Four-fiber Family Research Articles

Convexity, polyconvexity and finite element implementation of a four-fiber anisotropic hyperelastic strain energy density—Application to the modeling of femoral, popliteal and tibial arteries

Computational analysis of the nonlinear mechanical properties of anisotropic hyperelastic materials aims at a better understanding of its physiology and pathophysiology under different loading conditions. This has an important role in biomechanics, surgical, clinical diagnostic and design of medical devices. This study investigates the modeling of arterial tissues made of a four-fiber family by using an anisotropic hyperelastic model. This model is based on the theory of polynomial invariant and was implemented in the university finite element code FER. The convex property of the strain energy function is investigated as well as the positive definite nature of the tangent stiffness matrix used within the framework of a finite element analysis. This allows us to guarantee the invertibility of the linearized problem and the uniqueness of the solution computed at each step of the Newton–Raphson scheme used to solve nonlinear problems.

Fitting of hyperplastic constitutive models in different sheep heart regions based on biaxial mechanical tests

Heart failure remains one of the leading causes of death especially among people over the age of 60 years worldwide. To develop effective therapy and suitable replace-ment materials for the heart muscle it is necessary to understand its biomechanical be-haviour under load. This paper investigates the passive mechanical response of the sheep myocardia excised from three different regions of the heart. Due to the relatively higher cost and huge ethical demands in acquisition and testing of real animal heart models, this paper evaluates the fitting performances of six different constitutive models on the myocardial tissue responses. Ten sheep were sacrificed, and their hearts were excised and transported within 3 h to the testing biomechanical laboratory. The upper sections of the hearts above the short axes were carefully dissected out. Tissues were dissected from the mid-sections of the left ventricle, mid-wall and right ventricle for each heart. The epicardia and endocardia were then carefully sliced off each tissue to leave the myocardia. Stress-strain curves were calculated, filtered and resampled. The results show that Choi-Vito model was found to provide the best fit to the left ventricle, the poly-nomial (anisotropic) model to right ventricle, the Four-Fiber Family model to right ventri-cle, Holzapfel (2000) to right ventricle, Holzapfel (2005) to right ventricle and the Fung model to left ventricle.

Biomechanical analysis of sheep oesophagus subjected to biaxial testing including hyperelastic constitutive model fitting

High quality computational model of soft tissues is a function of accurate and reliable mechanical properties. Hyperelastic constitutive models are normally utilised in developing reliable computational models. Therefore, section of proper and reliable constitutive models for soft tissue is critical. This work presents the biomechanical properties of oesophagus subjected to biaxial mechanical tensile test. Additionally, six hyperelastic constitutive models commonly used for modelling behaviour of soft tissues were selected. The experimental data were then fitted on Fung, Choi-Vito, Holzapfel (2000), Holzapfel (2005), Polynomial (Anisotropic) and Four-Fiber Family hyperelastic constitutive models. The sheep oesophagus subjected to equi-biaxial tension has exhibited different stress magnitude in both longitudinal and circumferential directions. There is significant difference between circumferential and longitudinal stresses (p = 0.0034). The average circumferential and longitudinal stresses are recorded to be 82.87 ± 30.36 kPa and 41.42 ± 32.02 kPa, respectively (p = 0.0034). Between six hyperelastic constitutive models, it was observed that Four-Fiber model has produced better fit when compared to others. After fitting biaxial mechanical properties of oesophagus, it was found that the Four-fiber family hyperelastic constitutive model would best fit.

Biomechanical Properties of Mouse Carotid Arteries With Diet-Induced Metabolic Syndrome and Aging.

Metabolic syndrome increases the risk of cardiovascular diseases. Arteries gradually stiffen with aging; however, it can be worsened by the presence of conditions associated with metabolic syndrome. In this study, we investigated the combined effects of diet-induced metabolic syndrome and aging on the biomechanical properties of mouse common carotid arteries (CCA). Male mice at 2 months of age were fed a normal or a high fat and high sucrose (HFHS) diet for 2 (young group), 8 (adult group) and 18–20 (old group) months. CCAs were excised and subjected to in vitro biaxial inflation-extension tests and the Cauchy stress-stretch relationships were determined in both the circumferential and longitudinal directions. The elastic energy storage of CCAs was obtained using a four-fiber family constitutive model, while the material stiffness in the circumferential and longitudinal directions was computed. Our study showed that aging is a dominant factor affecting arterial remodeling in the adult and old mice, to a similar extent, with stiffening manifested with a significantly reduced capability of energy storage by ∼50% (p < 0.05) and decreases in material stiffness and stress (p < 0.05), regardless of diet. On the other hand, high fat high sucrose diet resulted in an accelerated arterial remodeling in the young group at pre-diabetic stage by affecting the circumferential material stiffness and stress (p < 0.05), which was eventually overshadowed by aging progression. These findings have important implications on the effects of metabolic syndrome on elastic arteries in the younger populations.

