A precision method to measure average viscoelastic parameters of erythrocyte populations

Suspensions of erythrocytes in media of low conductivity are subjected to homogenous high frequency electric fields (1 MHz, approximately 10 to 40 kV/m). The resulting transient deformation of the cells is measured by laser light diffraction. Employing a viscoelastic model of the erythrocyte membrane, relative values of membrane shear modulus and response time can currently be determined to within 7% or better. With a measurement time of one minute the average values of some 10(5) cells can be obtained. As a test of the method, osmotic swelling and deflation of the cells and crosslinking their membrane skeleton by diamide are used to alter the viscoelastic properties of the erythrocytes.     

生物组织弹性成像方法及其新技术进展

弹性是一种描述物质物理意义的重要参数,在描述物质在热力学和动力学的变化过程中有着重要的意义。在医学上,弹性的变化往往和病变联系在一起。然而,绝大多数生物组织在他们的力学特性上所表现出的复杂性并不是弹性模量一项参数就可以完全表述的,在对于他们的粘弹性表征和流变学行为的描述中,粘滞性往往和弹性一样的重要。现在被广泛用来对生物组织机械特性表征的成像技术是弹性成像,其基本原理是给组织施加一个激励,组织会产生一个响应,而该响应的分布结合技术的处理方法,可以反映出其弹性模量等力学属性的差异。本文介绍了生物组织常见的弹性成像方法:超声弹性成像,磁共振弹性成像以及光学相干弹性成像;详细阐述了新发展起来的技术-光声弹性成像和光声粘弹成像,并讨论分析其应用前景。     

Static indentation of anisotropic biomaterials using axially asymmetric indenters--a computational study

Indentation has historically been used by biomechanicians to extract the small strain elastic or viscoelastic properties of biological tissues. Because of the axisymmetry of indenters used in these studies however, analysis of the results requires the assumption of material isotropy and often yields an "effective" elastic modulus. Since most biological tissues such as bone and myocardium are known to be anisotropic, the use of conventional indentation techniques for estimating material properties is therefore limited. The feasibility of using an axially asymmetric indenter to determine material directions and in-plane material properties for anisotropic tissue is explored here using finite element analysis. The load versus displacement curves as would be measured by an indenter depend on the orientation of the indenter cross section relative to the in-plane material axes, thus suggesting a method for determining the underlying material directions. Additionally, the stiffness of the tissue response to indentation is sensitive to the values of the in-plane anisotropic material properties and prestretches, and thus test results can be used to back out relevant constitutive parameters.     

Large deformation shear properties of liver tissue

Characterization of the mechanical properties of soft biological tissues is important for establishing the mechanical tolerances of the tissues, and for input to computational models. In this work, the viscoelastic properties of bovine liver tissue in shear loading have been measured using relaxation and constant shear rate loading. The tissue is nonlinearly viscoelastic for strains greater than 0.2%, has a yield strain of approximately 10, and shows moderate strain-rate sensitivity. The response can be modelled using a nonlinear viscoelastic differential model previously developed for brain tissue.     

Transformation of the viscoelastic functions of calcified tissues and interfacial biomaterials into a common representation

Since both connective and calcified tissues are markedly viscoelastic in nature, an understanding of the behavior of these tissues intrinsically as materials on their own, as well as in composite formation with synthetic implants, is of prime importance in order to predict and anticipate materials' design and function. Thus considerable interest has developed in recent years with respect to measurements of the viscoelastic properties of biological materials. However, attempts to characterize the viscoelasticity of calcified tissues have involved many different experimental procedures; hence results appear in terms of different functions, e.g. relaxation modulus, creep compliance. Since this diversity precludes a simple useful comparison of the results, the present study was initiated so that measured functions could be cast into a common representation, and thus compared. Linear viscoelasticity theory implies definite exact relationships between the functions. Using these relations, experimental results on bone, dentin and implant materials presently used to interface to the natural tissues, e.g. polymethyl methacrylate and high density linear polyethylene, were transformed into the complex dynamic modulus representation. Analysis shows that the results of experiments on bone are not in agreement as to dispersion (i.e. change of modulus with frequency) and its variation with strain. Further, analysis of the internal consistency of some experiments demonstrates a violation of the Boltzmann integral which indicates that linear viscoelasticity (almost invariably assumed by workers in the field) fails for bone in compression. It is concluded that the dynamic behavior of bone is not as well understood as has been thought heretofore; direction is given for future experiments. Contribution No. 59 from the Laboratory for Crystallographic Biophysics; supported by USPHS through NIDR Grant Number 5T1-DE-117-10.     

