A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments

Constituent-based quasi-linear viscoelasticity: a revised quasi-linear modelling framework to capture nonlinear viscoelasticity in arteries

Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 [Formula: see text] 0.03 (mean [Formula: see text] standard deviation) at 80-40 mmHg to 1.58 [Formula: see text] 0.22 at 160-120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity.

Identifiability of tissue material parameters from uniaxial tests using multi-start optimization

Determining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Parameter optimization in tissue mechanics often comes down to the "identifiability" or "uniqueness" of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is currently no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs and establish a generalizable procedure for other applications. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We then fit this data using a multi-start optimization technique based on the nonlinear least-squares method with multiple initial parameter guesses. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.

How preconditioning and pretensioning of grafts used in ACLigaments surgical reconstruction are influenced by their mechanical time-dependent characteristics: Can we optimize their initial loading state?

PURPOSE

Consensus about a pre-implant preparation protocol adaptable to any graft used in Anterior Cruciate Ligament reconstruction is still lacking. In fact, there is not agreement on reliable metrics that consider both specific graft dimensional characteristics, such as its diameter, and the inherent properties of its constitutive material, i.e. ligaments or tendons. Aim of the present study was to investigate and propose the applied engineering stress as a possible metrics.

METHODS

Preconditioning and pretensioning protocol involved groups of grafts with different section (10 or 32 mm²) and materials (i.e. human patellar and hamstring tendons, and synthetic grafts). A 140 N load was applied to the grafts and maintained for 100 s. Initial stress and following stress-relaxation (a mechanical characteristic that can be related to knee laxity) were specifically analysed.

FINDINGS

Initial stress, ranging between 4 and 12 MPa, was affected primarily by the graft cross-section area and secondarily by the choice of the graft material. In terms of loss of the initial stress, stress-relaxation behaviour varied instead on a narrower range, namely 13-17%.

INTERPRETATION

Engineering stress can be identified as the correct metrics to optimize the initial state of each graft to avoid excessive stiffness, laxity or fatigue rupture phenomena.

Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee

In this paper the authors introduce a nonlinear model of fractional-order hereditariness used to capture experimental data obtained on human tendons of the knee. Creep and relaxation data on fibrous tissues have been obtained and fitted with logarithmic relations that correspond to power-laws with nonlinear dependence of the coefficients. The use of a proper nonlinear transform allows one to use Boltzmann superposition in the transformed variables yielding a fractional-order model for the nonlinear material hereditariness. The fundamental relations among the nonlinear creep and relaxation functions have been established, and the results from the equivalence relations have been contrasted with measures obtained from the experimental data. Numerical experiments introducing polynomial and harmonic stress and strain histories have been reported to assess the provided equivalence relations. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Mutual Sliding Motion of Wrapped Filaments for Biomedical and Engineering Applications

Here we aim at understanding and modeling of macroscopic interactions and sliding motion of curved filaments during muscles' isometric action in which tension is developed without overall contraction. A generic dynamic model of a curved elastic filament undergoing sliding, twisting, and unraveling around a cylindrical filament affected by the interfilament friction force is developed in full detail. In particular, the dynamic equations describing the general sliding motion of a curved filament wrapped around a cylindrical filament and pulled by a constant force applied to a free end are derived and solved numerically; the other end of the curved filament is considered to be fixed at the cylindrical one. The model predicts propagation of an elastic wave over the wrapped filament determined by the filament stiffness and the interfilament friction. The wrapped filament deformation and its ultimate arrest are predicted, and the final configurations of such filaments are revealed. Accordingly, the wrapped filament strain is predicted as a function of time for different values of the friction coefficient. The potential applications and possible biomechanical links of the proposed generic model are also discussed.

Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness

Non-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linear model of the springpot is defined in terms of a single integral with separable kernel endowed with a non-linear transform of the state variable that allows for the use of Boltzmann superposition. The model represents a self-similar hierarchy that allows for a time-invariance as the result of the application of the conservation laws at any resolution scale. It is shown that the non-linear springpot possess an equivalent mechanical hierarchy in terms of a functionally-graded elastic column resting on viscous dashpots with power-law decay of the material properties. Some numerical applications are reported to show the capabilities of the proposed model.

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in TI, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean elastic materials subjected to the same deformation. Its presence is explained by the anisotropic relaxation response of the medium.

Mechanobiological modelling of tendons: Review and future opportunities

Tendons are adapted to carry large, repeated loads and are clinically important for the maintenance of musculoskeletal health in an increasing, actively ageing population, as well as in elite athletes. Tendons are known to adapt to mechanical loading. Also, their healing and disease processes are highly sensitive to mechanical load. Computational modelling approaches developed to capture this mechanobiological adaptation in tendons and other tissues have successfully addressed many important scientific and clinical issues. The aim of this review is to identify techniques and approaches that could be further developed to address tendon-related problems. Biomechanical models are identified that capture the multi-level aspects of tendon mechanics. Continuum whole tendon models, both phenomenological and microstructurally motivated, are important to estimate forces during locomotion activities. Fibril-level microstructural models are documented that can use these estimated forces to detail local mechanical parameters relevant to cell mechanotransduction. Cell-level models able to predict the response to such parameters are also described. A selection of updatable mechanobiological models is presented. These use mechanical signals, often continuum tissue level, along with rules for tissue change and have been applied successfully in many tissues to predict in vivo and in vitro outcomes. Signals may include scalars derived from the stress or strain tensors, or in poroelasticity also fluid velocity, while adaptation may be represented by changes to elastic modulus, permeability, fibril density or orientation. So far, only simple analytical approaches have been applied to tendon mechanobiology. With the development of sophisticated computational mechanobiological models in parallel with reporting more quantitative data from in vivo or clinical mechanobiological studies, for example, appropriate imaging, biochemical and histological data, this field offers huge potential for future development towards clinical applications.

Modelling approaches for evaluating multiscale tendon mechanics

Tendon exhibits anisotropic, inhomogeneous and viscoelastic mechanical properties that are determined by its complicated hierarchical structure and varying amounts/organization of different tissue constituents. Although extensive research has been conducted to use modelling approaches to interpret tendon structure-function relationships in combination with experimental data, many issues remain unclear (i.e. the role of minor components such as decorin, aggrecan and elastin), and the integration of mechanical analysis across different length scales has not been well applied to explore stress or strain transfer from macro- to microscale. This review outlines mathematical and computational models that have been used to understand tendon mechanics at different scales of the hierarchical organization. Model representations at the molecular, fibril and tissue levels are discussed, including formulations that follow phenomenological and microstructural approaches (which include evaluations of crimp, helical structure and the interaction between collagen fibrils and proteoglycans). Multiscale modelling approaches incorporating tendon features are suggested to be an advantageous methodology to understand further the physiological mechanical response of tendon and corresponding adaptation of properties owing to unique in vivo loading environments.

Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient

The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery.

THE DIFFERENTIAL CONSTITUTIVE EQUATION AND MODEL OF ABALONE NACRE BY NANOINDENTER

Nacre has a complex hierarchical microarchitecture that spans over multiple length scales from nanoscale to macroscale. Its structures are optimized leading to extraordinary mechanical performance and energy absorption. Nacre's special characteristics of the self-assembly method have attracted the interest of material scientists to develop laminated composite materials, molecular scale self-assembly and biomineralization. Nanoindentation testing can determine a material's anisotropic properties through a single indentation. In the present study, nanoindentation stress–strain curves were used to characterize the complete mechanical behavior of nacre of abalone shell. A differential constitutive equation was developed with time-dependent spring constants k and viscosities η. Furthermore, to describe the complex viscoelastic behavior of abalone nacre, a descriptive representation of the linear viscoelasticity law for the multilayer matrix was formulated. A qualitative model for the relationship between nacre structure and mechanical properties of nacre may help develop bionic composite materials for micro-aircraft, bionic tribology, bionic medical apparatus and bionic organs (tissue engineering).

