Anisotropic Skeletal Muscle Research Articles

Magnetically-Assisted Microfluidic Printing for the Fabrication of Anisotropic Skeletal Muscle Structure

Microfluidic printing provides a novel tool to facilitate the bulk assembly of cell-aligned microfibers for the fabrication of artificial skeletal muscle structure. However, due to the poor controllability for the deposition position of the microfiber, it is still difficult to realize the anisotropic assembly. In this paper, we developed a magnetically-assisted microfluidic printing system to solve this problem. Magnetic nanoparticles (MNPs) were encapsulated in the microfluidic spun microfibers, and a spiral magnet was designed as a microfiber deposition substrate. A robotic visual serving was utilized to control the orifice posture of the microfluidic spinning systemrelative to the axis direction of the spiral magnet, and then the spun microfibers were continuously deposited layer by layer to form an anisotropic assembly structure. Our proposed method demonstrates that the magnetic attraction mechanism is a novel microfiber-specific micromanipulation strategy for stable deposition in liquid environment. Furthermore, the preliminary cell experiments show that our methodhas highbiocompatibility to be further used in the fabrication of anisotropic skeletal muscle tissue.

On a three–dimensional model for the description of the passive characteristics of skeletal muscle tissue

In this work, a three–dimensional model was developed to describe the passive mechanical behaviour of anisotropic skeletal muscle tissue. To validate the model, orientation–dependent axial (0^circ, 45^circ, 90^circ) and semi–confined compression experiments (mode I, II, III) were performed on soleus muscle tissue from rabbits. In the latter experiments, specimen deformation is prescribed in the loading direction and prevented in an additional spatial direction, fibre compression at 0^circ (mode I), fibre elongation at 90^circ (mode II) and a neutral state of the fibres at 90^circ where their length is kept constant (mode III). Overall, the model can adequately describe the mechanical behaviour with a relatively small number of model parameters. The stiffest tissue response during orientation–dependent axial compression (-,7.7,pm ,1.3 kPa) occurs when the fibres are oriented perpendicular to the loading direction (90^circ) and are thus stretched during loading. Semi–confined compression experiments yielded the stiffest tissue (-,36.7,pm ,11.2 kPa) in mode II when the muscle fibres are stretched. The extensive data set collected in this study allows to study the different error measures depending on the deformation state or the combination of deformation states.

Estimation method for the anisotropic electrical conductivity of in vivo human muscles and fat between 10 kHz and 1 MHz

Objective. In low frequency dosimetry the variability in the electrical conductivity values assigned to body model tissues represents a major source of uncertainty. The aim of this study is to propose a method for estimating the conductivity of human anisotropic skeletal muscle and fat in vivo in the frequency range from 10 kHz to 1 MHz. Approach. A method based on bounded electrical impedance tomography was used. Bioimpedance measurements were performed on the legs of ten subjects. Anatomically realistic models of the legs were then created using magnetic resonance images. The inverse problem of the tissue conductivities was solved using the finite element method. The results were validated using resampling techniques. These findings were also used to study the effects of muscle anisotropy on magnetic field exposure. Main results. The estimated conductivities for anisotropic muscle were found to be in good agreement with values found in existing literature and the anisotropy was shown to decrease with increasing frequency, with the ratio of lateral to longitudinal conductivity increasing from 37% to 64%. The conductivity of fat was found to be almost a constant 0.07 S m−1 in the frequency range considered. Significance. The proposed method was shown to be a viable option when estimating in vivo conductivity of human tissue. The results can be used in numerical dosimetry calculations or as limits in future investigations studying conductivity with bioimpedance measurements.

Approximate complex electrical potential distribution in the monodomain model with unequal conductivity and relative permittivity anisotropy ratios

Objective: Electrical conductivity and relative permittivity are properties that indicate muscle health and they have different values parallel and perpendicular to the direction of the myofiber, a concept known as anisotropy. When the intrinsic electrical properties of muscle have ratios of anisotropy that are different then there is no analytical solution that can describe the electrical potential distribution in the tissue. Approach: Here, we present approximate analytical solutions to monodomain equations with unequal anisotropy ratios. For this, we base our analysis on perturbation theory where the electrical potential is approximated by the sum of the zeroth- and first-order terms of an infinite series. Main results: The validity of the approach is confirmed using experimental data for healthy and diseased muscle available online. Significance: A better understanding of electrical potential distribution in anisotropic skeletal muscle tissue will allow the development of improved diagnostic tools for neuromuscular diseases.

