structure. The questions addressed are if these two consequences of cell death influence the development of cell injury in the remaining cells. The results show that weakening of dead cells indeed affects the damage accumulation in other cells. Further, the fact that cells stop consuming oxygen after they have died, delays cell death of other cells.

Delivering a drug into and through the skin is of interest as the skin can act as an alternative drug administration route for oral delivery. The development of new delivery methods, such as microneedles, makes it possible to not only deliver small molecules into the skin, which are able to pass the outer layer of the skin in therapeutic amounts, but also macromolecules. To provide insight into the administration of these molecules into the skin, the aim of this study was to assess the transport of macromolecules within and between its various layers. The diffusion coefficients in the epidermis and several locations in the papillary and reticular dermis were determined for fluorescein dextran of 40 and 500 kDa using a combination of fluorescent recovery after photobleaching experiments and finite element analysis. The diffusion coefficient was significantly higher for 40 kDa than 500 kDa dextran, with median values of 23 and 9 µm(2)/s in the dermis, respectively. The values only marginally varied within and between papillary and reticular dermis. For the 40 kDa dextran, the diffusion coefficient in the epidermis was twice as low as in the dermis layers. The adopted method may be used for other macromolecules, which are of interest for dermal and transdermal drug delivery. The knowledge about diffusion in the skin is useful to optimize (trans)dermal drug delivery systems to target specific layers or cells in the human skin.

Although the mechanical behavior of the top layer of the skin, the epidermis, is an important consideration in several clinical and cosmetic applications, there are few reported studies on this layer. The in vivo mechanical behavior of the upper skin layer (here defined as epidermis and papillar dermis) was characterized using a combined experimental and modeling approach. The work was based on the hypothesis that experiments with different length scales represent the mechanical behavior of different skin layers. Suction measurements with aperture diameters of 1, 2 and 6 mm were combined with ultrasound and optical coherence tomography to study the deformation of the skin layers. The experiments were simulated for small displacements with a two-layered finite element model representing the upper layer and the reticular dermis. An identification method compared the experimental and numerical results to identify the material parameters of the model. For one subject the whole parameter estimation procedure was completed, leading to a stiffness of C(10,ul) = 0.11 kPa for the top-layer and C(10,rd) = 0.16 MPa for the reticular dermis. This unexpected, extreme stiffness ratio of the material parameters let to convergence problems of the finite element software for most of the individuals.

Eukaryotic cells are continuously subjected to mechanical forces under normal physiological conditions. These forces and associated cellular deformations induce a variety of biological processes. The degree of deformation depends on the mechanical properties of the cell. As most cells are anchorage dependent for normal functioning, it is important to study the mechanical properties of cells in their attached configuration. The goal of the present study was to obtain the mechanical and failure properties of attached cells. Individual, attached C2C12 mouse myoblasts were subjected to unconfined compression experiments using a recently developed loading device. The device allows global compression of the cell until cell rupture and simultaneously measures the associated forces. Cell bursting was characterized by a typical reduction in the force, referred to as the bursting force. Mean bursting forces were calculated as 8.7 ± 2.5 μ N at an axial strain of 72 ± 4 %. Visualization of the cell using confocal microscopy revealed that cell bursting was preceded by the formation of bulges at the cell membrane, which eventually led to rupturing of the cell membrane. Finite element calculations were performed to simulate the obtained force–deformation curves. A finite element mesh was built for each cell to account for its specific geometrical features. Using an axisymmetric approximation of the cell geometry, and a Neo–Hookean constitutive model, excellent agreement between predicted and measured force–deformation curves was obtained, yielding an average Young's modulus of 1.14 ± 0.32 kPa .

The viscoelastic properties of single, attached C2C12 myoblasts were measured using a recently developed cell loading device. The device allows global compression of an attached cell, while simultaneously measuring the associated forces. The viscoelastic properties were examined by performing a series of dynamic experiments over two frequency decades (0.1-10 Hz) and at a range of axial strains (approximately 10-40%). Confocal laser scanning microscopy was used to visualize the cell during these experiments. To analyze the experimentally obtained force-deformation curves, a nonlinear viscoelastic model was developed. The nonlinear viscoelastic model was able to describe the complete series of dynamic experiments using only a single set of parameters, yielding an elastic modulus of 2120 +/- 900 Pa for the elastic spring, an elastic modulus of 1960 +/- 1350 for the nonlinear spring, and a relaxation time constant of 0.3 +/- 0.12 s. To our knowledge, it is the first time that the global viscoelastic properties of attached cells have been quantified over such a wide range of strains. Furthermore, the experiments were performed under optimal environmental conditions and the results are, therefore, believed to reflect the viscoelastic mechanical behavior of cells, such as would be present in vivo.