Experimental Characterization and Finite Element Implementation of Soft Tissue Nonlinear Viscoelasticity

Finite element (FE) models of articular joint structures do not typically implement the fully nonlinear viscoelastic behavior of the soft connective tissue components. Instead, contemporary whole joint FE models usually represent the transient soft tissue behavior with significantly simplified formulations that are computationally tractable. The resultant fidelity of these models is greatly compromised with respect to predictions under temporally varying static and dynamic loading regimes. In addition, models based upon experimentally derived nonlinear viscoelastic coefficients that do not account for the transient behavior during the loading event(s) may further reduce the model’s predictive accuracy. The current study provides the derivation and validation of a novel, phenomenological nonlinear viscoelastic formulation (based on the single integral nonlinear superposition formulation) that can be directly inputted into FE algorithms. This formulation and an accompanying experimental characterization technique, which incorporates relaxation manifested during the loading period of stress relaxation experiments, is compared to a previously published characterization method and validated against an independent analytical model. The results demonstrated that the static and dynamic FE approximations are in good agreement with the analytical solution. Additionally, the predictive accuracy of these approximations was observed to be highly dependent upon the experimental characterization technique. It is expected that implementation of the novel, computationally tractable nonlinear viscoelastic formulation and associated experimental characterization technique presented in the current study will greatly improve the predictive accuracy of the individual connective tissue components for whole joint FE simulations subjected to static and dynamic loading regimes.

Numerical modelling of the fibre-matrix interaction in biaxial loading for hyperelastic soft tissue models

This paper assumes that a neo-Hookean matrix with neo-Hookean fibres is representative of soft tissue. Under this assumption, a unit cell model is proposed to investigate the fibre-matrix interfacial stress field for biological soft tissue under biaxial loadings. In this unit cell model, the soft tissue is treated as a composite where the matrix is unidirectionally reinforced with a single family of aligned fibres. The results are compared with the model of Guo et al., which accounts for the fibre-matrix interfacial stress field, and Qiu and Pence's model, which does not proceed from the assumption that the fibres are themselves neo-Hookean. It is found that the stress representative of the fibre-matrix interface plays an important role in the deformation of the composite, and the model of Guo et al. underestimates this stress under large biaxial deformation.

Time-dependent properties of human umbilical fascia

This investigation is devoted to the study of the viscoelastic behavior of human abdominal fascia from the umbilical region. Seventeen samples 10 mm wide and up to 70 mm long were cut along the primary fiber direction (group FL) or perpendicular to it (group FT) and subjected to relaxation tests. The viscoelastic response of the tissue at three different strain levels (4%, 5%, and 6%) was investigated. The relaxation curves were fitted using a two-stage decaying exponential form. The following parameters were determined: initial stress σ(0), relaxation times τ(1) and τ(2), stress reduction Δσ, initial relaxation modulus E and equilibrium relaxation modulus E(eq), as well as the ratio E/E(eq). Fiber orientation and strain levels were varied to determine their influence on the viscoelastic properties of fascia. The results highlight the inherent viscoelastic mechanical properties of umbilical fascia. The values of the viscoelastic parameters determined for the longitudinal and transverse directions varied markedly. Significant differences were found between the two groups FL and FT for the initial stress at 5% and 6% strain (p < 0.038) and for the initial and equilibrium moduli at the 6% strain level (p < 0.046). The stress reduction in samples from the FL group (45-55%) was less than that in samples from the FT group (37-54%), but this difference was not significant (p > 0.388). The influence of strain level on the parameter values was not statistically significant (p > 0.121). The nonlinear response of the tissue was demonstrated over the chosen strain range.

The effect of cyclic loading simulating oscillatory joint mobilization on the posterior capsule of the glenohumeral joint: a cadaveric study

STUDY DESIGN

Experimental laboratory design.