4D anisotropic skeletal muscle tissue constructs fabricated by staircase effect strategy

Like the morphology of native tissue fiber arrangement (such as skeletal muscle), unidirectional anisotropic scaffolds are highly desired as a means to guide cell behavior in anisotropic tissue engineering. In contrast, contour-like staircases exhibit directional topographical cues and are judged as an inevitable defect of fused deposition modeling (FDM). In this study, we will translate this staircase defect into an effective bioengineering strategy by integrating FDM with surface coating technique (FCT) to investigate the effect of topographical cues on regulating behaviors of human mesenchymal stem cells (hMSCs) toward skeletal muscle tissues. This integrated approach serves to fabricate shape-specific, multiple dimensional, anisotropic scaffolds using different biomaterials. 2D anisotropic scaffolds, first demonstrated with different polycaprolactone concentrations herein, efficiently direct hMSC alignment, especially when the scaffold is immobilized on a support ring. By surface coating the polymer solution inside FDM-printed sacrificial structures, 3D anisotropic scaffolds with thin wall features are developed and used to regulate seeded hMSCs through a self-established rotating bioreactor. Using layer-by-layer coating, along with a shape memory polymer, smart constructs exhibiting shape fix and recovery processes are prepared, bringing this study into the realm of 4D printing. Immunofluorescence staining and real-time quantitative polymerase chain reaction analysis confirm that the topographical cues created via FCT significantly enhance the expression of myogenic genes, including myoblast differentiation protein-1, desmin, and myosin heavy chain-2. We conclude that there are broad application potentials for this FCT strategy in tissue engineering as many tissues and organs, including skeletal muscle, possess highly organized and anisotropic extracellular matrix components.

New electrical impedance methods for the in situ measurement of the complex permittivity of anisotropic skeletal muscle using multipolar needles

This paper provides a rigorous analysis on the measurement of the permittivity of two-dimensional anisotropic biological tissues such as skeletal muscle using the four-electrode impedance technique. The state-of-the-art technique requires individual electrodes placed at the same depth in contact with the anisotropic material, e.g. using monopolar needles. In this case, the minimum of measurements in different directions needed to estimate the complex permittivity and its anisotropy direction is 3, which translates into 12 monopolar needle insertions (i.e. 3 directions × 4 electrodes in each direction). Here, we extend our previous work and equip the reader with 8 new methods for multipolar needles, where 2 or more electrodes are spaced along the needle’s shaft in contact with the tissue at different depths. Using multipolar needles, the new methods presented reduce the number of needle insertions by a factor of 2 with respect to the available methods. We illustrate the methods with numerical simulations and new experiments on ex vivo ovine skeletal muscle (n = 3). Multi-frequency longitudinal and transverse permittivity data from 30 kHz to 1 MHz is made publicly available in the supplementary material. The methods presented here for multipolar needles bring closer the application of needle electrical impedance to patients with neuromuscular diseases.

Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images.

We present a new way to extract characteristic features of the Mueller matrix images based on their frequency distributions and the central moments. We take the backscattering Mueller matrices of tissues with distinctive microstructures, and then analyze the frequency distribution histograms (FDHs) of all the matrix elements. For anisotropic skeletal muscle and isotropic liver tissues, we find that the shapes of the FDHs and their central moment parameters, i.e., variance, skewness, and kurtosis, are not sensitive to the sample orientation. Comparisons among different tissues further indicate that the frequency distributions of Mueller matrix elements and their corresponding central moments can be used as indicators for the characteristic microstructural features of tissues. A preliminary application to human cervical cancerous tissues shows that the distribution curves and central moment parameters may have the potential to give quantitative criteria for cancerous tissues detections.

Three-parameter shear wave inversion in MR elastography of incompressible transverse isotropic media: Application to in vivo lower leg muscles.