Backgrounds/aims Human skin is a complex tissue consisting of different layers. To gain better insight into the mechanical behaviour of different skin layers, the mechanical response was studied with experiments of various length scales. Also, the influence of (superficial) hydration on the mechanical response is studied. The work is based on the hypothesis that experiments with different length scales represent the mechanical behaviour of different skin layers. For suction, this means that a large aperture diameter reflects the behaviour of mainly dermis, whereas a very small diameter reflects the behaviour of only the top layer of the skin. Methods Suction measurements at varying pressures and aperture sizes were performed on the volar forearm of 13 subjects aged 29-47 years. The deformation of the skin was visualized using ultrasound (US) (dermis) and optical coherence tomography (OCT) (epidermis and dermis). US measurements were performed on hydrated skin, OCT measurements on dry and hydrated skin. The experiment was simulated by a finite element model (FEM) exhibiting extended Mooney material behaviour. An identification method was used to compare the experimental and numerical results to identify the parameters of the material. Results The material parameters C(10) and C(11) were calculated for four subjects: C(10)=29.6+/-21.1 kPa and C(11)=493+/-613 kPa for 6 mm aperture diameter, C(10)=11.5+/-8.7 kPa and C(11)=18.3+/-12.6 kPa for 2 mm aperture diameter and C(10)=10.8+/-9.5 kPa and C(11)=9.3+/-7.7 kPa for 1 mm aperture diameter. Skin hydration caused ambiguous effects on the mechanical response. Conclusions US and OCT, combined with suction, using varying apertures sizes, proved to be a valuable tool to study the mechanical behaviour of different skin layers. With increasing experimental length scale, increasing values for the parameters of the material model were found. This indicates the need of a multi-layered material layer FEM, which can be used to identify mechanical behaviour of epidermis and dermis.

Quantifying three-dimensional deformation of cells under mechanical load is relevant when studying cell deformation in relation to cellular functioning. Because most cells are anchorage dependent for normal functioning, it is desired to study cells in their attached configuration. This study reports new three-dimensional morphometric measurements of cell deformation during stepwise compression experiments with a recently developed cell loading device. The device allows global, unconfined compression of individual, attached cells under optimal environmental conditions. Three-dimensional images of fluorescently stained myoblasts were recorded with confocal microscopy and analyzed with image restoration and three-dimensional image reconstruction software to quantify cell deformation. In response to compression, cell width, cross-sectional area, and surface area increased significantly with applied strain, whereas cell volume remained constant. Interestingly, the cell and the nucleus deformed perpendicular to the direction of actin filaments present along the long axis of the cell. This strongly suggests that this anisotropic deformation can be attributed to the preferred orientation of actin filaments. A shape factor was introduced to quantify the global shape of attached cells. The increase of this factor during compression reflected the anisotropic deformation of the cell.

