Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.     

Viscoelastic properties of the tongue and soft palate using MR elastography

Biomechanical properties of the human tongue are needed for finite element models of the upper airway and may be important to elucidate the pathophysiology of obstructive sleep apneoa. Tongue viscoelastic properties have not been characterized previously. Magnetic resonance elastography (MRE) is an emerging imaging technique that can measure the viscoelastic properties of soft tissues in-vivo. In this study, MRE was used to measure the viscoelastic properties of the tongue and soft palate in 7 healthy volunteers during quiet breathing. Results show that the storage shear modulus of the tongue and soft palate is 2.67±0.29 and 2.53±0.31 kPa (mean ± SD), respectively. This is the first study to investigate the mechanical properties of the tongue using MRE, and it provides necessary data for future studies of patient groups with altered upper airway function.     

Magnetic resonance elastography in nonlinear viscoelastic materials under load

Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material’s rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy’s equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of \(4910.4 \pm 635.8\) Pa in unloaded state, the biased stiffness increases to 9767.5 \(\pm \,\)1949.9 Pa under a load of \(\approx \) 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

     

Viscoelastic properties of human cerebellum using magnetic resonance elastography

BackgroundThe cerebellum has never been mechanically characterised, despite its physiological importance in the control of motion and the clinical prevalence of cerebellar pathologies. The aim of this study was to measure the linear viscoelastic properties of the cerebellum in human volunteers using Magnetic Resonance Elastography (MRE).MethodsCoronal plane brain 3D MRE data was performed on eight healthy adult volunteers, at 80 Hz, to compare the properties of cerebral and cerebellar tissues. The linear viscoelastic storage (G′) and loss moduli (G″) were estimated from the MRE wave images by solving the wave equation for propagation through an isotropic linear viscoelastic solid. Contributions of the compressional wave were removed via application of the curl-operator.ResultsThe storage modulus for the cerebellum was found to be significantly lower than that for the cerebrum, for both white and grey matter. Cerebrum: white matter (mean±SD) G′=2.41±0.23 kPa, grey matter G′=2.34±0.22 kPa; cerebellum: white matter, G′=1.85±0.18 kPa, grey matter G′=1.77±0.24 kPa; cerebrum vs cerebellum, p<0.001. For the viscous behaviour, there were differences in between regions and also by tissue type, with the white matter being more viscous than grey matter and the cerebrum more viscous than the cerebellum. Cerebrum: white matter G″=1.21±0.21 kPa, grey matter G″=1.11±0.03 kPa; cerebellum: white matter G″=1.1±0.23 kPa, grey matter G″=0.94±0.17 kPa.DiscussionThese data represent the first available data on the viscoelastic properties of cerebellum, which suggest that the cerebellum is less physically stiff than the cerebrum, possibly leading to a different response to mechanical loading. These data will be useful for modelling of the cerebellum for a range of purposes.     

Towards an Elastographic Atlas of Brain Anatomy

Cerebral viscoelastic constants can be measured in a noninvasive, image-based way by magnetic resonance elastography (MRE) for the detection of neurological disorders. However, MRE brain maps of viscoelastic constants are still limited by low spatial resolution. Here we introduce three-dimensional multifrequency MRE of the brain combined with a novel reconstruction algorithm based on a model-free multifrequency inversion for calculating spatially resolved viscoelastic parameter maps of the human brain corresponding to the dynamic range of shear oscillations between 30 and 60 Hz. Maps of two viscoelastic parameters, the magnitude and the phase angle of the complex shear modulus, |G*| and φ, were obtained and normalized to group templates of 23 healthy volunteers in the age range of 22 to 72 years. This atlas of the anatomy of brain mechanics reveals a significant contrast in the stiffness parameter |G*| between different anatomical regions such as white matter (WM; 1.252±0.260 kPa), the corpus callosum genu (CCG; 1.104±0.280 kPa), the thalamus (TH; 1.058±0.208 kPa) and the head of the caudate nucleus (HCN; 0.649±0.101 kPa). φ, which is sensitive to the lossy behavior of the tissue, was in the order of CCG (1.011±0.172), TH (1.037±0.173), CN (0.906±0.257) and WM (0.854±0.169). The proposed method provides the first normalized maps of brain viscoelasticity with anatomical details in subcortical regions and provides useful background data for clinical applications of cerebral MRE.     

Extraction of quasi-linear viscoelastic parameters for lower limb soft tissues from manual indentation experiment.