To develop and demonstrate MR elastography (MRE) for the measurement of three independent viscoelastic constants of skeletal muscle according to the theory of linear elasticity of incompressible materials with transverse isotropy (TI). Three-dimensional multifrequency MRE was applied to soleus, gastrocnemius, and tibialis anterior muscles in 10 healthy volunteers. The rotational wave fields were solved for complex-valued viscoelastic parameters μ12, μ13, and E3 corresponding to two shear moduli (within the planes of isotropy and symmetry of TI materials) and Young's modulus (along the principal fiber axis). Anisotropy was represented by the inequality μ12 < μ13 < 1/3E3 considering storage and loss properties of the soleus and gastrocnemius muscles, whereas storage shear moduli of tibialis were indistinguishable. Storage moduli were: 1.06 ± 0.12, 1.33 ± 0.10, 6.92 ± 0.95 kPa (soleus); 0.90 ± 0.11, 1.30 ± 0.15, 8.22 ± 1.37 kPa (gastrocnemius); 1.26 ± 0.16, 1.27 ± 0.11, 9.29 ± 1.42 kPa (tibialis), for μ12, μ13, and E3, respectively. The muscles were different in their μ12 and E3 values, whereas μ13 was less sensitive to the muscle type. Leg differences were observed in the soleus and gastrocnemius muscles. Recovery of the full elasticity tensor in incompressible TI materials is feasible by three-dimensional inversion of the time-harmonic shear wave equation. The method is potentially useful for the clinical evaluation of skeletal muscle anisotropy.

Forward Problem of Electrocardiography

The relationship between epicardial and body surface potentials defines the forward problem of electrocardiography. A robust formulation of the forward problem is instrumental to solving the inverse problem, in which epicardial potentials are computed from known body surface potentials. Here, the accuracy of different forward models has been evaluated experimentally. Body surface and epicardial potentials were recorded simultaneously in anesthetized closed-chest pigs (n=5) during sinus rhythm, and epicardial and endocardial ventricular pacing (65 records in total). Body surface potentials were simulated from epicardial recordings using experiment-specific volume conductor models constructed from magnetic resonance imaging. Results for homogeneous (isotropic electric properties) and inhomogeneous (incorporating lungs, anisotropic skeletal muscle, and subcutaneous fat) forward models were compared with measured body surface potentials. Correlation coefficients were 0.85±0.08 across all animals and activation sequences with no significant difference between homogeneous and inhomogeneous solutions (P=0.85). Despite this, there was considerable variance between simulated and measured body surface potential distributions. Differences between the body surface potential extrema predicted with homogeneous forward models were 55% to 78% greater than observed (P<0.05) and attenuation of potentials adjacent to extrema were 10% to 171% greater (P<0.03). The length and orientation of the vector between potential extrema were also significantly different. Inclusion of inhomogeneous electric properties in the forward model reduced, but did not eliminate these differences. These results demonstrate that homogeneous volume conductor models introduce substantial spatial inaccuracies in forward problem solutions. This probably affects the precision of inverse reconstructions of cardiac potentials, in which this assumption is made.

Anisotropic conductivity tensor imaging using magnetic induction tomography

Magnetic induction tomography aims to reconstruct the electrical conductivity distribution of the human body using non-contact measurements. The potential of the method has been demonstrated by various simulation studies and a number of phantom experiments. These studies have all relied on models having isotropic distributions of conductivity, although the human body has a highly heterogeneous structure with partially anisotropic properties. Therefore, whether the conventional modeling approaches used so far are appropriate for clinical applications or not is still an open question. To investigate the problem, we performed a simulation study to investigate the feasibility of (1) imaging anisotropic perturbations within an isotropic medium and (2) imaging isotropic perturbations inside a partially anisotropic background. The first is the case for the imaging of anomalies that have anisotropic characteristics and the latter is the case e.g. in lung imaging where an anisotropic skeletal muscle tissue surrounds the lungs and the rib cage. An anisotropic solver based on the singular value decomposition was used to attain conductivity tensor images to be compared with the ones obtained from isotropic solvers. The results indicate the importance of anisotropic modeling in order to obtain satisfactory reconstructions, especially for the imaging of the anisotropic anomalies, and address the resolvability of the conductivity tensor components.