Soft tissues are sensitive to prolonged compressive loading, eventually leading to tissue necrosis in the form of pressure ulcers [1]. Pressure ulcers can occur in situations where people are subjected to sustained mechanical loads, such as when bedridden, sitting in a wheelchair or from wearing prostheses. Pressure ulcers severely affect the patient's quality of life, since the ulcers are painful, difficult to heal and often prolong hospitalization periods. Despite considerable attempts to prevent pressure ulcers, prevalence figures remain unacceptably high. In a prevalence study involving more than 16,000 patients in the Netherlands, a mean prevalence of 23.1% in health care institutions was reported [6]. Pressure ulcers are often classified in four different stages, ranging from discoloration of intact skin (Stage I) to full thickness skin loss involving tissue damage that extends to underlying bone involving both fat and muscle tissues (Stage IV). Although this classification is widely used in clinical practice, it does not necessarily relate to the origin of the ulcers. Depending on the nature of loading, pressure ulcers can either initiate superficially at the skin [15][33], or initiate in deeper layers such as muscle tissue [14][18][20][28]. The present study focuses on deep pressure ulcers that initiate in muscle tissue, since deeper ulcers are more harmful and show more extensive ulceration. In addition, muscle tissue is more susceptible to the development of pressure ulcers [2][23] and, hence, deep ulcers develop at a faster rate than superficial ulcers, making them particularly dangerous [2][14]. Yet, these deep ulcers are difficult to prevent and identify, since they are rarely visible at the skin surface at the time of initiation. As such, the four stage classification scheme can be misleading, since it does not represent an ordinal scale. In literature, a number of theories have been proposed to explain the pathophysiology of pressure ulcers. These theories suggest that compression of a tissue can lead to localized ischaemia, impaired interstitial fluid flow and/or insufficient lymphatic drainage. Furthermore, relieving the tissue after sustained compression may lead to reperfusion injury. Recently, it was demonstrated that the deformation of cells due to external loading of the tissue can directly induce cell damage [8]. The primary cause of deep pressure ulcers is the external load applied at the patient support interface, resulting in compression of the tissue between the skin surface and the bony prominences. However, the externally applied load is not indicative of the local mechanical conditions in underlying muscle tissue (for example expressed in terms of stresses and strains), and thus not directly related to tissue damage [12][24][30]. In particular, when a tissue is compressed against an irregularly shaped bony prominence, the local mechanical condition within the muscle tissue may well exceed the measured loading condition at the skin interface. Therefore, the local mechanical loading condition could prove a more reliable predictor for the onset of tissue damage in these deeper tissue layers. When considering the local mechanical tissue condition, it should be noticed that an averaged mechanical condition associated with a small volume within the tissue, is not representative of the mechanical condition experienced at the cellular level. This is due to the heterogeneity of the microstructure [10][17][31]. Since tissue damage initiates with local cellular damage [7][11][20][23], it is necessary to consider this microstructure. In addition, the microstructural behavior must be considered since it inevitably determines the macroscopic constitutive behavior of the tissue. For example, when cell damage occurs, the microstructure is likely to change, which will be reflected in the macroscopic behavior of the tissue. In this case, it is not possible to describe the macroscopic behavior with a conventional constitutive law [10][21]. Since local mechanical conditions are difficult to measure experimentally, theoretical and numerical models have been developed, which relate externally applied pressures to the local mechanical condition within a tissue. In a theoretical model based on dimensional analyses, Sacks [27] derived a relationship between tolerable external pressure and duration of pressure. The rationale behind this analysis was that there is a definable pressure that causes a pressure ulcer, which is a function of both tissue properties and the blood flow through the tissue. The model did not take into account the local geometry of, for example, a bony prominence, leading to load distributions in the tissues. Zhang and coworkers [33] performed a theoretical analysis on the stress distribution within the tissue after application of shear and normal forces at the skin. To allow calculation of an analytical solution, both skin and muscle tissue were assumed to behave as linear, isotropic elastic materials. This model demonstrated that the highest stress concentrations were found within deeper layers of the soft tissue. To analyze more complex geometries and material behavior, the use of computer models, in particular the finite-element (FE) approach, is indispensable. Chow and Odell [12] and Todd and Tacker [30] developed finite element models of the human buttocks. In the model of Todd and Tacker [30], seated positions were simulated, thereby manipulating boundary conditions of the model. The authors concluded that there is no clear correlation between interface pressure and the local mechanical conditions. Oomens and coworkers [24] created a FE model of a human subject sitting on a cushion, which incorporated three different tissue layers overlaying the human ischial tuberositas, muscle, fat and skin. These soft tissues were modeled as nonlinear viscoelastic materials. Despite the uncertainties in material properties, the high peak stresses were consistently found near the bone prominences and in the fat layer. Furthermore, models based on mixture theory have been proposed to examine the transient biomechanical response of a skin layer as a result of tissue fluid flow within the tissue [22][33]. The numerical models described in literature focus on determination of local mechanical conditions in skin and underlying tissues in terms of homogenized tissue stresses and strains [12][22][25][30][32][33]. However, from the previous discussion it is clear that a microstructural analysis is required to determine the mechanical conditions that a cell experiences. Moreover, knowledge of the local mechanical condition alone is not sufficient to predict tissue damage initiation and evolution. Also the loading history of the tissue is essential, since the time that a tissue is subjected to a sustained compression is a major determinant of tissue damage [26]. A second aspect that, to date, has received relatively little attention, is the tissue tolerance against compression. Different tissues, such as skin, fat and muscle, may have a different tolerance level, which in turn may be patient dependent. The objective of the present study is to illustrate that prediction of pressure ulcer initiation on the basis of external load measurements is inadequate. By considering local load-time threshold curves, it is illustrated which variables quantitatively influence the threshold curves and, therefore, should be considered for the prediction of damage initiation. To this end, a numerical model was developed, which is based on a multilevel FE approach. This model can relate external loads applied to the skin, to the local mechanical conditions at the cell level. With this model, simulations were performed in which muscle tissue is compressed against a bony prominence. As a starting point, the model focuses on the role of cell deformations on cell damage. The model incorporates both the time aspect and a tissue tolerance level for damage in the form of a damage law that was derived from in vitro experiments [9]. A parameter study was performed to illustrate the effect of the cell tolerance and cell stiffness on the macroscopic tissue damage evolution.