Micropipette aspiration method for characterizing biological materials with surface energy

Many soft biological tissues possess a considerable surface stress, which plays a significant role in their biophysical functions, but most previous methods for characterizing their mechanical properties have neglected the effects of surface stress. In this work, we investigate the micropipette aspiration method to measure the mechanical properties of soft tissues and cells with surface effects. The neo-Hookean constitutive model is adopted to describe the hyperelasticity of the measured biological material, and the surface effect is taken into account by the finite element method. It is found that when the pipette radius or aspiration length is comparable to the elastocapillary length, surface energy may distinctly alter the aspiration response. Generally, both the aspiration length and the bulk normal stress decrease with increasing surface energy, and thus neglecting the surface energy would lead to an overestimation of elastic modulus. Through dimensional analysis and numerical simulations, we provide an explicit relation between the imposed pressure and the aspiration length. This method can be applied to determine the mechanical properties of soft biological tissues and organs, e.g., livers, tumors and embryos.     

Non-invasive in situ simultaneous measurement of multi-parameter mechanical properties of red blood cell membrane

The purpose of this study was to develop a new dynamic image analyzing technique that will give us the ability to measure the viscoelastic parameters of individual living red blood cells non-invasively, in situ and in real time. With this technique, the bending modulus Kc, the shear elasticity μ and their ratio ε were measured under different temperatures, oxygen partial pressures and osmotic pressures. The results not only show the effects of external conditions on mechanical properties of cell membranes including deformability,flexibility, adhesive ability and plasticity, but also demonstrate that the technique can be used to measure cell membrane parameters continuously under several physiological and pathological conditions.     

Characterization of structure and properties of bone by spectral measure method

Novel mathematical method called spectral measure method (SMM) is developed for characterization of bone structure and indirect estimation of bone properties. The spectral measure method is based on an inverse homogenization technique which allows to derive information about the structure of composite material from measured effective electric or viscoelastic properties. The mechanical properties and ability to withstand fracture depend on the structural organization of bone as a hierarchical composite. Information about the bone structural parameters is contained in the spectral measure in the Stieltjes integral representation of the effective properties. The method is based on constructing the spectral measure either by calculating it directly from micro-CT images or using measurements of electric or viscoelastic properties over a frequency range. In the present paper, we generalize the Stieltjes representation to the viscoelastic case and show how bone microstructure, in particular, bone volume or porosity, can be characterized by the spectral function calculated using measurements of complex permittivity or viscoelastic modulus. For validation purposes, we numerically simulated measured data using micro-CT images of cancellous bone. Recovered values of bone porosity are in excellent agreement with true porosity estimated from the micro-CT images. We also discuss another application of this method, which allows to estimate properties difficult to measure directly. The spectral measure method based on the derived Stieltjes representation for viscoelastic composites, has a potential for non-invasive characterization of bone structure using electric or mechanical measurements. The method is applicable to sea ice, porous rock, and other composite materials.     

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.     