Constitutive modeling using structural information on collagen fiber direction and dispersion in human superficial femoral artery specimens of different ages

Arterial mechanics plays an important role in vascular pathophysiology and repair, and advanced imaging can inform constitutive models of vascular behavior. We have measured the mechanical properties of 14 human superficial femoral arteries (SFAs) (age 12–70, mean 48±19 years) using planar biaxial extension, and determined the preferred collagen fiber direction and dispersion using multiphoton microscopy. The collagen fiber direction and dispersion were evaluated using second-harmonic generation imaging and modeled using bivariate von Mises distributions. The microstructures of elastin and collagen were assessed using two-photon fluorescence imaging and conventional bidirectional histology. The mechanical and structural data were used to describe the SFA mechanical behavior using two- and four-fiber family invariant-based constitutive models. Older SFAs were stiffer and mechanically more nonlinear than younger specimens. In the adventitia, collagen fibers were undulated and diagonally-oriented, while in the media, they were straight and circumferentially-oriented. The media was rich in collagen that surrounded the circumferentially-oriented smooth muscle cells, and the elastin was present primarily in the internal and external elastic laminae. Older SFAs had a more circumferential collagen fiber alignment, a decreased circumferential-radial fiber dispersion, but the same circumferential-longitudinal fiber dispersion as younger specimens. Both the two- and the four-fiber family constitutive models were able to capture the experimental data, and the fits were better for the four-fiber family formulation. Our data provide additional details on the SFA intramural structure and inform structurally-based constitutive models.

Alterations with age in the biomechanical behavior of human ureteral wall: Microstructure-based modeling

The human ureters have not been thoroughly explored from the biomechanics perspective, despite the wealth of such data for other soft-tissue types. This study was motivated by the need to use relevant biomechanical data from human ureters and microstructure-based material formulations for simulations of ureteral peristalsis and stenting. Our starting choice was the four-fiber family model that has proven its validity as a descriptor of the multiaxial response of cardiovascular tissues. The degree of model complexity, required for rigorous fits to passive quasi-static pressure-diameter-force data at several axial stretches, was systematically investigated. Ureteral segments from sixteen human autopsy subjects were evaluated. A diagonal and axial family model allowed equally-good fits as the full model for all age groups and ureteral regions; considerably better than those allowed by the phenomenological Fung-type model whose root-mean-square error of fitting was three-fold greater. This reduced model mimicked the structure seen in histologic sections, namely plentiful diagonal collagen fibers in the lamina propria and axial fibers in the muscle and adventitia. The paucity of elastin fibers and mixed muscle orientation justified the use of isotropic muscle-dominated matrix with small neo-Hookean parameter values. The significantly thicker lamina propria in the lower than the upper ureter of young subjects (312 ± 27 vs. 232 ± 26 μm; mean ± standard error) corroborated the significant regional differences in diagonal-fiber family parameter values. The significant muscle thickening with age (upper ureter: 373 ± 48 vs. 527 ± 67 μm; middle: 388 ± 29 vs. 575 ± 69 μm; lower: 440 ± 21 vs. 602 ± 71 μm) corroborated the significant age-related increase in axial-fiber family parameter values.

Biomechanical characterization of murine pulmonary arteries

The biomechanical properties of the major pulmonary arteries play critical roles in normal physiology as well as in diverse pathophysiologies and clinical interventions. Importantly, advances in medical imaging enable simulations of pulmonary hemodynamics, but such models cannot reach their full potential until they are informed with region-specific material properties. In this paper, we present passive and active biaxial biomechanical data for the right and left main pulmonary arteries from wild-type mice. We also evaluate the suitability of a four-fiber family constitutive model as a descriptor of the passive behavior. Despite regional differences in size, the biaxial mechanical properties, including passive stiffness and elastic energy storage, the biaxial wall stresses at in vivo pressures, and the overall contractile capacity in response to smooth muscle cell stimulation under in vivo conditions are remarkably similar between the right and left branches. The proposed methods and results can serve as baseline protocols and measurements for future biaxial experiments on murine models of pulmonary pathologies, and the constitutive model can inform computational models of normal pulmonary growth and remodeling. Our use of consistent experimental protocols and data analyses can also facilitate comparative studies in health and disease across the systemic and pulmonary circulations as well as studies seeking to understand remodeling in surgeries such as the Fontan procedure, which involves different types of vessels.