Background/aims: Human skin is a complex tissue consisting of several distinct layers. Each layer consists of various components with a specific structure. To gain a better insight into the overall mechanical behaviour of the skin, we wish to study the mechanical properties of the different layers. A numerical-experimental method was developed to characterize the non-linear mechanical behaviour of human dermis. Methods: Suction measurements at varying pressures were performed on the volar forearm skin of 10 subjects aged 19–24 years old. Deformation of dermis and fat during suction was measured using ultrasound. The experiment was simulated by a finite element model exhibiting extended Mooney material behaviour to account for the non-linear stress–strain relationship. An identification method is used to compare the experimental and numerical results to identify the parameters of the material model. Results:C10, dermis was found to be 9.4 ± 3.6 kPa and C11, dermis to be 82 ± 60 kPa. A first rough estimate of C10, fat was 0.02 kPa. Conclusions: The resulting finite element model demonstrated its ability to describe the response of the skin to suction at various pressures. In the future, this method can be used to characterize the mechanical behaviour of different skin layers using various aperture sizes and to characterize the skin behaviour under various loading conditions.

Skeletal muscle cells are sensitive to sustained compression, which can lead to the development of pressure sores. Although it is known that this type of tissue breakdown depends on the magnitude and duration of the applied load, the exact relationship between cell deformation and damage remains unclear. To gain more insight into this process, a method has been developed, that incorporates the use of a new loading device and confocal microscopy. The loading device is able to compress individual cells, either statically or dynamically, while measuring the resulting forces. Experiments can be performed under ideal environmental conditions, comparable with those of a CO2 incubator. First compression experiments on C2C12 mouse myoblasts showed the shape changes that cells undergo during static compression by the loading device. Calculations using the three-dimensional confocal images showed no change in volume and an increase in the surface area of the cell as a result of compression. The device presented here provides a useful way to monitor the biomechanical response of skeletal muscle cells during long-term compression experiments. Therefore it will contribute to the knowledge about strain-induced cell damage, as seen in pressure sores and other mechanically induced clinical conditions.

Spatial and temporal heterogeneity of superficial muscle strain during in situ fixed-end contractions.Drost MR, Maenhout M, Willems PJ, Oomens CW, Baaijens FP, Hesselink MK.Department of Movement Sciences, Nutrition and Toxicology Research Institute Maastricht, Maastricht University, P.O. Box 616, 6200, Maastricht, The Netherlands. maarten.drost@bw.unimaas.nlNumerical models of contracting muscle offer a powerful tool to study local mechanical load. For validation of these models, the spatial and temporal distribution of strain was quantified in fixed-end contracting rat tibialis anterior muscle in situ at optimal muscle length (L(o)) and at 120 degrees plantar flexion as well as at 125 and 33Hz stimulation frequency. We studied the hypothesis that after termination of stimulation in situ muscle segments near the motor endplates elongate while segments away from the endplates shorten. We show that both spatial and temporal inhomogeneities in muscle deformation occurred during contraction. Muscle plateau shortening strain equalled 4.1%. Maximal plateau shortening of a muscle segment was much larger (9.6%) and occurred distally (at 0.26 of the scaled length of the muscle). Manipulating torque levels by decreasing the stimulation frequency at the same muscle length induced a decrease in torque ( approximately 20%) with a smaller effect on the level and no effect on the pattern of muscle deformation. During relaxation, distal segments actively shortened at the expense of proximal muscle segments, which elongated. The segments undergoing lengthening were nearer to motor endplates than segments undergoing shortening.In conclusion, the present study provides experimental data on magnitude of contraction-induced deformation needed for validation of numerical models. Local muscle deformation is heterogeneous both temporally and spatially and may be related to proximity to the motor endplates

A multilevel finite element approach is applied to predict local cell deformations in engineered tissue constructs. Cell deformations are predicted from detailed nonlinear FE analysis of the microstructure, consisting of an arrangement of cells embedded in matrix material. Effective macroscopic tissue behavior is derived by a computational homogenization procedure. To illustrate this approach, we simulated the compression of a skeletal muscle tissue construct and studied the influence of microstructural heterogeneity on local cell deformations. Results show that heterogeneity has a profound impact on local cell deformations, which highly exceed macroscopic deformations. Moreover, microstructural heterogeneity and the presence of neighboring cells leads to complex cell shapes and causes non-uniform deformations within a cell.