OBJECTIVES

To examine the effect of force and repetition during oscillatory joint mobilizations on the posterior capsule of the glenohumeral joint.

BACKGROUND

The optimal external force and frequency to be used during joint mobilization to elongate the posterior capsule of the glenohumeral joint has yet to be identified.

METHODS

Twenty-one posterior capsules were harvested from fresh-frozen shoulders. A cyclic loading test simulating oscillatory posterior joint mobilization on the shoulder specimens was performed with a material testing machine. The specimens were assigned to 3 different loading groups simulating joint mobilization in the toe (5 N), transition (20 N), and beginning of the linear regions (40 N) of the load displacement curve. Displacement of the humeral head at an applied load of 5 N was recorded at the 1st, 100th, 200th, 300th, 400th, 500th, and 600th cycles and at 1 hour after completion of the cyclic loading. Furthermore, stiffness was calculated after the 1st and 600th cycles and 1 hour after testing.

RESULTS

Humeral head displacement was significantly greater for the 100th to 600th cycle, compared to the 1st cycle, for all 3 loading groups. Significant increases in displacement and stiffness were observed between the 1st cycle and 1 hour after completion of the cyclic tests for both the 20-N and 40-N loading groups.

CONCLUSION

While oscillatory joint mobilization to a force of 5 N resulted in temporary elongation of the posterior capsule, mobilization to loads of 20 and 40 N resulted in sustained elongation of the capsule for up to 1 hour. Our findings also suggest that mobilization up to loads that represent the beginning of the linear region of the load displacement curve could be performed without serious damage to the posterior capsule.

A nonlinear constituent based viscoelastic model for articular cartilage and analysis of tissue remodeling due to altered glycosaminoglycan-collagen interactions

A constituent based nonlinear viscoelastic (VE) model was modified from a previous study (Vena, et al., 2006, "A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments," J. Biomech. Eng., 128, pp. 449-457) to incorporate a glycosaminoglycan (GAG)-collagen (COL) stress balance using compressible elastic stress constitutive equations specific to articular cartilage (AC). For uniaxial loading of a mixture of quasilinear VE constituents, time constant and relaxation ratio equations are derived to highlight how a mixture of constituents with distinct quasilinear VE properties is one mechanism that produces a nonlinear VE tissue. Uniaxial tension experiments were performed with newborn bovine AC specimens before and after approximately 55% and approximately 85% GAG depletion treatment with guanidine. Experimental tissue VE parameters were calculated directly from stress relaxation data, while intrinsic COL VE parameters were calculated by curve fitting the data with the nonlinear VE model with intrinsic GAG viscoelasticity neglected. Select tissue and intrinsic COL VE parameters were significantly different from control and experimental groups and correlated with GAG content, suggesting that GAG-COL interactions exist to modulate tissue and COL mechanical properties. Comparison of the results from this and other studies that subjected more mature AC tissue to GAG depletion treatment suggests that the GAGs interact with the COL network in a manner that may be beneficial for rapid volumetric expansion during developmental growth while protecting cells from excessive matrix strains. Furthermore, the underlying GAG-COL interactions appear to diminish as the tissue matures, indicating a distinctive remodeling response during developmental growth.

A generalized Maxwell model for creep behavior of artery opening angle

An artery ring springs open into a sector after a radial cut. The opening angle characterizes the residual strain in the unloaded state, which is fundamental in understanding stress and strain in the vessel wall. A recent study revealed that the opening angle decreases with time if the artery is cut from the loaded state, while it increases if the cut is made from the no-load state due to viscoelasticity. In both cases, the opening angle approaches the same value in 3 h. This implies that the characteristic relaxation time is about 10,000 s. Here, the creep function of a generalized Maxwell model (a spring in series with six Voigt bodies) is used to predict the temporal change of opening angle in multiple time scales. It is demonstrated that the theoretical model captures the salient features of the experimental results. The proposed creep function may be extended to study the viscoelastic response of blood vessels under various loading conditions.

