Wideband MRE and static mechanical indentation of human liver specimen: Sensitivity of viscoelastic constants to the alteration of tissue structure in hepatic fibrosis

Despite the success of elastography in grading hepatic fibrosis by stiffness related noninvasive markers the relationship between viscoelastic constants in the liver and tissue structure remains unclear. We therefore studied the mechanical properties of 16 human liver specimens with different degrees of fibrosis, inflammation and steatosis by wideband magnetic resonance elastography (MRE) and static indentation experiments providing the specimens? static Young?s modulus (E), dynamic storage modulus (G′) and dynamic loss modulus (G″). A frequency-independent shear modulus μ and a powerlaw exponent α were obtained by fitting G′ and G″ using the two-parameter sprinpot model. The mechanical parameters were compared to the specimens? histology derived parameters such as degree of Fibrosis (F), inflammation score and fat score, amount of hydroxyproline (HYP) used for quantification of collagen, blood markers and presurgery in vivo function tests.     

Using static preload with magnetic resonance elastography to estimate large strain viscoelastic properties of bovine liver

Traditional magnetic resonance elastography (MRE) applies small amplitude vibration to tissues. Thus currently MRE measures only the small deformation behaviour of tissues. MRE has the potential to estimate the strain-varying shear modulus of soft tissues, if applied at different static strains, which may allow prediction of the large-strain behaviour of tissues. This study uses MRE of bovine liver specimens under various levels of static compressive pre-strain up to 30%. Storage and loss moduli measured using MRE increased non-linearly with static compressive pre-strain, and exponential models fit well to these data to describe this relationship (R²>0.93). Based on these models, a 10% linear compression of liver would result in a 47% overestimate of the ‘true’ storage modulus of the uncompressed tissue. The results of this study have implications for MRE transducer design and interpretation of results from in vivo MRE studies.     

Magnetic Resonance Elastography Methodology for the Evaluation of Tissue Engineered Construct Growth

Traditional mechanical testing often results in the destruction of the sample, and in the case of long term tissue engineered construct studies, the use of destructive assessment is not acceptable. A proposed alternative is the use of an imaging process called magnetic resonance elastography. Elastography is a nondestructive method for determining the engineered outcome by measuring local mechanical property values (i.e., complex shear modulus), which are essential markers for identifying the structure and functionality of a tissue. As a noninvasive means for evaluation, the monitoring of engineered constructs with imaging modalities such as magnetic resonance imaging (MRI) has seen increasing interest in the past decade¹. For example, the magnetic resonance (MR) techniques of diffusion and relaxometry have been able to characterize the changes in chemical and physical properties during engineered tissue development². The method proposed in the following protocol uses microscopic magnetic resonance elastography (μMRE) as a noninvasive MR based technique for measuring the mechanical properties of small soft tissues³. MRE is achieved by coupling a sonic mechanical actuator with the tissue of interest and recording the shear wave propagation with an MR scanner⁴. Recently, μMRE has been applied in tissue engineering to acquire essential growth information that is traditionally measured using destructive mechanical macroscopic techniques⁵. In the following procedure, elastography is achieved through the imaging of engineered constructs with a modified Hahn spin-echo sequence coupled with a mechanical actuator. As shown in Figure 1, the modified sequence synchronizes image acquisition with the transmission of external shear waves; subsequently, the motion is sensitized through the use of oscillating bipolar pairs. Following collection of images with positive and negative motion sensitization, complex division of the data produce a shear wave image. Then, the image is assessed using an inversion algorithm to generate a shear stiffness map⁶. The resulting measurements at each voxel have been shown to strongly correlate (R²>0.9914) with data collected using dynamic mechanical analysis⁷. In this study, elastography is integrated into the tissue development process for monitoring human mesenchymal stem cell (hMSC) differentiation into adipogenic and osteogenic constructs as shown in Figure 2.     

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.     

