Ruth J. Okamoto

Epicardial Suction: A New Approach to Mechanical Testing of the Passive Ventricular Wall

The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular epicardium to introduce a complex deformation in the region of interest, with transmural variations in the magnitude and sign of nearly all six strain components. The resulting deformation is measured throughout the region of interest using magnetic resonance tagging. A nonlinear, three-dimensional, finite element model is used to predict these measurements at several suction pressures. Parameters defining the material properties of this model are optimized by comparing the measured and predicted myocardial deformations. We used this technique to estimate material parameters of the intact passive canine left ventricular free wall using an exponential, transversely isotropic constitutive relation. We tested two possible models of the heart wall: first, that it was homogeneous myocardium, and second, that the myocardium was covered with a thin epicardium with different material properties. For both models, in agreement with previous studies, we found that myocardium was nonlinear and anisotropic with greater stiffness in the fiber direction. We obtained closer agreement to previously published strain data from passive filling when the ventricular wall was modeled as having a separate, isotropic epicardium. These results suggest that epicardium may play a significant role in passive ventricular mechanics.

The Fragile Fiber1 Kinesin Contributes to Cortical Microtubule-Mediated Trafficking of Cell Wall Components

A microtubule-associated kinesin moves processively along cortical microtubules and contributes to the production of both primary and secondary walls by mediating membrane trafficking. The cell wall consists of cellulose microfibrils embedded within a matrix of hemicellulose and pectin. Cellulose microfibrils are synthesized at the plasma membrane, whereas matrix polysaccharides are synthesized in the Golgi apparatus and secreted. The trafficking of vesicles containing cell wall components is thought to depend on actin-myosin. Here, we implicate microtubules in this process through studies of the kinesin-4 family member, Fragile Fiber1 (FRA1). In an fra1-5 knockout mutant, the expansion rate of the inflorescence stem is halved compared with the wild type along with the thickness of both primary and secondary cell walls. Nevertheless, cell walls in fra1-5 have an essentially unaltered composition and ultrastructure. A functional triple green fluorescent protein-tagged FRA1 fusion protein moves processively along cortical microtubules, and its abundance and motile density correlate with growth rate. Motility of FRA1 and cellulose synthase complexes is independent, indicating that FRA1 is not directly involved in cellulose biosynthesis; however, the secretion rate of fucose-alkyne-labeled pectin is greatly decreased in fra1-5, and the mutant has Golgi bodies with fewer cisternae and enlarged vesicles. Based on our results, we propose that FRA1 contributes to cell wall production by transporting Golgi-derived vesicles along cortical microtubules for secretion.

Requirements for accurate estimation of anisotropic material parameters by magnetic resonance elastography: A computational study

To establish the essential requirements for characterization of a transversely isotropic material by magnetic resonance elastography (MRE).

Contraction and stress-dependent growth shape the forebrain of the early chicken embryo.

During early vertebrate development, local constrictions, or sulci, form to divide the forebrain into the diencephalon, telencephalon, and optic vesicles. These partitions are maintained and exaggerated as the brain tube inflates, grows, and bends. Combining quantitative experiments on chick embryos with computational modeling, we investigated the biophysical mechanisms that drive these changes in brain shape. Chemical perturbations of contractility indicated that actomyosin contraction plays a major role in the creation of initial constrictions (Hamburger-Hamilton stages HH11-12), and fluorescent staining revealed that F-actin is circumferentially aligned at all constrictions. A finite element model based on these findings shows that the observed shape changes are consistent with circumferential contraction in these regions. To explain why sulci continue to deepen as the forebrain expands (HH12-20), we speculate that growth depends on wall stress. This idea was examined by including stress-dependent growth in a model with cerebrospinal fluid pressure and bending (cephalic flexure). The results given by the model agree with observed morphological changes that occur in the brain tube under normal and reduced eCSF pressure, quantitative measurements of relative sulcal depth versus time, and previously published patterns of cell proliferation. Taken together, our results support a biphasic mechanism for forebrain morphogenesis consisting of differential contractility (early) and stress-dependent growth (late).