A manual indentation protocol was established to assess the quasi-linear viscoelastic (QLV) properties of lower limb soft tissues. The QLV parameters were extracted using a curve-fitting procedure on the experimental indentation data. The load-indentation responses were obtained using an ultrasound indentation apparatus with a hand-held pen-sized probe. Limb soft tissues at four sites of eight normal young subjects were tested in three body postures. Four QLV model parameters were extracted from the experimental data. The initial modulus E0 ranged from 0.22 kPa to 58.4 kPa. The nonlinear factor E1 ranged from 21.7 kPa to 547 kPa. The time constant tau ranged from 0.05 s to 8.93 s. The time-dependent materials parameter alpha ranged from 0.029 to 0.277. Large variations of the parameters were noted among subjects, sites, and postures.     

Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo

The mechanical properties of human soft tissue are crucial for impact biomechanics, rehabilitation engineering, and surgical simulation. Validation of these constitutive models using human data remains challenging and often requires the use of non-invasive imaging and inverse finite element (FE) analysis. Post-processing data from imaging methods such as tagged magnetic resonance imaging (MRI) can be challenging. Digital image correlation (DIC), however, is a relatively straightforward imaging method. DIC has been used in the past to study the planar and superficial properties of soft tissue and excised soft tissue layers. However, DIC has not been used to non-invasive study of the bulk properties of human soft tissue in vivo. Thus, the goal of this study was to assess the use of DIC in combination with FE modelling to determine the bulk material properties of human soft tissue. Indentation experiments were performed on a silicone gel soft tissue phantom. A two camera DIC setup was then used to record the 3D surface deformation. The experiment was then simulated using a FE model. The gel was modelled as Neo-Hookean hyperelastic, and the material parameters were determined by minimising the error between the experimental and FE data. The iterative FE analysis determined material parameters (μ=1.80 kPa, K=2999 kPa) that were in close agreement with parameters derived independently from regression to uniaxial compression tests (μ=1.71 kPa, K=2857 kPa). Furthermore the FE model was capable of reproducing the experimental indentor force as well as the surface deformation found (R²=0.81). It was therefore concluded that a two camera DIC configuration combined with FE modelling can be used to determine the bulk mechanical properties of materials that can be represented using hyperelastic Neo-Hookean constitutive laws.     

Wide-range dynamic magnetic resonance elastography

Tissue mechanical parameters have been shown to be highly sensitive to disease by elastography. Magnetic resonance elastography (MRE) in the human body relies on the low-dynamic range of tissue mechanics <100 Hz. In contrast, MRE suited for investigations of mice or small tissue samples requires vibration frequencies 10–20 times higher than those used in human MRE. The dispersion of the complex shear modulus (G^?) prevents direct comparison of elastography data at different frequency bands and, consequently, frequency-independent viscoelastic models that fit to G^* over a wide dynamic range have to be employed. This study presents data of G^* of samples of agarose gel, liver, brain, and muscle measured by high-resolution MRE in a 7T-animal scanner at 200–800 Hz vibration frequency. Material constants μ and α according to the springpot model and related to shear elasticity and slope of the G^*-dispersion were determined. Both μ and α of calf brain and bovine liver were found to be similar, while a sample of fibrotic human liver (METAVIR score of 3) displayed about fifteen times higher shear elasticity, similar to μ of bovine muscle measured in muscle fiber direction. α was the highest in fibrotic liver, followed by normal brain and liver, while muscle had the lowest α-values of all biological samples investigated in this study. As expected, the least G^*-dispersion was seen in soft gel. The proposed technique of wide-range dynamic MRE can provide baseline data for both human MRE and high-dynamic MRE for better understanding tissue mechanics of different tissue structures.     

Non-identifiability of the Rayleigh damping material model in Magnetic Resonance Elastography

Magnetic Resonance Elastography (MRE) is an emerging imaging modality for quantifying soft tissue elasticity deduced from displacement measurements within the tissue obtained by phase sensitive Magnetic Resonance Imaging (MRI) techniques. MRE has potential to detect a range of pathologies, diseases and cancer formations, especially tumors. The mechanical model commonly used in MRE is linear viscoelasticity (VE). An alternative Rayleigh damping (RD) model for soft tissue attenuation is used with a subspace-based nonlinear inversion (SNLI) algorithm to reconstruct viscoelastic properties, energy attenuation mechanisms and concomitant damping behavior of the tissue-simulating phantoms. This research performs a thorough evaluation of the RD model in MRE focusing on unique identification of RD parameters, _μI${\mu }_I$ and _ρI${\rho }_I$.     