Sensitivity of multifrequency magnetic resonance elastography and diffusion-weighted imaging to cellular and stromal integrity of liver tissue

Microscopic structural alterations of liver tissue induced by freeze-thaw cycles give rise to palpable property changes. However, the underlying damage to tissue architecture is difficult to quantify histologically, and published data on macroscopic changes in biophysical properties are sparse.To better understand the influence of hepatic cells and stroma on global biophysical parameters, we studied rat liver specimens freshly taken (within 30 min after death) and treated by freeze-thaw cycles overnight at either −20 °C or –80 °C using diffusion-weighted imaging (DWI) and multifrequency magnetic resonance elastography (MRE) performed at 0.5 T in a tabletop MRE scanner. Tissue structure was analyzed histologically and rheologic data were analyzed using fractional order derivatives conceptualized by a called spring-pot component that interpolates between pure elastic and viscous responses.Overnight freezing and thawing induced membrane disruptions and cell detachment in the space of Disse, resulting in a markedly lower shear modulus μ and apparent diffusion coefficient (ADC) (μ[−20 °C] = 1.23 ± 0.73 kPa, μ[−80 °C] = 0.66 ± 0.75 kPa; ADC[–20 °C] = 0.649 ± 0.028 μm²/s, ADC[−80 °C] = 0.626 ± 0.025 μm²/s) compared to normal tissue (μ = 9.92 ± 3.30 kPa, ADC = 0.770 ± 0.023 μm²/s, all p < 0.001). Furthermore, we analyzed the springpot-powerlaw coefficient and observed a reduction in −20 °C specimens (0.22 ± 0.14) compared to native tissue (0.40 ± 0.10, p = 0.033) and −80 °C specimens (0.54 ± 0.22, p = 0.002), that correlated with histological observations of sinusoidal dilation and collagen distortion within the space of Disse. Overall, the results suggest that shear modulus and water diffusion in liver tissue markedly decrease due to cell membrane degradation and cell detachment while viscosity-related properties appear to be more sensitive to distorted stromal and microvascular architecture.     

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.     

Brain viscoelasticity alteration in chronic-progressive multiple sclerosis

Introduction

Viscoelastic properties indicate structural alterations in biological tissues at multiple scales with high sensitivity. Magnetic Resonance Elastography (MRE) is a novel technique that directly visualizes and quantitatively measures biomechanical tissue properties in vivo. MRE recently revealed that early relapsing-remitting multiple sclerosis (MS) is associated with a global decrease of the cerebral mechanical integrity. This study addresses MRE and MR volumetry in chronic-progressive disease courses of MS.

Methods

We determined viscoelastic parameters of the brain parenchyma in 23 MS patients with primary or secondary chronic progressive disease course in comparison to 38 age- and gender-matched healthy individuals by multifrequency MRE, and correlated the results with clinical data, T2 lesion load and brain volume. Two viscoelastic parameters, the shear elasticity μ and the powerlaw exponent α, were deduced according to the springpot model and compared to literature values of relapsing-remitting MS.

Results

In chronic-progressive MS patients, μ and α were reduced by 20.5% and 6.1%, respectively, compared to healthy controls. MR volumetry yielded a weaker correlation: Total brain volume loss in MS patients was in the range of 7.5% and 1.7% considering the brain parenchymal fraction. All findings were significant (P<0.001).

Conclusions

Chronic-progressive MS disease courses show a pronounced reduction of the cerebral shear elasticity compared to early relapsing-remitting disease. The powerlaw exponent α decreased only in the chronic-progressive stage of MS, suggesting an alteration in the geometry of the cerebral mechanical network due to chronic neuroinflammation.     