Microneedles represent promising tools for delivery of drugs to the skin. However, before these microneedles can be used in clinical practice, it is essential to understand the process of skin penetration by these microneedles. The present study was designed to monitor both penetration depth and force of single solid microneedles with various tip diameters ranging from 5 to 37 µm to provide insight into the penetration process into the skin of these sharp microneedles. To determine the microneedle penetration depth, single microneedles were inserted in human ex vivo skin while monitoring the surface of the skin. Simultaneously, the force on the microneedles was measured. The average penetration depth at 1.5 mm displacement was similar for all tip diameters. However, the process of penetration depth was significantly different for the various microneedles. Microneedles with a tip diameter of 5 µm were smoothly inserted into the skin, while the penetration depth of microneedles with a larger tip diameter suddenly increased after initial superficial penetration. In addition, the force at insertion (defined as the force at a sudden decrease in measured force) linearly increased with tip diameter ranging from 20 to 167 mN. The force drop at insertion was associated with a measured penetration depth of approximately 160 μm for all tip diameters, suggesting that the drop in force was due to the penetration of a deeper skin layer. This study showed that sharp microneedles are essential to insert microneedles in a well-controlled way to a desired depth.

Med Eng Phys 2001 Apr;23(3):195-200 Related Articles, Books, LinkOut Quantification and localisation of damage in rat muscles after controlled loading; a new approach to study the aetiology of pressure sores.Bosboom EM, Bouten CV, Oomens CW, van Straaten HW, Baaijens FP, Kuipers H.Department of Materials Technology, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands. e.m.h.bosboom@tue.nlTo obtain more insight in the aetiology of deep pressure sores, an animal model was developed to relate controlled external loading to local muscle damage. The tibialis anterior muscle (TA) and overlying skin of a rat were compressed between indentor and tibia. Loads of 10, 70 and 250kPa at skin surface were applied for 2 or 6h. During half of the 10 and 250kPa experiments interstitial fluid pressure (IFP) in the TA was measured. The TAs were excised 24h after load application. Both amount and location of damage were assessed by histological examination using a semi-automated image-processing program. In six of eleven loaded muscles damage was found. The damage was located from superficial to deep muscle tissue in a zone never exceeding the diameter of the indentor. The IFP measurements interfered with the occurrence of damage; application of 10 and 70kPa loads only caused damage when combined with IFP measurements, whereas IFP measurements increased damage at 250kPa loads. The results showed that the developed animal model can be used to provoke local damage by applying a controlled load and that the amount and location of damage can be assessed using the newly developed techniques.

J Biomech 2001 Oct;34(10):1365-8 Related Articles, Books, LinkOut Passive transverse mechanical properties of skeletal muscle under in vivo compression.Bosboom EM, Hesselink MK, Oomens CW, Bouten CV, Drost MR, Baaijens FP.Department of Materials Technology, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands. e.m.h.bosboom@tue.nlThe objective of the present study is to determine the passive transverse mechanical properties of skeletal muscle. Compression experiments were performed on four rat tibialis anterior muscles. To assess the stress- and strain-distributions in the muscle during the experiment, a plane stress model of the cross section was developed for each muscle. The incompressible viscoelastic Ogden model was used to describe the passive muscle behaviour. The four material parameters were determined by fitting calculated indentation forces on measured indentation forces. The elastic parameters, mu and alpha, were 15.6+/-5.4 kPa and 21.4+/-5.7, respectively. The viscoelastic parameters, delta and tau, were 0.549+/-0.056 and 6.01+/-0.42 s. When applying the estimated material parameters in a three-dimensional finite element model, the measured behaviour can be accurately simulated.

The aim of this work is to characterise the in-plane mechanical behaviour of human skin in vivo. For this purpose the structural skin model proposed by Lanir [I] is employed and a mixed numerical-experimental method is developed. The numerical-experimental method is based on the confrontation of measured data from an experiment, with calculated data from a finite element model, eventually leading to the determination of some of the parameters of a constitutive model, in the present case Lanir's Skin Model. Since collagen, the main constituent of skin, dominates the anisotropic and non-linear behaviour of skin, the parameters of Lanir's Skin Model concerning the mechanical behaviour of the collagen fibres are estimated. In vivo experiments were carried out on the volar forearm. During the experiments, reaction forces and the displacement field at different states of deformation are measured. Both data sets are used for the determination of the parameters.