A simple polyconvex strain energy density with new invariants for modeling four-fiber family biomaterials

We introduce in this paper a new hyperelastic model for the prediction of nonlinear mechanical properties of anisotropic hyperelastic materials under biaxial stretching. The proposed strain energy function (SEF) can be applied for understanding the nature of behavior laws for materials with four-fiber family structures, which has a large potential of applications, particularly in biomechanics, surgical and interventional therapies for peripheral artery disease (PAD). This SEF is built with a recent and new invariant system based on the mathematical theory of invariant polynomials. By recombining them in an appropriate manner, we demonstrate that it is possible to build a polyconvex integrity basis of invariants. Accuracy and reliability of the corresponding numerical model were validated by a comparison with experimental and numerical results extracted from Kamenskiy et al. (2014).11We warmly thank Assistant Professor Kamenskiy to have kindly provided us the numerical data corresponding to the measurements included in Kamenskiy et al. (2014). These results concerned diseased superficial femoral (SFA), popliteal (PA) and tibial arteries (TA) from one patient under planar biaxial extension. For each kind of arteries tested with 5 combinations of different biaxial stretches, the predicted results of the proposed model and the experimental data are consistent. Our model includes 7 material parameters and their identification result in a single solution because of the linear form we have chosen for the SEF with respect to the material parameters.

Characterization of the mechanical behavior of the optic nerve sheath and its role in spaceflight-induced ophthalmic changes.

Visual impairment and intracranial pressure (VIIP) syndrome is characterized by a number of permanent ophthalmic changes, including loss of visual function. It occurs in some astronauts during long-duration spaceflight missions. Thus, understanding the pathophysiology of VIIP is currently a major priority in space medicine research. It is hypothesized that maladaptive remodeling of the optic nerve sheath (ONS), in response to microgravity-induced elevations in intracranial pressure (ICP), contributes to VIIP. However, little is known about ONS biomechanics. In this study, we developed a custom mechanical testing system that allowed for unconfined lengthening, twisting, and circumferential distension of the porcine ONS during inflation and axial loading. Data were fit to a four-fiber family constitutive equation to extract material and structural parameters. Inflation testing showed a characteristic "cross-over point" in the pressure-diameter curves under different axial loads in all samples that were tested; the cross-over pressure was [Formula: see text]mmHg ([Formula: see text]). Large sample-to-sample variations were observed in the circumferential strain, while only modest variations were observed in the circumferential stress. Multiphoton microscopy revealed that the collagen fibers of the ONS were primarily oriented axially when the tissue was loaded. The existence of this cross-over behavior is expected to be neuroprotective, as it would avoid optic nerve compression during routine changes in gaze angle, so long as ICP was within the normal range. Including these observations into computational models of VIIP will help provide insight into the pathophysiology of VIIP and could help identify risk factors and potential interventions.

Layer-dependent wall properties of abdominal aortic aneurysms: Experimental study and material characterization

Mechanical testing and in-depth characterization of the abdominal aortic aneurysm wall from fifteen patients undergoing open surgery was performed to establish the layer-dependent tissue properties that are non-available in the literature. Quantitative microscopic evaluation was performed to identify the spatial organization of collagen-fiber network. Among a number of candidate models, the four-fiber family (microstructure-motivated) model, especially that including dispersions of fiber angles about the main directions, was superior to the Fung- and Gasser-type models in the fitting quality allowed, though it presented a practical difficulty in parameter estimation, so that an analysis was conducted aiding the identification of a more specific diagonal- and circumferential-fiber family model for all three layers. The adventitia was stiffer and stronger than the other layers, owing to its increased collagen content, and its contribution to the response of the intact wall was augmented being under greater residual tension than the media, whereas the intima was under residual compression. All layers were stiffer circumferentially than longitudinally, due to preferential collagen arrangement along that axis. The histologically-guided material characterization of layered wall presented herein is expected to assist clinical decision, by developing reliable criteria to predict the rupture risk of abdominal aortic aneurysms, and optimize endovascular interventions.