High-resolution mechanical imaging of the kidney

The objective of this study was to test the feasibility and reproducibility of in vivo high-resolution mechanical imaging of the asymptomatic human kidney. Hereby nine volunteers were examined at three different physiological states of urinary bladder filling (a normal state, urinary urgency, and immediately after urinary relief). Mechanical imaging was performed of the in vivo kidney using three-dimensional multifrequency magnetic resonance elastography combined with multifrequency dual elastovisco inversion. Other than in classical elastography, where the storage and loss shear moduli are evaluated, we analyzed the magnitude |G^?| and the phase angle φ of the complex shear modulus reconstructed by simultaneous inversion of full wave field data corresponding to 7 harmonic drive frequencies from 30 to 60 Hz and a resolution of 2.5 mm cubic voxel size.     

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.     

The influence of physiological aging and atrophy on brain viscoelastic properties in humans

Physiological aging of the brain is accompanied by ubiquitous degeneration of neurons and oligodendrocytes. An alteration of the cellular matrix of an organ impacts its macroscopic viscoelastic properties which can be detected by magnetic resonance elastography (MRE) – to date the only method for measuring brain mechanical parameters without intervention. However, the wave patterns detected by MRE are affected by atrophic changes in brain geometry occurring in an individual''s life span. Moreover, regional variability in MRE-detected age effects is expected corresponding to the regional variation in atrophy. Therefore, the sensitivity of brain MRE to brain volume and aging was investigated in 66 healthy volunteers aged 18–72. A linear decline in whole-brain elasticity was observed (−0.75%/year, R-square = 0.59, p<0.001); the rate is three times that determined by volume measurements (−0.23%/year, R-square = 0.4, p<0.001). The highest decline in elasticity (−0.92%/year, R-square = 0.43, p<0.001) was observed in a region of interest placed in the frontal lobe with minimal age-related shrinkage (−0.1%, R-square = 0.06, p = 0.043). Our results suggest that cerebral MRE can measure geometry-independent viscoelastic parameters related to intrinsic tissue structure and altered by age.     

Characterization of blood clot viscoelasticity by dynamic ultrasound elastography and modeling of the rheological behavior

Dynamic elastography (DE) is a new tool to study mechanical behavior of soft tissues via their motion response to propagating shear waves. This technique characterized viscoelasticity of 9 porcine whole blood samples (3 animals) during coagulation for a shearing frequency of 70 Hz, and after complete clot formation between 50 and 160 Hz. Clot storage (G′) and loss (G″) moduli were calculated from shear wave velocity and attenuation. Temporal evolutions of G′ and G″ during coagulation were typified with 4 parameters: maximum change in elasticity (G′ slope_max), elasticity after 120 min of coagulation (G′_max), time occurrence of G″ maximum (t_e) and G″ at the plateau (G″_plateau). G′ and G″ frequency dependence of completely formed blood clots was fitted with 5 standard rheological models: Maxwell, Kelvin–Voigt, Jeffrey, Zener and third-order generalized Maxwell. DE had sufficient sensitivity to follow the coagulation kinetics described by a progressive increase in G′, while G″ transitory increased followed by a rapid stabilization. Inter- and intra-animal dispersions (InterAD and IntraAD) of G′_max (InterAD=15.9%, IntraAD=9.1%) showed better reproducibility than G′ slope_max (InterAD=40.4%, IntraAD=21.9%), t_e (InterAD=27.4%, IntraAD=18.7%) and G″_plateau (InterAD=58.6%, IntraAD=40.2%). G′ evolution within the considered range of frequency exhibited an increase, followed by stabilization to a plateau, whereas G″ presented little variations with convergence at a quasi-constant value at highest frequencies. Residues χ^?, describing the goodness of fit between models and experimental data, showed statistically (p<0.05) that the Kelvin–Voigt model was less in agreement with experimental data than other models. The Zener model is recommended to predict G′ and G″ dispersion of coagulated blood over the explored frequency range.     

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.     