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. Keywords : Heart valve tissue engineering; Stress generation; Retraction; Myofibroblast; Finite element method

Tissue engineering represents a promising technique to overcome the limitations of the current valve replacements, since it allows for creating living autologous heart valves that have the potential to grow and remodel. However, also this approach still faces a number of challenges. One particular problem is regurgitation, caused by cell-mediated tissue retraction or the mismatch in geometrical and material properties between tissue-engineered heart valves (TEHVs) and their native counterparts. The goal of the present study was to assess the influence of valve geometry and tissue anisotropy on the deformation profile and closed configuration of TEHVs. To achieve this aim, a range of finite element models incorporating different valve shapes was developed, and the constitutive behavior of the tissue was modeled using an established computational framework, where the degree of anisotropy was varied between values representative of TEHVs and native valves. The results of this study suggest that valve geometry and tissue anisotropy are both important to maximize the radial strains and thereby the coaptation area. Additionally, the minimum degree of anisotropy that is required to obtain positive radial strains was shown to depend on the valve shape and the pressure to which the valves are exposed. Exposure to pulmonary diastolic pressure only yielded positive radial strains if the anisotropy was comparable to the native situation, whereas considerably less anisotropy was required if the valves were exposed to aortic diastolic pressure.

Mechanical loading of soft tissues covering bony prominences can cause skeletal muscle damage, ultimately resulting in a severe pressure ulcer termed deep tissue injury (DTI). Deformation plays an important role in the aetiology of DTI. Therefore, it is essential to minimise internal muscle deformations in subjects at risk of DTI. As an example, spinal cord-injured (SCI) individuals exhibit structural changes leading to a decrease in muscle thickness and stiffness, which subsequently increase the tissue deformations. In the present study, an animal-specific finite element model, where the geometry and boundary conditions were derived from magnetic resonance images, was developed. It was used to investigate the internal deformations in the muscle, fat and skin layers of the porcine buttocks during loading. The model indicated the presence of large deformations in both the muscle and the fat layers, with maximum shear strains up to 0.65 in muscle tissue and 0.63 in fat. Furthermore, a sensitivity analysis showed that the tissue deformations depend considerably on the relative stiffness values of the different tissues. For example, a change in muscle stiffness had a large effect on the muscle deformations. A 50% decrease in stiffness caused an increase in maximum shear strain from 0.65 to 0.99, whereas a 50% increase in stiffness resulted in a decrease in maximum shear strain from 0.65 to 0.49. These results indicate the importance of restoring tissue properties after SCI, with the use of, for example, electrical stimulation, to prevent the development of DTI.

Skin is a multilayer composite and exhibits highly non-linear, viscoelastic, anisotropic material properties. In many consumer product and medical applications (e.g. during shaving, needle insertion, patient re-positioning), large tissue displacements and deformations are involved; consequently large local strains in the skin tissue can occur. Here, we present a novel imaging-based method to study skin deformations and the mechanics of interacting skin layers of full-thickness skin. Shear experiments and real-time video recording were combined with digital image correlation and strain field analysis to visualise and quantify skin layer deformations during dynamic mechanical testing. A global shear strain of 10% was applied to airbrush-patterned porcine skin (thickness: 1.2–1.6 mm) using a rotational rheometer. The recordings were analysed with ARAMIS image correlation software, and local skin displacement, strain and stiffness profiles through the skin layers determined. The results of this pilot study revealed inhomogeneous skin deformation, characterised by a gradual transition from a low (2.0–5.0%; epidermis) to high (10–22%; dermis) shear strain regime. Shear moduli ranged from 20 to 130 kPa. The herein presented method will be used for more extended studies on viable human skin, and is considered a valuable foundation for further development of constitutive models which can be used in advanced finite element analyses of skin

Although subcutaneous adipose tissue undergoes large deformations on a daily basis, there is no adequate mechanical model to describe the transfer of mechanical load from the skin throughout the tissue to deeper layers. In order to develop such a non-linear model, a set of experimental data is required. Accordingly, this study examines the long term behavior of adipose tissue under small strain and its response to various large strain profiles. The results show that the shear modulus dramatically increases to about an order of magnitude after a loading period between 250 and 1250 s, but returns to its initial value within 3 h of recovery from loading. In addition, it was observed that the stress–strain responses for various large strain history sequences are reproducible up to a strain of 0.15. For increasing strains, the stress decreases for subsequent loading cycles and, above 0.3 strain, tissue structure changes such that the stress becomes independent of the applied strain. From the results, it can be concluded that adipose tissue likely behaves as an (anti-) thixotropic material and that a Mooney–Rivlin model might be appropriate to simulate behavior at physiologically relevant high strains. However, before the model is developed more fully, further experimental research is needed to ratify that the material is (anti-)thixotropic.

