A new model for the mechanochemical response of smooth muscle is presented. The focus is on the response of the actin-myosin complex and on the related generation of force (or stress). The chemical (kinetic) model describes the cross-bridge interactions with the thin filament in which the calcium-dependent myosin phosphorylation is the only regulatory mechanism. The new mechanical model is based on Hill's three-component model and it includes one internal state variable that describes the contraction/relaxation of the contractile units. It is characterized by a strain-energy function and an evolution law incorporating only a few material parameters with clear physical meaning. The proposed model satisfies the second law of thermodynamics. The results of the combined coupled model are broadly consistent with isometric and isotonic experiments on smooth muscle tissue. The simulations suggest that the matrix in which the actin-myosin complex is embedded does have a viscous property. It is straightforward for implementation into a finite element program in order to solve more complex boundary-value problems such as the control of short-term changes in lumen diameter of arteries due to mechanochemical signals.

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A new method is proposed for estimating the elastic properties of the inhomogeneous and anisotropic structure of saccular cerebral aneurysms by inverse analysis. The aneurysm is modelled as a membrane and the constitutive response of each individual layer of the passive tissue is characterized by a transversely isotropic strain energy function of exponential type. The collagen fibres in the aneurysm wall are assumed to govern the mechanical response. Four parameters characterize the constitutive behaviour of the tissue: two initial stiffnesses of the collagen fabric in the two in-plane principal directions, one parameter describing the degree of nonlinearity that the collagen fibres exhibit and the other structural parameter, i.e. the angle which defines the orientation of the collagen fibres. The parameter describing the fibre nonlinearity is assumed to be constant, while all others are assumed to vary continuously over the aneurysm surface. Two model aneurysms, with the same initial geometry, boundary and loading conditions, constitutive behaviour and finite-element discretization, are defined: a 'reference model' with known distributions of material and structural properties and an 'estimation model' whose properties are to be estimated. An error function is defined quantifying the deviations between the deformations from the reference and the estimation models. The error function is minimized with respect to the unknown parameters in the estimation model, and in this way the reference parameter distributions are re-established. In order to achieve a robust parameter estimation, a novel element partition method is employed. The accordance between the estimated and the reference distributions is satisfactory. The deviations of the maximum stress distributions between the two models are below 1%. Consequently, the wall stresses in the cerebral aneurysm estimated by inverse analysis are accurate enough to facilitate the assessment of the risk of aneurysm rupture.

A new theoretical model for the growth of saccular cerebral aneurysms is proposed by extending the recent constitutive framework of Kroon and Holzapfel (J. Theor. Biol., 247:775-787, 2007). The continuous turnover of collagen is taken to be the driving mechanism in aneurysmal growth. The collagen production rate depends on the magnitude of the cyclic deformation of fibroblasts, caused by the pulsating blood pressure during the cardiac cycle. The volume density of fibroblasts in the aneurysmal tissue is taken to be constant throughout the growth process. The growth model is assessed by considering the inflation of an axisymmetric membranous piece of aneurysmal tissue, with material characteristics representative of a cerebral aneurysm. The diastolic and systolic states of the aneurysm are computed, together with its load-free state. It turns out that the value of collagen pre-stretch, that determines growth speed and stability of the aneurysm, is of pivotal importance. The model is able to predict aneurysms with typical berry-like shapes observed clinically, and the predicted wall stresses correlate well with the experimentally obtained ultimate stresses of this type of tissue. The model predicts that aneurysms should fail when reaching a size of about 1.2-3.6 mm, which is smaller than what has been clinically observed. With some refinements, the model may, however, be used to predict future growth of diagnosed aneurysms.

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Several industrial applications involve rubber and rubber-like materials, and it is important to be able to predict the constitutive response of these materials. In the present paper, a new constitutive model for rubber-like solids is proposed. The model is based on the 8-chain concept introduced by Arruda and Boyce (J. Mech. Phys. Solids 41, 389-412, 1993) to which two new components are added. Real polymer networks do not deform affinely, and in the proposed model this is accounted for by the inclusion of an elastic spring, acting in series with the representative polymer chain. Furthermore, real polymer chains are not completely free to move, which is modelled by imposing a topological constraint on the transverse motions of the representative polymer chain. The model contains five model parameters and these need to be determined on the basis of experimental data. Three experimental studies from the literature were used to assess the proposed model. The model was able to reproduce experimental data performed under conditions of uniaxial tension, generalised plane deformation, and biaxial tension with an excellent accuracy. The strong predictive abilities together with the numerically efficient structure of the model make it suitable for implementation in a finite element context.

A new constitutive model for the biomechanical behaviour of smooth muscle tissue is proposed. The active muscle contraction is accomplished by the relative sliding between actin and myosin filaments, comprising contractile units in the smooth muscle cells. The model includes a chemical part, governing the cross-bridge (myosin head) cycling, that is responsible for the filament sliding. The number of activated cross-bridges govern the contractile force generated and also the contraction speed. A strain-energy function is used to describe the mechanical behaviour of the smooth muscle tissue. Besides the active contractile apparatus, the mechanical model also incorporates a passive viscoelastic part. The constitutive model was calibrated with respect to experiments on smooth muscle tissue from swine carotid artery and guinea pig taenia coli, in terms of isometric and isotonic tensile test results. The model was fully able to reproduce the experimental results.