Quantitative estimates of steric effects: Intramolecular strain energy effects on the activation energy for aquation of some trans-dichlorotetraaminecobalt(III) complexes

In an effort to quantitatively estimate steric contributions to the aquation rates of a series of structurally related cobalt(III) tetraamine complexes, strain energy minimization calculations have been performed on the reactant and some plausible transition state structures. Free energies of activation ΔG*_obs, are factored as: ΔG*_obs, = ΔG*_bb + ΔG*_strain + Δ_G*_CF + ΔG*_solvation + … where ΔG*_bb is the free energy change associated with bond breaking, ΔG*_solvation is the solvation free energy difference between the reactant and a proposed transition stare, ΔG*_CF is the difference in crystal field stabilization between the reactant and a proposed transition state, and ΔG*_strain is the strain energy difference between the reactant complex and a proposed transition state. The activation energy for the aquation of a hypothetical ‘strain free’ complex is defined as ΔG*_int and reflects the energy required for the bond breaking step with all other terms. For the cations trans-(RR,SS)-dichloro-1,8- diamino-3,6-diazaoctanecobalt(III)(trans [Co(2,2,2- tet)Cl₂]⁺), trans-(RR,SS)- or trans-(RS)-dichloro-1.9- diamino-3,7-diazanonanecobalt(III)(trans [Co(2,3,2- tet)Cl₂]⁺ and trans-(RS)-dichloro-1,10-diamino-4,7- diazadecanecobalt(III)(trans[Co(3,2,3-tet)Cl₂]⁺) ΔG*_int is found to be a constant 123 kJ/mol. For the trans-dichlorocobalt(III) complexes with the ligands 1,4,7,10-tetraazacyclotridecane([13]-ane-N₄), 1,4,8, 11-tetraazacyclotetradecane([14]-ane-N₄), 1,4,8,12- tetraazacyclopentadecane([15]-ane-N₄) and 1,5,9,13- tetraazacyclohexadecane([16]-ane-N₄), ΔG*_int lies in the range 133–139 kJ/mol.     

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.     

Ultrasound elastographic assessment of plantar fascia in runners using rearfoot strike and forefoot strike

Forefoot strike is increasingly being adopted by runners because it can better attenuate impact than rearfoot strike. However, forefoot strike may overload the plantar fascia and alter the plantar fascia elasticity. This study aimed to use ultrasound elastography to investigate and compare shear wave elasticity of the plantar fascia between rearfoot strikers and forefoot strikers. A total of 35 participants (21 rearfoot strikers and 14 forefoot strikers), who were free of lower limb injuries and diseases, were recruited from a local running club. Individual foot strike patterns were identified through the measured plantar pressure during treadmill running. The B-Mode ultrasound images and shear wave elastographic images of the plantar fascia were collected from each runner. Two independent investigators reviewed the images and examined the plantar fascia qualitatively and quantitatively. The results demonstrated an overall good agreement between the investigators in the image review outcomes (ICC:0.96–0.98, κ: 0.89). There were no significant differences in the fascial thickness (p = 0.50) and hypoechogenicity on the gray-scale images (p = 0.54) between the two groups. Shear wave elastography showed that forefoot strikers exhibited reduced plantar fascia elasticity compared to rearfoot strikers (p = 0.01, Cohen’s d = 0.91). A less elastic fascial tissue was more easily strained under loading. Tissue overstrain is frequently related to the incidence of plantar fasciitis. While further study is needed for firm conclusions, runners using forefoot strike were encouraged to enhance their foot strength for better protection of the plantar fascia.     