A method for measuring linearly viscoelastic properties of human tympanic membrane using nanoindentation

A viscoelastic nanoindentation technique was developed to measure both in-plane and through-thickness viscoelastic properties of human tympanic membrane (TM). For measurement of in-plane Young's relaxation modulus, the TM sample was clamped on a circular hole and a nanoindenter tip was used to apply a concentrated force at the center of the TM sample. In this setup, the resistance to nanoindentation displacement can be considered due primarily to the in-plane stiffness. The load-displacement curve obtained was used along with finite element analysis to determine the in-plane viscoelastic properties of TM. For measurements of Young's relaxation modulus in the through-thickness (out-of-plane) direction, the TM sample was placed on a relatively rigid solid substrate and nanoindentation was made on the sample surface. In this latter setup, the resistance to nanoindentation displacement arises primarily due to out-of-plane stiffness. The load-displacement curve obtained in this manner was used to determine the out-of-plane relaxation modulus using the method appropriate for viscoelastic materials. From our sample tests, we obtained the steady-state values for in-plane moduli as approximately 17.4 MPa and approximately 19.0 MPa for posterior and anterior portions of TM samples, respectively, and the value for through-thickness modulus as approximately 6.0 MPa for both posterior and anterior TM samples. Using this technique, the local out-of-plane viscoelastic modulus can be determined for different locations over the entire TM, and the in-plane properties can be determined for different quadrants of the TM.     

The role of mucus gel viscosity, spinnability, and adhesive properties in clearance by simulated cough

We investigated the role of the viscoelastic and adhesive properties of mucus gel simulants on the clearance of mucus by simulated cough. Mucus-like gels with widely varying viscoelastic properties were prepared from polysaccharides crosslinked with sodium borate. Cough was simulated by opening a solenoid valve connecting a model trachea to a pressurized tank. The clearance of gels lining the model trachea was quantified by observing marker particle transport. Viscosity elastic modulus, relaxation time and yield stress were measured with a steady-shear viscoelastometer. Spinnability (thread formation) was determined with a filancemeter. Adhesivity (surface tension) was measured by the platinum ring technique. The viscoelastic and adhesive properties of the mucus gel simulants spanned the ranges observed for bronchial secretions from patients with COPD. The relationship between simulated cough clearance and the viscoelastic and adhesive properties of the gels was analyzed by stepwise linear regression of the non-zero data matrix. The major independent variable relating to clearance was viscosity. Secondary, but highly significant dependences, were also found for spinnability and adhesivity. Elastic modulus, relaxation time and yield stress had no independent effect on cough clearance over the investigated range. The results indicate that, in the absence of airway surface liquid, cough-type clearance relates primarily with mucus gel viscosity. For a given viscosity, clearance is also impaired by spinnability, i.e. the capacity of the mucus to form threads. At constant viscosity and spinnability, clearance is further impaired by an increase in the adhesivity of the mucus. The negative dependence of each of these physical factors can be rationalized in terms of their inhibitory effect on wave formation in the mucus lining layer during high velocity airflow interaction.     

The Viscoelastic Properties of Passive Eye Muscle in Primates. II: Testing the Quasi-Linear Theory

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung''s quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung''s theory.We found that the basic properties assumed under the QLV theory (separability and superposition) are not typical of passive eye muscles. We show that some recent extensions of Fung''s model can deal successfully with the lack of separability, but fail to reproduce the deviation from superposition.While appealing for their elegance, the QLV model and its descendants are not able to capture the complex mechanical properties of passive eye muscles. In particular, our measurements suggest that in a passive extraocular muscle the force does not depend on the entire length history, but to a great extent is only a function of the last elongation to which it has been subjected. It is currently unknown whether other passive biological tissues behave similarly.     

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.     