Passive biaxial mechanical properties and in vivo axial pre-stretch of the diseased human femoropopliteal and tibial arteries

Surgical and interventional therapies for atherosclerotic lesions of the infrainguinal arteries are notorious for high rates of failure. Frequently, this leads to expensive reinterventions, return of disabling symptoms or limb loss. Interaction between the artery and repair material likely plays an important role in reconstruction failure, but data describing the mechanical properties and functional characteristics of human femoropopliteal and tibial arteries are currently not available. Diseased superficial femoral (SFA, n=10), popliteal (PA, n=8) and tibial arteries (TA, n=3) from 10 patients with critical limb ischemia were tested to determine passive mechanical properties using planar biaxial extension. All specimens exhibited large nonlinear deformations and anisotropy. Under equibiaxial loading, all arteries were stiffer in the circumferential direction than in the longitudinal direction. Anisotropy and longitudinal compliance decreased distally, but circumferential compliance increased, possibly to maintain a homeostatic multiaxial stress state. Constitutive parameters for a four-fiber family invariant-based model were determined for all tissues to calculate in vivo axial pre-stretch that allows the artery to function in the most energy efficient manner while also preventing buckling during extremity flexion. Calculated axial pre-stretch was found to decrease with age, disease severity and more distal arterial location. Histological analysis of the femoropopliteal artery demonstrated a distinct sub-adventitial layer of longitudinal elastin fibers that appeared thicker in healthier arteries. The femoropopliteal artery characteristics and properties determined in this study may assist in devising better diagnostic and treatment modalities for patients with peripheral arterial disease.

Time-course of venous wall biomechanical adaptation in pressure and flow-overload: Assessment by a microstructure-based material model

Arteriovenous fistulae have been previously created by our group, through implantation of e-PTFE grafts between the carotid artery and jugular vein in healthy pigs, to gather comprehensive data on the time-course of the adapted geometry, composition, and biomechanical properties of the venous wall exposed to chronic increases in pressure and flow. The aim of this study was to mathematically assess the biomechanical adaptation of venous wall, by characterizing our previous in vitro inflation/extension testing data obtained 2, 4, and 12 weeks post-fistula, using a microstructure-based material model. Our choice for such a model considered a quadratic function for elastin with a four-fiber family term for collagen, and permitted realistic data characterization for both overloaded and control veins. As structural validation to the hemodynamically-driven differences in the material response, computerized histology was employed to quantitate the composition and orientation of collagen and elastin-fiber networks. The parameter values optimized showed marked differences among the overloaded and control veins, namely decrease in the quadratic function parameters and increase in the four-fiber family parameters. Differences among the two vein types were highlighted with respect to the underlying microstructure, namely the reduced elastin and increased collagen contents induced by pressure and flow-overload. Explicit correlations were found of the material parameters with the two basic scleroprotein contents, substantiating the material model used and the characterization findings presented. Our results are expected to improve the current understanding of the dynamics of venous adaptation under sustained pressure- and flow-overload conditions, for which data are largely unavailable and contradictory.

Structurally-motivated characterization of the passive pseudo-elastic response of esophagus and its layers

This paper reports on the implementation of microstructurally-motivated models for material characterization of the passive esophagus and its layers. The principal findings afforded herewith were that the comprehensive model with two- and four-fiber family terms for elastin and collagen fitted more accurately the inflation/extension data of healthy rabbit esophagus than traditional phenomenological models. An analysis of material constant behavior was also performed from which concise, specific models were derived, neither missing essential collagen and elastin structures in mucosa, submucosa, and muscle layers nor being over-parameterized, while providing equally-accurate fits with all the advantages of computational economy and material constant interpretability.

Experimental investigation and constitutive modeling of the 3D histomechanical properties of vein tissue