A Visco-Hyperelastic-Damage Constitutive Model for the Analysis of the Biomechanical Response of the Periodontal Ligament

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.

Creep and the in vivo assessment of human patellar tendon mechanical properties

BACKGROUND

Owing to the viscoelastic nature of tendons it may be that the total excursion and hence strain experienced by the tendon under load may be affected by the duration of contraction. Here we examine the effect of contraction duration on the measured in vivo mechanical properties of the patellar tendon.

METHODS

Nine healthy young men aged 21 (SEM 0.5 years) performed three short (3-4s) and three long (10-12s) maximal ramped isometric contractions on an isokinetic dynamometer, with real-time recordings of patellar excursions using B-mode ultrasonography synchronised with forces to determine tendon mechanical properties.

FINDINGS

Maximal patellar excursion was approximately 42% (P<0.001, effect size (r)=0.9) lower for the short 3.6 (SEM 0.4mm) vs. the long 6.2 (SEM 0.4mm) contractions. Similarly, across the range of forces tested, strain was approximately 42% (P<0.001, r=0.9) lower for the short vs. the long contractions 4.5 (SEM 0.5) vs. 8.0 (SEM 0.9%), respectively. Tendon stiffness however, was approximately 77% greater (4648 SEM 434 vs. 2633 SEM 257 N mm(-1), P<0.001, r=0.9) for short vs. long contractions.

INTERPRETATION

Contraction duration significantly affects tendon strain and associated measures of stiffness at all levels of force. The implications of this finding are twofold in that the results: (a) indicate that in order to compare tendon mechanical properties within or across studies, duration of contraction must be standardised and (b) have possible implications on training protocols and associated injury risks.

Viscoelasticity reduces the dynamic stresses and strains in the vessel wall: implications for vessel fatigue

The mechanical behavior of blood vessels is known to be viscoelastic rather than elastic. The functional role of viscoelasticity, however, has remained largely unclear. The hypothesis of this study is that viscoelasticity reduces the stresses and strains in the vessel wall, which may have a significant impact on the fatigue life of the blood vessel wall. To verify the hypothesis, the pulsatile stress in rabbit thoracic artery at physiological loading condition was investigated with a quasi-linear viscoelastic model, where the normalized stress relaxation function is assumed to be isotropic, while the stress-strain relationship is anisotropic and nonlinear. The artery was subjected to the same boundary condition, and the mechanical equilibrium equation was solved for both the viscoelastic and an elastic (which has a constant relaxation function) model. Numerical results show that, compared with purely elastic response, the viscoelastic property of arteries reduces the magnitudes and temporal variations of circumferential stress and strain. The radial wall movement is also reduced due to viscoelasticity. These findings imply that viscoelasticity may be beneficial for the fatigue life of blood vessels, which undergo millions of cyclic mechanical loadings each year of life.

A rate-insensitive linear viscoelastic model for soft tissues

It is well known that many biological soft tissues behave as viscoelastic materials with hysteresis curves being nearly independent of strain rate when loading frequency is varied over a large range. In this work, the rate-insensitive feature of biological materials is taken into account by a generalized Maxwell model. To minimize the number of model parameters, it is assumed that the characteristic frequencies of Maxwell elements form a geometric series. As a result, the model is characterized by five material constants: micro(0), tau, m, rho and beta, where micro(0) is the relaxed elastic modulus, tau the characteristic relaxation time, m the number of Maxwell elements, rho the gap between characteristic frequencies, and beta=micro(1)/micro(0) with micro(1) being the elastic modulus of the Maxwell body that has relaxation time tau. The physical basis of the model is motivated by the microstructural architecture of typical soft tissues. The novel model shows excellent fit of relaxation data on the canine aorta and captures the salient features of vascular viscoelasticity with significantly fewer model parameters.