Precision of nanoindentation protocols for measurement of viscoelasticity in cortical and trabecular bone

Nanoindentation has recently gained attention as a characterization technique for mechanical properties of biological tissues, such as bone, on the sub-micron level. However, optimal methods to characterize viscoelastic properties of bones are yet to be established. This study aimed to compare the time-dependent viscoelastic properties of bone tissue obtained with different nanoindentation methods. Bovine cortical and trabecular bone samples (n=8) from the distal femur and proximal tibia were dehydrated, embedded and polished. The material properties determined using nanoindentation were hardness and reduced modulus, as well as time-dependent parameters based on creep, loading-rate, dissipated energy and semi-dynamic testing under load control. Each loading protocol was repeated 160 times and the reproducibility was assessed based on the coefficient of variation (CV). Additionally, three well-characterized polymers were tested and CV values were calculated for reference.The employed methods were able to characterize time-dependent viscoelastic properties of bone. However, their reproducibility varied highly (CV 9–40%). The creep constant increased with increasing dwell time. The reproducibility was best with a 30 s creep period (CV 18%). The dissipated energy was stable after three repeated load cycles, and the reproducibility improved with each cycle (CV 23%). The viscoelastic properties determined with semi-dynamic test increased with increase in frequency. These measurements were most reproducible at high frequencies (CV 9–10%). Our results indicate that several methods are feasible for the determination of viscoelastic properties of bone material. The high frequency semi-dynamic test showed the highest precision within the tested nanoindentation protocols.     

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.     

Characterization of human passive muscles for impact loads using genetic algorithm and inverse finite element methods

The objective of this study is to identify the dynamic material properties of human passive muscle tissues for the strain rates relevant to automobile crashes. A novel methodology involving genetic algorithm (GA) and finite element method is implemented to estimate the material parameters by inverse mapping the impact test data. Isolated unconfined impact tests for average strain rates ranging from 136 s⁻¹ to 262 s⁻¹ are performed on muscle tissues. Passive muscle tissues are modelled as isotropic, linear and viscoelastic material using three-element Zener model available in PAMCRASH^TM explicit finite element software. In the GA based identification process, fitness values are calculated by comparing the estimated finite element forces with the measured experimental forces. Linear viscoelastic material parameters (bulk modulus, short term shear modulus and long term shear modulus) are thus identified at strain rates 136 s⁻¹, 183 s⁻¹ and 262 s⁻¹ for modelling muscles. Extracted optimal parameters from this study are comparable with reported parameters in literature. Bulk modulus and short term shear modulus are found to be more influential in predicting the stress-strain response than long term shear modulus for the considered strain rates. Variations within the set of parameters identified at different strain rates indicate the need for new or improved material model, which is capable of capturing the strain rate dependency of passive muscle response with single set of material parameters for wide range of strain rates.     

Characterizing viscoelastic properties of breast cancer tissue in a mouse model using indentation

Breast cancer is one of the leading cancer forms affecting females worldwide. Characterizing the mechanical properties of breast cancer tissue is important for diagnosis and uncovering the mechanobiology mechanism. Although most of the studies were based on human cancer tissue, an animal model is still describable for preclinical analysis. Using a custom-build indentation device, we measured the viscoelastic properties of breast cancer tissue from 4T1 and SKBR3 cell lines. A total of 7 samples were tested for each cancer tissue using a mouse model. We observed that a viscoelastic model with 2-term Prony series could best describe the ramp and stress relaxation of the tissue. For long-term responses, the SKBR3 tissues were stiffer in the strain levels of 4–10%, while no significant differences were found for the instantaneous elastic modulus. We also found tissues from both cell lines appeared to be strain-independent for the instantaneous elastic modulus and for the long-term elastic modulus in the strain level of 4–10%. In addition, by inspecting the cellular morphological structure of the two tissues, we found that SKBR3 tissues had a larger volume ratio of nuclei and a smaller volume ratio of extracellular matrix (ECM). Compared with prior cellular mechanics studies, our results indicated that ECM could contribute to the stiffening the tissue-level behavior. The viscoelastic characterization of the breast cancer tissue contributed to the scarce animal model data and provided support for the linear viscoelastic model used for in vivo elastography studies. Results also supplied helpful information for modeling of the breast cancer tissue in the tissue and cellular levels.     

Diffusing wave spectroscopy microrheology of actin filament networks.