The compressive material properties of the plantar soft tissue

The plantar soft tissue is the primary means of physical interaction between a person and the ground during locomotion. Dynamic loads greater than body weight are borne across the entire plantar surface during each step. However, most testing of these tissues has concentrated on the structural properties of the heel pad. The purpose of this study was to determine the material properties of the plantar soft tissue from six locations beneath: the great toe (subhallucal), the 1st, 3rd and 5th metatarsal heads (submetatarsal), the lateral midfoot (lateral submidfoot) and the heel (subcalcaneal). We obtained specimens from these locations from 11 young, non-diabetic donors; the tissue was cut into 2 cm x 2 cm blocks and the skin was removed. Stress relaxation experiments were conducted and the data were fit using the quasi-linear viscoelastic (QLV) theory. To determine tissue modulus, energy loss and the effect of test frequency, we also conducted displacement controlled triangle waves at five frequencies ranging from 0.005 to 10 Hz. The subcalcaneal tissue was found to have an increased relaxation time compared to the other areas. The subcalcaneal tissue was also found to have an increased modulus and decreased energy loss compared to the other areas. Across all areas, the modulus and energy loss increased for the 1 and 10 Hz tests compared to the other testing frequencies. This study is the first to generate material properties for all areas of the plantar soft tissue, demonstrating that the subcalcaneal tissue is different than the other plantar soft tissue areas. These data will have implications for foot computational modeling efforts and potentially for orthotic pressure reduction devices.     

Determination of strain energy function for arterial elastin: Experiments using histology and mechanical tests

The long-range reversible deformation of vertebrate arteries is primarily mediated by elastin networks that endure several million deformation cycles without appreciable fatigue. To determine how elastin contributes to the composite arterial properties, we studied the three-dimensional microstructure and biomechanics of isolated elastin. We initially estimated the sensitivity of these studies by comparing two elastin isolation protocols, autoclaving and alkali-extraction, and measured their effect on isolated elastin using uniaxial tests and histology. These studies show that autoclaved tissues have a trend for higher modulus (900.79+/-678.02 kPa) than alkali-extracted samples (417.74+/-162.23 kPa)albeit with higher collagen-proteoglycan impurities, and (2) greater optical density (78.6+/-9.1%) than alkali-extracted groups (46.2+/-5.9%), suggesting that autoclaving is superior to alkali-extraction for biomechanical tests on elastin. Using these data we show that an isotopic Mooney-Rivlin model cannot adequately represent arterial elastin. The neo-Hookean model, with coefficient 162.57 (+/-115.44) kPa for autoclaved and 76.94 (+/-27.76) kPa for alkali-extracted samples, fits the uniaxial data better. Autoclaved elastins also show linear stress-strain response and equal stiffness in circumferential and axial directions suggesting equal number of layers in these directions and that elastin may help distribute tensile stresses during vessel inflation. Histology of autoclaved and control porcine arteries reveals axial elastin fibers in intimal and adventitial layers but circumferential medial fibers. We propose an orthotropic material symmetry for arterial elastin with two orthogonally oriented and symmetrically placed mechanically equivalent fibers. An exact form of the constitutive equation will be obtained in a future study.     

Mechanical properties of porcine brain tissue in vivo and ex vivo estimated by MR elastography

The mechanical properties of brain tissue in vivo determine the response of the brain to rapid skull acceleration. These properties are thus of great interest to the developers of mathematical models of traumatic brain injury (TBI) or neurosurgical simulations. Animal models provide valuable insight that can improve TBI modeling. In this study we compare estimates of mechanical properties of the Yucatan mini-pig brain in vivo and ex vivo using magnetic resonance elastography (MRE) at multiple frequencies. MRE allows estimations of properties in soft tissue, either in vivo or ex vivo, by imaging harmonic shear wave propagation. Most direct measurements of brain mechanical properties have been performed using samples of brain tissue ex vivo. It has been observed that direct estimates of brain mechanical properties depend on the frequency and amplitude of loading, as well as the time post-mortem and condition of the sample. Using MRE in the same animals at overlapping frequencies, we observe that porcine brain tissue in vivo appears stiffer than porcine brain tissue samples ex vivo at frequencies of 100 Hz and 125 Hz, but measurements show closer agreement at lower frequencies.     