Numerous studies have provided material models of arterial walls, but limited information is available on the pseudo-elastic response of vein walls and their underlying microstructure, and only few constitutive formulations have been proposed heretofore. Accordingly, we identified the histomechanics of healthy porcine jugular veins by applying an integrated approach of inflation/extension tests and histomorphometric evaluation. Several alternate phenomenological and microstructure-based strain-energy functions (SEF) were attempted to mimic the material response. Evaluation of their descriptive/predictive capacities showed that the exponential Fung-type SEF alone or in tandem with the neo-Hookean term did not capture the deformational response at high pressures. This problem was solved to a degree with the neo-Hookean and two-fiber (diagonally arranged) family SEF, but altogether the least reliable fit was generated. Fitting precision was much improved with the four-fiber (diagonally, circumferentially, longitudinally arranged) family model, as the inability of neo-Hookean function with force data was alleviated by use of the longitudinal-fiber family. Implementation of a quadratic term as a descriptor of low-pressure anisotropy facilitated the simulation of low-pressure and force data, and the four-fiber families simulated more faithfully than the two-fiber families the physiologic and high-pressure response. Importantly, this SEF was consistent with vein angioarchitecture, namely the occurrence of extensive elastin fibers along the longitudinal axis and few orthogonal fibers attached to them and of three collagen sets with circumferential, longitudinal, and diagonal arrangement, respectively. Our findings help to establish the relationship between vein microstructure and its biomechanical response, yet additional observations are obligatory prior to endeavoring generalizations to other veins.

Differential histomechanical response of carotid artery in relation to species and region: mathematical description accounting for elastin and collagen anisotropy

The selection of a mathematical descriptor for the passive arterial mechanical behavior has been long debated in the literature and customarily constrained by lack of pertinent data on the underlying microstructure. Our objective was to analyze the response of carotid artery subjected to inflation/extension with phenomenological and microstructure-based candidate strain-energy functions (SEFs), according to species (rabbit vs. pig) and region (proximal vs. distal). Histological variations among segments were examined, aiming to explicitly relate them with the differential material response. The Fung-type model could not capture the biphasic response alone. Combining a neo-Hookean with a two-fiber family term alleviated this restraint, but force data were poorly captured, while consideration of low-stress anisotropy via a quadratic term allowed improved simulation of both pressure and force data. The best fitting was achieved with the quadratic and Fung-type or four-fiber family SEF. The latter simulated more closely than the two-fiber family the high-stress response, being structurally justified for all artery types, whereas the quadratic term was justified for transitional and muscular arteries exhibiting notable elastin anisotropy. Diagonally arranged fibers were associated with pericellular medial collagen, and circumferentially and longitudinally arranged fibers with medial and adventitial collagen bundles, evidenced by the significant correlations of SEF parameters with quantitative histology.

Differential Passive and Active Biaxial Mechanical Behaviors of Muscular and Elastic Arteries: Basilar Versus Common Carotid

Cerebrovascular disease continues to be responsible for significant morbidity and mortality. There is, therefore, a pressing need to understand better the biomechanics of both intracranial arteries and the extracranial arteries that feed these vessels. We used a validated four-fiber family constitutive relation to model passive biaxial stress-stretch behaviors of basilar and common carotid arteries and we developed a new relation to model their active biaxial responses. These data and constitutive relations allow the first full comparison of circumferential and axial biomechanical behaviors between a muscular (basilar) and an elastic (carotid) artery from the same species. Our active model describes the responses by both types of vessels to four doses of the vasoconstrictor endothelin-1 (10(-10)M, 10(-9)M, 10(-8)M, and 10(-7)M) and predicts levels of smooth muscle cell activation associated with basal tone under specific in vitro testing conditions. These results advance our understanding of the biomechanics of intracranial and extracranial arteries, which is needed to understand better their differential responses to similar perturbations in hemodynamic loading.

Biomechanical and Microstructural Properties of Common Carotid Arteries from Fibulin-5 Null Mice

Alteration in the mechanical properties of arteries occurs with aging and disease, and arterial stiffening is a key risk factor for subsequent cardiovascular events. Arterial stiffening is associated with the loss of functional elastic fibers and increased collagen content in the wall of large arteries. Arterial mechanical properties are controlled largely by the turnover and reorganization of key structural proteins and cells, a process termed growth and remodeling. Fibulin-5 (fbln5) is a microfibrillar protein that binds tropoelastin, interacts with integrins, and localizes to elastin fibers; tropoelastin and microfibrillar proteins constitute functional elastic fibers. We performed biaxial mechanical testing and confocal imaging of common carotid arteries (CCAs) from fibulin-5 null mice (fbln5 ⁻(/)⁻) and littermate controls (fbln5 (+/+)) to characterize the mechanical behavior and microstructural content of these arteries; mechanical testing data were fit to a four-fiber family constitutive model. We found that CCAs from fbln5 ⁻(/)⁻ mice exhibited lower in vivo axial stretch and lower in vivo stresses while maintaining a similar compliance over physiological pressures compared to littermate controls. Specifically, for fbln5 ⁻(/)⁻ the axial stretch λ = 1.41 ± 0.07, the circumferential stress σ(θ) = 101 ± 32 kPa, and the axial stress σ ( z ) = 74 ± 28 kPa; for fbln5 (+/+) λ = 1.64 ± 0.03, σ(θ) = 194 ± 38 kPa, and σ(z) = 159 ± 29 kPa. Structurally, CCAs from fbln5 ⁻(/)⁻ mice lack distinct functional elastic fibers defined by the lamellar structure of alternating layers of smooth muscle cells and elastin sheets. These data suggest that structural differences in fbln5 ⁻(/)⁻ arteries correlate with significant differences in mechanical properties. Despite these significant differences fbln5 ⁻(/)⁻ CCAs exhibited nearly normal levels of cyclic strain over the cardiac cycle.

