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.     

Modified Bilston nonlinear viscoelastic model for finite element head injury studies

This paper proposes a modified nonlinear viscoelastic Bilston model (Bilston et al., 2001, Biorheol., 38, pp. 335-345). for the modeling of brain tissue constitutive properties. The modified model can be readily implemented in a commercial explicit finite element (FE) code, PamCrash. Critical parameters of the model have been determined through a series of rheological tests on porcine brain tissue samples and the time-temperature superposition (TTS) principle has been used to extend the frequency to a high region. Simulations by using PamCrash are compared with the test results. Through the use of the TTS principle, the mechanical and rheological behavior at high frequencies up to 10(4) rads may be obtained. This is important because the properties of the brain tissue at high frequencies and impact rates are especially relevant to studies of traumatic head injury. The averaged dynamic modulus ranges from 130 Pa to 1500 Pa and loss modulus ranges from 35 Pa to 800 Pa in the frequency regime studied (0.01 rads to 3700 rads). The errors between theoretical predictions and averaged relaxation test results are within 20% for strains up to 20%. The FEM simulation results are in good agreement with experimental results. The proposed model will be especially useful for application to FE analysis of the head under impact loads. More realistic analysis of head injury can be carried out by incorporating the nonlinear viscoelastic constitutive law for brain tissue into a commercial FE code.     

Viscoelastic properties of single attached cells under compression

The viscoelastic properties of single, attached C2C12 myoblasts were measured using a recently developed cell loading device. The device allows global compression of an attached cell, while simultaneously measuring the associated forces. The viscoelastic properties were examined by performing a series of dynamic experiments over two frequency decades (0.1-10 Hz) and at a range of axial strains (approximately 10-40%). Confocal laser scanning microscopy was used to visualize the cell during these experiments. To analyze the experimentally obtained force-deformation curves, a nonlinear viscoelastic model was developed. The nonlinear viscoelastic model was able to describe the complete series of dynamic experiments using only a single set of parameters, yielding an elastic modulus of 2120 +/- 900 Pa for the elastic spring, an elastic modulus of 1960 +/- 1350 for the nonlinear spring, and a relaxation time constant of 0.3 +/- 0.12 s. To our knowledge, it is the first time that the global viscoelastic properties of attached cells have been quantified over such a wide range of strains. Furthermore, the experiments were performed under optimal environmental conditions and the results are, therefore, believed to reflect the viscoelastic mechanical behavior of cells, such as would be present in vivo.     

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.     

Characterization of bone-implant fixation using modal analysis: Application to a press-fit implant model

Orthopaedic implant fixation is strongly dependant upon the effective mechanical properties of newly formed tissue. In this study, we evaluated the potential of modal analysis to derive viscoelastic properties of periprosthetic tissue. We hypothesized that Young's modulus and loss factor could be obtained by a combined theoretical, computational and experimental modal analysis approach. This procedure was applied to ex vivo specimens from a cylindrical experimental implant placed in cancellous bone in an unloaded press-fit configuration, obtained after a four week observation period. Four sections each from seven textured titanium implants were investigated. The first resonant frequency and loss factor were measured. Average experimentally determined loss factor was 2% (SD 0.4%) and average first resonant frequency was 2.1 KHz (SD: 50). A 2D axisymmetric finite element (FE) model identified effective Young's modulus of tissue using experimental resonant frequencies as input. Average value was 42 MPa (SD: 2.4) and no significant difference between specimens was observed.In this pilot study, the non-destructive method allowed accurate measure of dynamic loss factor and resonant frequency and derivation of effective Young's modulus. Prior to implementing this dynamic protocol for broader mechanical evaluation of experimental implant fixation, further work is needed to determine if this affects results from subsequent destructive shear push-out tests.     

Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry.