Quantifying the Elastic Property of Nine Thigh Muscles Using Magnetic Resonance Elastography

BackgroundPathologies of the muscles can manifest different physiological and functional changes. To adapt treatment, it is necessary to characterize the elastic property (shear modulus) of single muscles. Previous studies have used magnetic resonance elastography (MRE), a technique based on MRI technology, to analyze the mechanical behavior of healthy and pathological muscles. The purpose of this study was to develop protocols using MRE to determine the shear modulus of nine thigh muscles at rest.MethodsTwenty-nine healthy volunteers (mean age = 26 ± 3.41 years) with no muscle abnormalities underwent MRE tests (1.5 T MRI). Five MRE protocols were developed to quantify the shear moduli of the nine following thigh muscles at rest: rectus femoris (RF), vastus medialis (VM), vastus intermedius (VI), vastus lateralis (VL), sartorius (Sr), gracilis (Gr), semimembranosus (SM), semitendinosus (ST), and biceps (BC). In addition, the shear modulus of the subcutaneous adipose tissue was analyzed.ResultsThe gracilis, sartorius, and semitendinosus muscles revealed a significantly higher shear modulus (μ_{_Gr} = 6.15 ± 0.45 kPa, μ_{_ Sr} = 5.15 ± 0.19 kPa, and μ_{_ ST} = 5.32 ± 0.10 kPa, respectively) compared to other tissues (from μ_{_ RF} = 3.91 ± 0.16 kPa to μ_{_VI} = 4.23 ± 0.25 kPa). Subcutaneous adipose tissue had the lowest value (μ_{_adipose tissue} = 3.04 ± 0.12 kPa) of all the tissues tested.ConclusionThe different elasticities measured between the tissues may be due to variations in the muscles'' physiological and architectural compositions. Thus, the present protocol could be applied to injured muscles to identify their behavior of elastic property. Previous studies on muscle pathology found that quantification of the shear modulus could be used as a clinical protocol to identify pathological muscles and to follow-up effects of treatments and therapies. These data could also be used for modelling purposes.     

Analysis of the dynamic strains in a fingertip exposed to vibrations: Correlation to the mechanical stimuli on mechanoreceptors

The reduction in vibrotactile sensitivity in the fingertip is assumed to be associated with the exposure of the tissues to repetitive, non-physiological strains during dynamic loading. Experimental results demonstrated that the magnitude of a vibration-induced temporary threshold shift is dependent upon the vibration frequency of both the exposure and testing stimuli. In the present study, the frequency-dependent strain imposed on cutaneous and subcutaneous tissues of the fingertip is analyzed theoretically using a finite element model. The proposed fingertip model is two-dimensional and includes major anatomical substructures: skin, subcutaneous tissue, bone, and nail. The soft tissues (skin and subcutaneous tissues) were assumed to be nonlinearly elastic and viscoelastic, while the bone and nail were considered as linearly elastic. Simulations were performed for the contact between the fingertip and a flat surface for four different pre-compressions (0.5, 1.0, 1.5, and 2.0 mm). The frequency-dependent distributions of the dynamic strain magnitudes in the soft tissues were investigated. The model predictions indicated that the vibration exposure at a frequency range from 63 to 250 Hz will induce excessive dynamic strain in the deep zone of the finger tissues, effectively inhibiting the high-frequency mechanoreceptors; while the vibration exposure at low frequency (less than 31.5 Hz) tends to induce excessive dynamic strain in superficial layer in the tissues, inhibiting the low-frequency mechanoreceptors. These theoretical predictions are consistent with the experimental observations in literature. The proposed model can be used to predict the responses of the soft tissues in different depths to vibration exposures, providing valuable information and data that are essential for improving vibrotactile perception tests.     