Until today mechanical properties of the subcutaneous fat layer have hardly been considered as important and, hence, a constitutive model describing its behavior is lacking. However, numerical models including the subcutaneous fat layer are needed in a wide field of applications such as skin device contact, needle insertion procedures, and the removal of skin adhesives. The aim of this study is to develop a thorough constitutive model describing the mechanical behaviour of subcutaneous adipose tissue, which can be implemented in numerical models. The constitutive model formulation is based on rheological experiments in vitro. Here, the first results are presented.

Many diffusive processes in biological systems refuse to obey the standard laws of diffusion. In normal diffusion, the diffusivity can be considered constant and the concentration of the diffusive particles follows Fick’s law. However, in highly heterogeneous materials such as tissues, the complex microgeometry of the medium imposes serious restrictions to the mobility of the particles. This scenario is known as anomalous diffusion. Experiments in diverse biological systems including diffusion in the extracellular space of the brain [1], morphogen movement in the extracellular environment [2], protein movement inside cells [3], identified anomalous, rather than Fickian, transport.Copyright © 2007 by ASME

Assessment of the functionality of tissue engineered cartilage constructs is hampered by the lack of correlation between global measurements of extra cellular matrix constituents and the global mechanical properties. Based on patterns of matrix deposition around individual cells, it has been hypothesized previously, that mechanical functionality arises when contact occurs between zones of matrix associated with individual cells. The objective of this study is to determine whether the local distribution of newly synthesized extracellular matrix components contributes to the evolution of the mechanical properties of tissue engineered cartilage constructs. A computational homogenization approach was adopted, based on the concept of a periodic representative volume element. Local transport and immobilization of newly synthesized matrix components were described. Mechanical properties were taken dependent on the local matrix concentration and subsequently the global aggregate modulus and hydraulic permeability were derived. The transport parameters were varied to assess the effect of the evolving matrix distribution during culture. The results indicate that the overall stiffness and permeability are to a large extent insensitive to differences in local matrix distribution. This emphasizes the need for caution in the visual interpretation of tissue functionality from histology and underlines the importance of complementary measurements of the matrix's intrinsic molecular organization.

A finite-element approach was formulated, aimed at enabling an integrated study of mechanical and biochemical factors that control the functional development of tissue engineered constructs. A nonlinear biphasic displacement-velocity-pressure description was combined with adjective and diffusive solute transport, uptake and biosynthesis. To illustrate the approach we focused on the synthesis and transport of macromolecules under influence of fluid flow induced by cyclic compression. In order to produce net transport the effect of dispersion was investigated. An abstract representation of biosynthesis was employed, three cases were distinguished: Synthesis dependent on a limited small solute, synthesis dependent on a limited large solute and synthesis independent of solute transport. Results show that a dispersion model can account for augmented solute transport by cyclic compression and indicate the different sensitivity to loading that can be expected depending on the size of the limiting solute.

A mixed numerical–experimental method is used to determine the parameters in elasto-plastic constitutive models. Aluminium plates of non-standard geometry are mounted in a uniaxial tensile-testing machine. On the surfaces of the plates retro-reflective markers are placed. The displacements of these markers are measured optically. These measurements are used to determine yield stresses in the isotropic Von Mises and the orthotropic Hill yield criterion. The models are evaluated by examining the estimated parameters and the residual displacements.

A mixed numerical-experimental method is used to determine parameters in elasto-plastic constitutive models. An aluminium plate of non-standard geometry is mounted in a uniaxial tensile testing machine at which some adjustments are made to carry out shear tests. The sample is loaded and the total clamp force in the shearing direction is recorded. Furthermore, the displacements of material points on the surface of the sample are measured optically. These measurements are used to determine parameters in two Von Mises plasticity models. The first model incorporates a linear hardening law and the second one a Nadai hardening law. The models are evaluated by examining the estimated parameter values and the differences between measured and calculated displacements and forces.

A numerical-experimental technique for the characterization of the mechanical behaviour of materials modeled as a mixture of an elastic solid matrix and an ideal fluid, is presented. Starting point is an identification technique, similar to the technique presented by Hendriks (1991). This technique uses the differences between measured and computed field quantities to adjust a priori estimates of material parameters.

The human skin is a very complex material: it has a high stiffness ratio, is time dependent and has inhomogeneous properties. One of these inhomogeneities is the fibre direction that varies with anatomical site. This fibre pattern is described by Langer’s lines. In the present paper a numerical/experimental way for the determination of the fibre layout is used. The method is based on numerical analysis, strain distribution measurement and system identification. By means of a numerical simulation it is shown that it is possible to determine material parameters for an inhomogeneous material. For that, the skin is modeled as a linear elastic solid with a varying fibre direction. The effects of noise and a modelling errors on the estimation results are shown.