Filamentous actin (F-actin), one of the constituents of the cytoskeleton, is believed to be the most important participant in the motion and mechanical integrity of eukaryotic cells. Traditionally, the viscoelastic moduli of F-actin networks have been measured by imposing a small mechanical strain and quantifying the resulting stress. The magnitude of the viscoelastic moduli, their concentration dependence and strain dependence, as well as the viscoelastic nature (solid-like or liquid-like) of networks of uncross-linked F-actin, have been the subjects of debate. Although this paper helps to resolve the debate and establishes the extent of the linear regime of F-actin networks' rheology, we report novel measurements of the high-frequency behavior of networks of F-actin, using a noninvasive light-scattering based technique, diffusing wave spectroscopy (DWS). Because no external strain is applied, our optical assay generates measurements of the mechanical properties of F-actin networks that avoid many ambiguities inherent in mechanical measurements. We observe that the elastic modulus has a small magnitude, no strain dependence, and a weak concentration dependence. Therefore, F-actin alone is not sufficient to generate the elastic modulus necessary to sustain the structural rigidity of most cells or support new cellular protrusions. Unlike previous studies, our measurements show that the mechanical properties of F-actin are highly dependent on the frequency content of the deformation. We show that the loss modulus unexpectedly dominates the elastic modulus at high frequencies, which are key for fast transitions. Finally, the measured mean square displacement of the optical probes, which is also generated by DWS measurements, offers new insight into the local bending fluctuations of the individual actin filaments and shows how they generate enhanced dissipation at short time scales.     

In vivo liver tissue mechanical properties by Transient Elastography: comparison with Dynamic Mechanical Analysis

Understanding the mechanical properties of human liver is one of the most critical aspects of its numerical modeling for medical applications or impact biomechanics. Generally, model constitutive laws come from in vitro data. However, the elastic properties of liver may change significantly after death and with time. Furthermore, in vitro liver elastic properties reported in the literature have often not been compared quantitatively with in vivo liver mechanical properties on the same organ. In this study, both steps are investigated on porcine liver. The elastic property of the porcine liver, given by the shear modulus G, was measured by both Transient Elastography (TE) and Dynamic Mechanical Analysis (DMA). Shear modulus measurements were realized on in vivo and in vitro liver to compare the TE and DMA methods and to study the influence of testing conditions on the liver viscoelastic properties. In vitro results show that elastic properties obtained by TE and DMA are in agreement. Liver tissue in the frequency range from 0.1 to 4 Hz can be modeled by a two-mode relaxation model. Furthermore, results show that the liver is homogeneous, isotropic and more elastic than viscous. Finally, it is shown in this study that viscoelastic properties obtained by TE and DMA change significantly with post mortem time and with the boundary conditions.     

Static versus dynamic gerbil tympanic membrane elasticity: derivation of the complex modulus

An accurate estimation of tympanic membrane stiffness is important for realistic modelling of middle ear mechanics. Tympanic membrane stiffness has been investigated extensively under either quasi-static or dynamic loading conditions. It is known that biological tissues are sensitive to strain rate. Therefore, in this work, the mechanical behaviour of the tympanic membrane was studied under both quasi-static and dynamic loading conditions. Experiments were performed on the pars tensa of four gerbil tympanic membranes. A custom-built indentation apparatus was used to perform in situ tissue indentations and testing was done applying both quasi-static and dynamic sinusoidal indentations up to 8.2?Hz. The unloaded shape of the tympanic membrane was measured and used to create specimen-specific finite element models to simulate the experiments. The frequency dependent Young's modulus of each specimen was then estimated by an inverse analysis in which the error between experimental and simulated indentation data was optimised for each indentation frequency separately. Using an 8?μm central region thickness, we found Young's moduli between 71 and 106?MPa (n = 4) at 0.2?Hz indentation frequency. A standard linear viscoelastic model and a viscoelastic model with a continuous relaxation spectrum were used to derive a complex modulus in the frequency domain. Due to experimental limitations, the indentation frequency upper limit was 8.2?Hz. The average relative modulus increase in this domain was 14% and the increase was the strongest below 6?Hz.