Distribution of the α-subunit of the Guanine Nucleotide-binding Protein Gi2 and its Comparison to Gαo

Abstract

Site specific antisera against a synthetic peptide corresponding to the sequence 3–17 of Gαi2 have been raised and the specificity examined using purified homogeneous G_o, G_i2 and G_i containing a 41 kDa α-subunit. The distribution of Gα_i2 was investigated in plasma membranes from different tissues and cells and compared to the distribution of Gα_o and other pertussis toxin sensitive Gα. Considerable amounts of Gα_io were found in endocrine tissue especially in membranes from the adrenal and thyroid, in leucocytes and platelets where it constitutes the major, if not only, pertussis toxin-sensitive Gα, as well as in some cell lines (C6, NG 108–15, S49 cyc^?); erythrocytes contained a 41 kDa Gα_i which was different from Gα_o. Gα_o was present abundantly in nervous tissue, adrenal medulla and cortex but also found in low amounts in other membranes except for lung, liver and blood cells. Subcellular fractionaltion of cardiac ventricular muscle demonstrated the presence of Gα_o and low amounts of Gα_i2 in sarcolemma, but only 41kDa Gα_i was present in sarcoplasmic reticulum. The importance of the distinct distribution in terms of signal transduction is discussed.     

Anisotropic mechanical properties of magnetically aligned fibrin gels measured by magnetic resonance elastography

The anisotropic mechanical properties of magnetically aligned fibrin gels were measured by magnetic resonance elastography (MRE) and by a standard mechanical test: unconfined compression. Soft anisotropic biomaterials are notoriously difficult to characterize, especially in vivo. MRE is well-suited for efficient, non-invasive, and non-destructive assessment of shear modulus. Direction-dependent differences in shear modulus were found to be statistically significant for gels polymerized at magnetic fields of 11.7 and 4.7 T compared to control gels. Mechanical anisotropy was greater in the gels polymerized at the higher magnetic field. These observations were consistent with results from unconfined compression tests. Analysis of confocal microscopy images of gels showed measurable alignment of fibrils in gels polymerized at 11.7 T. This study provides direct, quantitative measurements of the anisotropy in mechanical properties that accompanies fibril alignment in fibrin gels.     

Stress relaxation of human ankles is only minimally affected by knee and ankle angle

Comprehensive characterization of stress relaxation in musculotendinous structures is needed to create robust models of viscoelastic behavior. The commonly used quasi-linear viscoelastic (QLV) theory requires that the relaxation response be independent of tissue strain (length). This study aims to characterize stress relaxation in the musculotendinous and ligamentous structures crossing the human ankle (ankle-only structures and the gastrocnemius muscle–tendon unit, which crosses the ankle and knee), and to determine whether stress relaxation is independent of the length of these structures. Two experiments were conducted on 8 healthy subjects. The first experiment compared stress relaxation over 10 min at different gastrocnemius muscle–tendon unit lengths keeping the length of ankle-joint only structures fixed. The second experiment compared stress relaxation at different lengths of ankle-joint only structures keeping gastrocnemius muscle–tendon unit length fixed. Stress relaxation data were fitted with a two-term exponential function (T=G₀+G₁e^?λ₁t+G₂e^?λ₂t). The first experiment demonstrated a significant effect of gastrocnemius muscle–tendon unit length on G₁, and the second experiment demonstrated an effect of the length of ankle-joint only structures on G₂, λ₁ and λ₂ (p<0.05). Nonetheless, the size of effects on stress relaxation was small (ΔG/G<10%), similar to experimental variability. We conclude that stress relaxation in the relaxed human ankle is minimally affected by changing gastrocnemius muscle–tendon unit length or by changing the lengths of ankle-joint only structures. Consequently quasi-linear viscoelastic models of the relaxed human ankle can use a common stress relaxation modulus at different knee and ankle angles with minimal error.     

Structure-Function Relations and Rigidity Percolation in the Shear Properties of Articular Cartilage

Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G^∗| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G^∗| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction v_c lead to orders-of-magnitude changes in the modulus with |G^∗| scaling as (v_c – v₀)^ξ. Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue’s surface.     

Structure-Function Relations and Rigidity Percolation in the Shear Properties of Articular Cartilage

Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G^∗| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G^∗| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction v_c lead to orders-of-magnitude changes in the modulus with |G^∗| scaling as (v_c – v₀)^ξ. Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue’s surface.