A method to describe the stress situation in a wrinkled membrane is presented. In this paper it will be shown that a special deformation tensor can be chosen which leads to the correct stress state of a membrane after wrinkling when it is substituted in the constitutive equation. The method can be used for anisotropic membranes in geometrically and physically nonlinear analysis. The case of simple shear and stretching of a membrane is considered to illustrate the potency of the method.

In vitro compression studies have been performed on layers of porcine skin and fat. The tissue layers have been loaded by means of various indentors. Indentor displacements and interstitial fluid pressures have been measured. The results have been compared to finite element calculations with mixture elements. A qualitative agreement between calculations and measurements is found. The results support the hypothesis that skin and fat behave like solid/fluid mixtures.

Using a weighted residual method, a geometrically and physically nonlinear membrane element is derived, which can be used in the analysis of anisotropic membranes. What is special about the formulation is that the wrinkling behavior of the element is incorporated. If wrinkling occurs the stress situation in the element is determined by making use of a modified deformation tensor. A structure may have completely slack regions, leading to a singular stiffness matrix. Because of this we have chosen to use a restricted step method for the iterative solution procedure. A simple shear test is used to compare numerical and analytical results which show good agreement.

In tissue engineered heart valves, cell-mediated stress development during culture results in leaflet retraction at time of implantation. This tissue retraction is partly active due to traction forces exerted by the cells and partly passive due to release of residual stress in the extracellular matrix and the cells. Within this study, we unraveled the passive and active contributions of cells and matrix to generated force and retraction in engineered heart valve tissues. Tissue engineered rectangular strips, fabricated from PGA/P4HB scaffolds and seeded with human myofibroblasts, were cultured for 4 weeks, after which the cellular contribution was changed at different levels. Elimination of the active cellular traction forces was achieved with Cytochalasin D and inhibition of the Rho-associated kinase pathway. Both active and passive cellular contributions were eliminated by lysation and/or decellularization of the tissue. Maximum cell activity was reached by increasing the fetal bovine serum concentration to 50%. The generated force decreased ~20% after elimination of the active cellular component, ~25% when the passive cellular component was removed as well and remained unaffected by increased serum concentrations. Passive retraction accounted for ~60% of total retraction, of which ~15% was residual stress in the matrix and ~45% was passive cell retraction. Cell traction forces accounted for the remainder ~40% of the retraction. Full activation of the cells increased retraction by ~45%. These results illustrate the importance of the cells in the process of tissue retraction, not only actively retracting the tissue, but also in a passive manner to a large extent. © 2012 The Author(s).

Constitutive models to characterize fibre-reinforced composites and biological tissues are complex and usually contain a large number of parameters. A common way to measure these parameters is to load samples of a simple shape in such a way, that a homogeneous stress and strain distribution is obtained in some part of the sample. In this way a direct coupling between stress and strain is possible. However, such a procedure has disadvantages when used for composites or biological materials: Due to the complex mechanical behaviour it is hardly possible to create a simple stress and strain field. Hence the field equations can only be solved numerically. As many unknown parameters are to be determined (due to anisotropy, nonlinear visco-elastic behaviour) the number of experiments needed for a sufficient characterization is enormous. Most biological materials have inhomogeneous properties, so homogeneous strain distributions can not be obtained.

Skin can be viewed upon as a biphasic material, consisting of a solid with a free movable fluid in it (Reddy et al., 1981). The solid matrix consists of collagen and elastin fibers, embedded in a ground substance that binds most of the water. The movable, interstitial fluid is not chemically bound and can flow when a pressure gradient is present. The biphasic character can explain a number of time dependent properties of the skin. In view of the above a model has been developed, which is based on the theory of mixtures (Bowen, 1976). The goal of the present study was to find a method to measure material properties of porcine skin, using a biphasic concept and to compare the results with theoretically obtained values. A suitable experiment which has been used with success on articular cartilage (Mow et dl., 1984) is a confined compression test. It appears from this study that this test can be used for skin also and that it confirms our hypothesis about the biphasic nature of skin.

A general model describing the wrinkling of thin membranes is given. The model is able to describe the wrinkling of anisotropic membranes in geometrically non-linear analysis. Wrinkling is accounted for by replacing a given deformation tensor, which by using the constitutive equation would give negative Cauchy stresses, by a modified deformation tensor.