Assessment of in vivo and post-mortem mechanical behavior of brain tissue using magnetic resonance elastography

The knowledge of in vivo brain tissue mechanical properties is essential in several biomedical engineering fields, such as injury biomechanics and neurosurgery simulation. Almost all existing available data have been obtained in vitro by invasive experimental protocols. However, the difference between in vivo and post-mortem mechanical properties remains poorly known, essentially due to the lack of a common method that could measure them both in vivo and ex vivo. In this study, we report the use of magnetic resonance elastography (MRE) for the non-invasive assessment of in vivo brain tissue viscoelastic properties and for the investigation of their evolution after the death. Experiments were performed on seven adult male rats. Shear storage and loss moduli were measured in vivo, just after death and at post-mortem time of approximately 24h. A significant increase in shear storage modulus G(') of approximately 100% was found to occur just after death (p=0.002), whereas no significant difference was found between in vivoG(') and G(') at 24h post-mortem time. No significant difference was found between shear loss modulus G(')in vivo and just after death, whereas a decrease of about 50% was found to occur after 24h (p=0.02). These results illustrate the ability of MRE to investigate some of the critical soft tissue biomechanics-related issues, as it can be used as a non-invasive tool for measuring soft tissue viscoelastic properties.     

Biomimicry in biomedical research

Biomimicry (literally defined as the imitation of life or nature) has sparked a variety of human innovations and inspired countless cutting-edge designs. From spider silk-made artificial skin to lotus leaf-inspired self-cleaning materials, biomimicry endeavors to solve human problems. Biomimetic approaches have contributed significantly to advances biomedical research during recent years. Using polyacrylamide gels to mimic the elastic modulus of different biological tissues, Disher’s lab has directed meschymal stem cell differentiation into specific lineages.¹ They have shown that soft substrates mimicking the elastic modulus of brain tissues (0.1~1 kPa) were neurogenic, substrates of intermediate elastic modulus mimicking muscle (8 ~17 kPa) were myogenic, and substrates with bone-like elastic modulus (25~40 kPa) were osteogenic. This work represents a novel way to regulate the fate of stem cells and exerts profound influence on stem cell research. Biomimcry also drives improvements in tissue engineering. Novel scaffolds have been designed to capture extracellular matrix-like structures, binding of ligands, sustained release of cytokines, and mechanical properties intrinsic to specific tissues for tissue engineering applications.^2,3 For example, tissue engineering skin grafts have been designed to mimic the cell composition and layered structure of native skin.⁴ Similarly, in the field of regenerative medicine, researchers aim to create biomimetic scaffolds to mimic the properties of a native stem cell environment (niche) to dynamically interact with the entrapped stem cells and direct their response.⁵     

Characterization of muscle architecture in children and adults using magnetic resonance elastography and ultrasound techniques

The purpose of this study is to characterize the muscle architecture of children and adults using magnetic resonance elastography and ultrasound techniques. Five children (8-12 yr) and seven adults (24-58 yr) underwent both tests on the vastus medialis muscle at relaxed and contracted (10% and 20% of MVC) states. Longitudinal ultrasonic images were performed in the same area as the phase image showing the shear wave's propagation. Two geometrical parameters were defined: the wave angle (α(_MRE)) corresponding to the shear wave propagation and the fascicule angle (α(_US)) tracking the path of fascicles. Moreover, shear modulus was measured at different localizations within the muscle and in the subcutaneous adipose tissue. The association of both techniques demonstrates that the shear wave propagation follows the muscle fascicles path, reflecting the internal muscle architecture. At rest, ultrasound images revealed waves propagating parallel to the children fascicle while adults showed oblique waves corresponding to already oriented (α(_US)=15.4±2.54°) muscle fascicles. In contraction, the waves' propagation were in an oblique direction for children (α(_US_10%MVC)=10.6±2.27°, α(_US_20%MVC)=10.2±2.29°) as well as adults (α(_US_10%MVC)=15.4±2.54°, α(_US_20%MVC)=17.2±2.44°). A stiffness variation (1 kPa) was found between the upper and lower parts of the adult VM muscle and a lower stiffness (1.85±0.17 kPa) was measured in the subcutaneous adipose tissue. This study demonstrates the feasibility of the MRE technique to provide geometrical insights from the children and adults muscles and to characterize different physiological media.     

Using in vivo Cine and 3D multi-contrast MRI to determine human atherosclerotic carotid artery material properties and circumferential shrinkage rate and their impact on stress/strain predictions