A magnetic bead microrheometer has been designed which allows the generation of forces up to 10(4) pN on 4.5 micron paramagnetic beads. It is applied to measure local viscoelastic properties of the surface of adhering fibroblasts. Creep response and relaxation curves evoked by tangential force pulses of 500-2500 pN (and approximately 1 s duration) on the magnetic beads fixed to the integrin receptors of the cell membrane are recorded by particle tracking. Linear three-phasic creep responses consisting of an elastic deflection, a stress relaxation, and a viscous flow are established. The viscoelastic response curves are analyzed in terms of a series arrangement of a dashpot and a Voigt body, which allows characterization of the viscoelastic behavior of the adhering cell surface in terms of three parameters: an effective elastic constant, a viscosity, and a relaxation time. The displacement field generated by the local tangential forces on the cell surface is visualized by observing the induced motion of assemblies of nonmagnetic colloidal probes fixed to the membrane. It is found that the displacement field decays rapidly with the distance from the magnetic bead. A cutoff radius of Rc approximately 7 micron of the screened elastic field is established. Partial penetration of the shear field into the cytoplasm is established by observing the induced deflection of intracellular compartments. The cell membrane was modeled as a thin elastic plate of shear modulus mu * coupled to a viscoelastic layer, which is fixed to a solid support on the opposite side; the former accounts for the membrane/actin cortex, and the latter for the contribution of the cytoskeleton to the deformation of the cell envelope. It is characterized by the coupling constant chi characterizing the elasticity of the cytoskeleton. The coupling constant chi and the surface shear modulus mu * are obtained from the measured displacements of the magnetic and nonmagnetic beads. By analyzing the experimental data in terms of this model a surface shear modulus of mu * approximately 2 . 10(-3) Pa m to 4 . 10(-3) Pa m is found. By assuming an approximate plate thickness of 0.1 micron one estimates an average bulk shear modulus of mu approximately (2 / 4) . 10(-4) Pa, which is in reasonable agreement with data obtained by atomic force microscopy. The viscosity of the dashpot is related to the apparent viscosity of the cytoplasm, which is obtained by assuming that the top membrane is coupled to the bottom (fixed) membrane by a viscous medium. By application of the theory of diffusion of membrane proteins in supported membranes we find a coefficient of friction of bc approximately 2 . 10(9) Pa s/m corresponding to a cytoplasmic viscosity of 2 . 10(3) Pa s.     

Improved measurement of brain deformation during mild head acceleration using a novel tagged MRI sequence

In vivo measurements of human brain deformation during mild acceleration are needed to help validate computational models of traumatic brain injury and to understand the factors that govern the mechanical response of the brain. Tagged magnetic resonance imaging is a powerful, noninvasive technique to track tissue motion in vivo which has been used to quantify brain deformation in live human subjects. However, these prior studies required from 72 to 144 head rotations to generate deformation data for a single image slice, precluding its use to investigate the entire brain in a single subject. Here, a novel method is introduced that significantly reduces temporal variability in the acquisition and improves the accuracy of displacement estimates. Optimization of the acquisition parameters in a gelatin phantom and three human subjects leads to a reduction in the number of rotations from 72 to 144 to as few as 8 for a single image slice. The ability to estimate accurate, well-resolved, fields of displacement and strain in far fewer repetitions will enable comprehensive studies of acceleration-induced deformation throughout the human brain in vivo.     

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.     

Experimental Study of the Vortex-Induced Vibration of Drilling Risers under the Shear Flow with the Same Shear Parameter at the Different Reynolds Numbers