Mechanics of Carotid Arteries in a Mouse Model of Marfan Syndrome

Mouse models of Marfan Syndrome (MFS) provide insight into the type and extent of vascular abnormalities manifested in this disease. Inclusion of the mgR mutation causes the otherwise normal extracellular matrix glycoprotein fibrillin-1 to be under-expressed at 15-25% of its normal level, a condition seen in MFS. Aortas in patients with MFS are generally less distensible and may experience dissecting aneurysms that lead to premature death, yet little is known about effects on other large arteries. In this study, common carotid arteries from mice heterozygous (R/+) and homozygous (R/R) for the mgR mutation were studied under biaxial loading and compared to results from wild-type controls (+/+). Carotids from +/+ and R/+ mice exhibited similar biomechanical behaviors whereas those from R/R mice were slightly stiffer in the circumferential direction while dramatically different in the axial direction. That is, R/R carotids were stiffer axially and had lower in vivo axial prestretches. Biaxial stress-stretch data were fit with a four-fiber family constitutive model. The fitted data yielded a lower value of an isotropic parameter for the R/R carotids, which reflects a compromised elastin-dominated amorphous matrix. Overall, it appeared that changes in axial mechanical properties afforded R/R carotids a means to compensate, at least early in maturity (9 weeks of age), for the loss of an important structural constituent as they attempted to maintain structural integrity in response to normal mean arterial pressures and thereby maintain mechanical homeostasis.

Quantification of the mechanical behavior of carotid arteries from wild-type, dystrophin-deficient, and sarcoglycan- δ knockout mice

As patients with muscular dystrophy live longer because of improved clinical care, they will become increasingly susceptible to many of the cardiovascular diseases that affect the general population. There is, therefore, a pressing need to better understand both the biology and the mechanics of the arterial wall in these patients. In this paper, we use nonlinear constitutive relations to model, for the first time, the biaxial mechanical behavior of carotid arteries from two common mouse models of muscular dystrophy (dystrophin-deficient and sarcoglycan- δ null) and wild-type controls. It is shown that a structurally motivated four-fiber family stress–strain relation describes the passive behavior of all three genotypes better than does a commonly used phenomenological exponential model, and that a Rachev–Hayashi model describes the mechanical contribution of smooth muscle contraction under basal tone. Because structurally motivated constitutive relations can be extended easily to model adaptations to altered hemodynamics, results from this study represent an important step toward the ultimate goal of understanding better the mechanobiology and pathophysiology of arteries in muscular dystrophy.

Normal basilar artery structure and biaxial mechanical behaviour

Much is known about cerebral vasospasm, a devastating sequela to ruptured intracranial aneurysms, yet underlying mechanisms remain unclear and clinical treatments have proven unsatisfactory. We have hypothesised that biochemical stimuli associated with the formation of extravascular blood clots dominate early maladaptive responses, leading to marked structural and functional changes in affected cerebral arteries. Before a precise picture of vasospasm can be obtained, however, we must understand better the structure and mechanical behaviour of normal cerebral arteries. Basilar arteries from rabbits were tested mechanically under biaxial loading conditions with and without active tone, segments were imaged using intravital nonlinear optical microscopy to quantify transmural orientations of fibrillar collagen, and passive mechanical data were fit with a four-fiber family stress–stretch relation. This constitutive model predicted well the overall mechanical behaviour and mean collagen fiber distributions, and thereby has promise to contribute to analyses of the biochemomechanics of cerebral vasospasm and similar cerebral pathologies. It is now time, therefore, to focus on mechanisms of vasospasm via mathematical models that incorporate growth and remodelling in terms of changes in the cross-linking and distributions of adventitial and medial collagen, primary contributors to the structural integrity of the arterial wall.