Measurement of Brain Biomechanics in vivo by Magnetic Resonance Imaging

Computer models of head-brain biomechanics offer enormous potential for improved understanding and prevention of traumatic brain injury (TBI). However existing computer models remain controversial because their predictions have yet to be rigorously compared to measured biomechanical data. The nonlinear, anisotropic, viscoelastic, heterogeneous character of brain tissue, and the intricate connections between the brain and skull, all complicate modeling efforts. In order to make progress toward the goal of accurate simulation of TBI, experimental techniques to address these issues must be developed. In this paper we describe two magnetic resonance (MR) imaging techniques to characterize brain deformation, estimate brain material properties, and illuminate the boundary conditions between brain and skull. MR tagging is used to estimate displacement and strain fields in response to rigid-body acceleration of the skull, and MR elastography is used to visualize shear wave propagation induced by oscillatory loading at the surface of the skull.

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.

MRE detection of heterogeneity using quantitative measures of residual error and uncertainty

In magnetic resonance elastography (MRE), displacement fields from shear waves are inverted to estimate underlying material properties. Modulus differences detected by MRE may be used to distinguish tumors or other localized pathology in tissue. The accuracy of modulus estimates depends on the choice of the assumed constitutive model, as well as on the inversion algorithm, image resolution, and signal-to-noise ratio. In particular, in simpler inversion methods such as direct inversion and three-dimensional local frequency estimation (3D-LFE) the constitutive model is minimal (linear, elastic or viscoelastic, and isotropic) and the simplifying assumption of local homogeneity is usually made. The assumption of local homogeneity is often inaccurate [1], since the shear wavelength is typically comparable to the size of the structures of interest. Notably, the residual error (in direct inversion) between the model and the experimental data increases sharply at the boundaries of inclusions, while the “certainty” of the 3D-LFE estimate decreases. These error metrics may be used to detect local stiffness heterogeneity, as well as indicate variations in appropriate constitutive models. The utility of model uncertainty is demonstrated in simulations and with MRE data from a heterogeneous gel phantom.

Identification of a Transversely Isotropic Material Model for White Matter in the Brain

Axonal fiber tracts in white matter of the brain form anisotropic structures. It is assumed that this structural anisotropy causes mechanical anisotropy, making white matter tissue stiffer along the axonal fiber direction. This, in turn, will affect the mechanical loading of axonal tracts during traumatic brain injury (TBI). The goal of this study is to use a combination of in-vitro tests to characterize the mechanical anisotropy of white matter and compare it to gray matter, which is thought to be structurally and mechanically isotropic. A more complete understanding of the mechanical anisotropy of brain tissue will provide more accurate information for computational simulations of brain injury.Copyright

Shear Wave Propagation of the Ferret Brain at Multiple Frequencies In Vivo

Mathematical modeling and computer simulations are widely used for understanding traumatic brain injury (TBI). However, accurate tissue parameters are needed, especially for the brain in vivo. In this study, we used the ferret as the animal model because it is the smallest mammal with a folded brain and significant white matter tracts. Magnetic resonance elastography (MRE) has proven useful for in vivo measurement of biological tissue properties. Mechanical properties of the ferret brain over a range of frequencies from 400–800 Hz were studied using MRE. Experiment results show both that storage and loss modulus increases with frequency and that dissipative effects in the white matter (characterized by the loss modulus G″) were significant larger than in gray matter.Copyright

Flexural Rigidity of Intact Chlamydomonas Flagella Measured With an Optical Trap

Flagella and cilia are thin, active organelles protruding from cells that are used to propel the cell or move fluid. The flagellated alga Chlamydomonas reinhardtii is a uni-cellular model organism well-suited for the study of flagellar and cilia mechanics.Copyright