A considerable number of studies for VIV under the uniform flow have been performed. However, research on VIV under shear flow is scarce. An experiment for VIV under the shear flow with the same shear parameter at the two different Reynolds numbers was conducted in a deep-water offshore basin. Various measurements were obtained by the fiber bragg grating strain sensors. Experimental data were analyzed by modal analysis method. Results show several valuable features. First, the corresponding maximum order mode of the natural frequency for shedding frequency is the maximum dominant vibration mode and multi-modal phenomenon is appeared in VIV under the shear flow, and multi-modal phenomenon is more apparent at the same shear parameter with an increasing Reynolds number under the shear flow effect. Secondly, the riser vibrates at the natural frequency and the dominant vibration frequency increases for the effect of the real-time tension amplitude under the shear flow and the IL vibration frequency is the similar with the CF vibration frequency at the Reynolds number of 1105 in our experimental condition and the IL dominant frequency is twice the CF dominant frequency with an increasing Reynolds number. In addition, the displacement trajectories at the different locations of the riser appear the same shape and the shape is changed at the same shear parameter with an increasing Reynolds number under the shear flow. The diagonal displacement trajectories are observed at the low Reynolds number and the crescent-shaped displacement trajectories appear with an increasing Reynolds number under shear flow in the experiment.     

The applicability of the time/temperature superposition principle to brain tissue

This paper deals with the mechanical characterization of brain tissue which behaves as a viscoelastic material. We focus on the linear viscoelastic behavior, which should apply for small strains at any strain rate, and demonstrate the applicability of the time/temperature superposition principle. This principle allows the opportunity to extend the range of shear rates for which the material is characterized, and makes the results applicable to impact conditions. This characterization of the linear behavior forms the basis for a further nonlinear characterization of the tissue.     

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.     

Dynamic, regional mechanical properties of the porcine brain: indentation in the coronal plane

Stress relaxation tests using a custom designed microindentation device were performed on ten anatomic regions of fresh porcine brain (postmortem time <3 h). Using linear viscoelastic theory, a Prony series representation was used to describe the shear relaxation modulus for each anatomic region tested. Prony series parameters fit to load data from indentations performed to ～10% strain differed significantly by anatomic region. The gray and white matter of the cerebellum along with corpus callosum and brainstem were the softest regions measured. The cortex and hippocampal CA1/CA3 were found to be the stiffest. To examine the large strain behavior of the tissue, multistep indentations were performed in the corona radiata to strains of 10%, 20%, and 30%. Reduced relaxation functions were not significantly different for each step, suggesting that quasi-linear viscoelastic theory may be appropriate for representing the nonlinear behavior of this anatomic region of porcine brain tissue. These data, for the first time, describe the dynamic and short time scale behavior of multiple anatomic regions of the porcine brain which will be useful for understanding porcine brain injury biomechanics at a finer spatial resolution than previously possible.     

Dynamic contact of the human fingerpad against a flat surface

This paper investigates the dynamic, distributed pressure response of the human fingerpad in vivo when it first makes contact with an object. A flat probe was indented against the fingerpad at a 20 to 40 degree angle. Ramp-and-hold and sinusoidal displacement trajectories were applied to the fingerpad within a force range of 0-2 N. The dynamic spatial distribution of the pressure response was measured using a tactile array sensor. Both the local pressure variation and the total force exhibited nonlinear stiffness (exponential with displacement) and significant temporal relaxation. The shape of the contact pressure distribution could plausibly be described by an inverted paraboloid. A model based on the contact of a rigid plane (the object) and a linear viscoelastic sphere (the fingerpad), modified to include a nonlinear modulus of elasticity, can account for the principal features of the distributed pressure response.     

In vivo imaging of rapid deformation and strain in an animal model of traumatic brain injury

In traumatic brain injury (TBI) rapid deformation of brain tissue leads to axonal injury and cell death. In vivo quantification of such fast deformations is extremely difficult, but important for understanding the mechanisms of degeneration post-trauma and for development of numerical models of injury biomechanics. In this paper, strain fields in the brain of the perinatal rat were estimated from data obtained in vivo during rapid indentation. Tagged magnetic resonance (MR) images were obtained with high spatial (0.2 mm) and temporal (3.9 ms) resolution by gated image acquisition during and after impact. Impacts were repeated either 64 or 128 times to obtain images of horizontal and vertical tag lines in coronal and sagittal planes. Strain fields were estimated by harmonic phase (HARP) analysis of the tagged images. The original MR data was filtered and Fourier-transformed to obtain HARP images, following a method originally developed by Osman et al. (IEEE Trans. Med. Imaging 19(3) (2000) 186). The displacements of material points were estimated from intersections of HARP contours and used to generate estimates of the deformation gradient and Lagrangian strain tensors. Maximum principal Lagrangian strains of >0.20 at strain rates >40/s were observed during indentations of 2 mm depth and 21 ms duration.     