In vivo magnetic resonance image (MRI)-based computational models have been introduced to calculate atherosclerotic plaque stress and strain conditions for possible rupture predictions. However, patient-specific vessel material properties are lacking in those models, which affects the accuracy of their stress/strain predictions. A noninvasive approach of combining in vivo Cine MRI, multicontrast 3D MRI, and computational modeling was introduced to quantify patient-specific carotid artery material properties and the circumferential shrinkage rate between vessel in vivo and zero-pressure geometries. In vivo Cine and 3D multicontrast MRI carotid plaque data were acquired from 12 patients after informed consent. For each patient, one nearly-circular slice and an iterative procedure were used to quantify parameter values in the modified Mooney-Rivlin model for the vessel and the vessel circumferential shrinkage rate. A sample artery slice with and without a lipid core and three material parameter sets representing stiff, median, and soft materials from our patient data were used to demonstrate the effect of material stiffness and circumferential shrinkage process on stress/strain predictions. Parameter values of the Mooney-Rivlin models for the 12 patients were quantified. The effective Young's modulus (YM, unit: kPa) values varied from 137 (soft), 431 (median), to 1435 (stiff), and corresponding circumferential shrinkages were 32%, 12.6%, and 6%, respectively. Using the sample slice without the lipid core, the maximum plaque stress values (unit: kPa) from the soft and median materials were 153.3 and 96.2, which are 67.7% and 5% higher than that (91.4) from the stiff material, while the maximum plaque strain values from the soft and median materials were 0.71 and 0.293, which are about 700% and 230% higher than that (0.089) from the stiff material, respectively. Without circumferential shrinkages, the maximum plaque stress values (unit: kPa) from the soft, median, and stiff models were inflated to 330.7, 159.2, and 103.6, which were 116%, 65%, and 13% higher than those from models with proper shrinkage. The effective Young's modulus from the 12 human carotid arteries studied varied from 137 kPa to 1435 kPa. The vessel circumferential shrinkage to the zero-pressure condition varied from 6% to 32%. The inclusion of proper shrinkage in models based on in vivo geometry is necessary to avoid over-estimating the stresses and strains by up 100%. Material stiffness had a greater impact on strain (up to 700%) than on stress (up to 70%) predictions. Accurate patient-specific material properties and circumferential shrinkage could considerably improve the accuracy of in vivo MRI-based computational stress/strain predictions.     

Quantifying dynamic mechanical properties of human placenta tissue using optimization techniques with specimen-specific finite-element models

Motor-vehicle crashes are the leading cause of fetal deaths resulting from maternal trauma in the United States, and placental abruption is the most common cause of these deaths. To minimize this injury, new assessment tools, such as crash-test dummies and computational models of pregnant women, are needed to evaluate vehicle restraint systems with respect to reducing the risk of placental abruption. Developing these models requires accurate material properties for tissues in the pregnant abdomen under dynamic loading conditions that can occur in crashes. A method has been developed for determining dynamic material properties of human soft tissues that combines results from uniaxial tensile tests, specimen-specific finite-element models based on laser scans that accurately capture non-uniform tissue-specimen geometry, and optimization techniques. The current study applies this method to characterizing material properties of placental tissue. For 21 placenta specimens tested at a strain rate of 12/s, the mean failure strain is 0.472±0.097 and the mean failure stress is 34.80±12.62 kPa. A first-order Ogden material model with ground-state shear modulus (μ) of 23.97±5.52 kPa and exponent (α₁) of 3.66±1.90 best fits the test results. The new method provides a nearly 40% error reduction (p<0.001) compared to traditional curve-fitting methods by considering detailed specimen geometry, loading conditions, and dynamic effects from high-speed loading. The proposed method can be applied to determine mechanical properties of other soft biological tissues.     

Viscoelastic properties of isolated collagen fibrils

Understanding the viscoelastic behavior of collagenous tissues with complex hierarchical structures requires knowledge of the properties at each structural level. Whole tissues have been studied extensively, but less is known about the mechanical behavior at the submicron, fibrillar level. Using a microelectromechanical systems platform, in vitro coupled creep and stress relaxation tests were performed on collagen fibrils isolated from the sea cucumber dermis. Stress-strain-time data indicate that isolated fibrils exhibit viscoelastic behavior that could be fitted using the Maxwell-Weichert model. The fibrils showed an elastic modulus of 123 ± 46 MPa. The time-dependent behavior was well fit using the two-time-constant Maxwell-Weichert model with a fast time response of 7 ± 2 s and a slow time response of 102 ± 5 s. The fibrillar relaxation time was smaller than literature values for tissue-level relaxation time, suggesting that tissue relaxation is dominated by noncollagenous components (e.g., proteoglycans). Each specimen was tested three times, and the only statistically significant difference found was that the elastic modulus is larger in the first test than in the subsequent two tests, indicating that viscous properties of collagen fibrils are not sensitive to the history of previous tests.