Elastic contributions dominate the viscoelastic properties of sputum from cystic fibrosis patients

Sputum samples from cystic fibrosis (CF) patients were investigated by oscillatory, creep and steady shear rheological techniques over a range of time scales from 10(-3) to 10(6) s. The viscoelastic changes obtained by mixing sputa with the actin-filament-severing protein gelsolin and with the thiol-reducing agent dithiothreitol (DTT) were also investigated. At small strains sputum behaves like a viscoelastic solid rather than a liquid. A nearly constant steady shear viscosity at low shear rates is only observed after long shearing times which cause irreversible changes in the samples. Creep-recovery tests confirm that sputa exhibit viscoelastic properties, with a significant elastic recovery. The results suggest that measurements of elastic moduli, rather than viscosities are more closely related to the mechanical properties of sputum in situ. Severing of actin filaments lowers the elastic modulus by 30-40%, but maintains viscoelastic integrity, while reduction of thiols in the glycoproteins nearly completely fluidizes the samples.     

Use of magnetic resonance to measure molecular diffusion within the brain extracellular space

Ion-selective microelectrode measurements of molecular diffusion have provided unique information about the structural characteristics of the extracellular compartment of brain tissue. Magnetic resonance (MR) techniques can also be used to perform diffusion measurements in living tissue in situ. In MR applications, the challenge to study a particular physiological compartment lies in achieving the appropriate specificity in the experimentally-observed MR signal, and many strategies have been used to provide measurements that reflect molecular diffusion within the extracellular space. This review describes how magnetic resonance and microelectrode diffusion measurements are performed, and applications using the MR technique are summarized. Comparisons of experimental results obtained from the two techniques indicate that their use in combination may further augment what is known about extracellular space structure.     

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.     

Mechanical properties of soft human tissues under dynamic loading

The dynamic response of soft human tissues in hydrostatic compression and simple shear is studied using the Kolsky bar technique. We have made modifications to the technique that allow loading of a soft tissue specimen in hydrostatic compression or simple shear. The dynamic response of human tissues (from stomach, heart, liver, and lung of cadavers) is obtained, and analyzed to provide measures of dynamic bulk modulus and shear response for each tissue type. The dynamic bulk response of these tissues is easily described by a linear fit for the bulk modulus in this pressure range, whereas the dynamic shearing response of these tissues is strongly non-linear, showing a near exponential growth of the shear stress.     

A mathematical model for the determination of viscoelastic behavior of brain in vivo. II. Relaxation response

In a recent experiment for determining the mechanical response of brain in vivo. a probe, inserted through scalp, skull and dura, is placed in contact with and normal to the brain, given a prescribed motion, and the time variation of corresponding force is measured. In the corresponding continuum mechanical model, brain is idealized as a linear isotropic viscoelastic solid constrained by a rigid skull. At the mating surface, the shear stress and normal displacement vanish everywhere except under the probe which exerts a local radial displacement. This model introduces effective viscoelastic moduli in shear, which is unknown, and in dilatation, which is considered known from other sources. Part II of this study is concerned with stress relaxation induced by a small step displacement of the probe. From the solution of the corresponding quasi-static boundary value problem, a nonlinear Volterra integral equation is established from which the shear stress relaxation function can be solved in terms of measured probe displacement and force. A numerical method of solution is developed.