Ranking the Influence of Tissue Conductivities on Forward-Calculated ECGs

This paper examined the effects that different tissue conductivities had on forward-calculated ECGs. To this end, we ranked the influence of tissues by performing repetitive forward calculations while varying the respective tissue conductivity. The torso model included all major anatomical structures like blood, lungs, fat, anisotropic skeletal muscle, intestine, liver, kidneys, bone, cartilage, and spleen. Cardiac electrical sources were derived from realistic atrial and ventricular simulations. The conductivity rankings were based on one of two methods: First, we considered fixed percental conductivity changes to probe the sensitivity of the ECG regarding conductivity alterations. Second, we set conductivities to the reported minimum and maximum values to evaluate the effects of the existing conductivity uncertainties. The amplitudes of both atrial and ventricular ECGs were most sensitive for blood, skeletal muscle conductivity and anisotropy as well as for heart, fat, and lungs. If signal morphology was considered, fat was more important whereas skeletal muscle was less important. When comparing atria and ventricles, the lungs had a larger effect on the atria yet the heart conductivity had a stronger impact on the ventricles. The effects of conductivity uncertainties were significant. Future studies dealing with electrocardiographic simulations should consider these effects.

The influence of skeletal muscle anisotropy on electroporation: in vivo study and numerical modeling

The aim of this study was to theoretically and experimentally investigate electroporation of mouse tibialis cranialis and to determine the reversible electroporation threshold values needed for parallel and perpendicular orientation of the applied electric field with respect to the muscle fibers. Our study was based on local electric field calculated with three-dimensional realistic numerical models, that we built, and in vivo visualization of electroporated muscle tissue. We established that electroporation of muscle cells in tissue depends on the orientation of the applied electric field; the local electric field threshold values were determined (pulse parameters: 8 × 100 μs, 1 Hz) to be 80 V/cm and 200 V/cm for parallel and perpendicular orientation, respectively. Our results could be useful electric field parameters in the control of skeletal muscle electroporation, which can be used in treatment planning of electroporation based therapies such as gene therapy, genetic vaccination, and electrochemotherapy.

Effects of skeletal muscle anisotropy on induced currents from low-frequency magnetic fields

Studies which take into account the anisotropy of tissue dielectric properties for the numerical assessment of induced currents from low-frequency magnetic fields are scarce. In the present study, we compare the induced currents in two anatomical models, using the impedance method. In the first model, we assume that all tissues have isotropic conductivity, whereas in the second one, we assume anisotropic conductivity for the skeletal muscle. Results show that tissue anisotropy should be taken into account when investigating the exposure to low-frequency magnetic fields, because it leads to higher induced current values.

Effects of skeletal muscle anisotropy on human organ dosimetry under 60 Hz uniform magnetic field exposure

The recent development of anatomically derived high-resolution voxel-based models of the human body suitable for electromagnetic modelling, and of effective methods for computing the associated induction, has resulted in numerical estimates of organ-specific dosimetry for human exposure to low-frequency magnetic fields. However, these estimates have used an isotropic conductivity model for all body components. More realistic estimates should account for the anisotropy of certain tissues, particularly skeletal muscle. In this work, high-resolution finite-difference computations of induced fields are used to estimate the effects of several extremal realizations of skeletal muscle anisotropy on field levels in various organs. It is shown that, under the present assumptions (anisotropy ratios up to 3.5:1), the resulting dosimetric values can vary by factors of between two or three for tissues other than muscle and up to 5.4 for muscle, despite the unchanged nature of the conductivity model used for all other body components.

The effects of inhomogeneities and anisotropies on electrocardiographic fields: a 3-D finite-element study.

The aim of this study was to quantify the effects of selected inhomogeneities and anisotropies on computed electric potential fields associated with the electrocardiographic forward problem. The model construction was based on the Utah Torso model and included geometry for major anatomical structures such as subcutaneous fat, skeletal muscle, and lungs, as well as for epicardial fatpads, major arteries and veins, and the sternum, ribs, spine, and clavicles. Measured epicardial potentials served as the electrical source for solutions to the electrocardiographic forward problems computed using the finite element method (FEM). The geometry of the torso model for each simulation was constant, but different combinations of conductivities were assigned to individual organs or tissues. Comparisons of different conductivity combinations followed one of two basic schemes: 1) a homogeneous torso served as the reference against which we compared simulations with a single organ or tissue and assigned its nominal conductivity, or 2) a fully inhomogeneous torso served as the reference and we removed the effect of individual organs or tissues by assigning it the homogeneous conductivity value. When single inhomogeneities were added to an otherwise homogeneous isotropic model, anisotropic skeletal muscle (at a 15:1 anisotropy ratio) and the right and left lung had larger average effects (12.8, 12.7, and 12.1% relative error (RE), respectively) than the other inhomogeneities tested. Our results for removing single inhomogeneities show that the subcutaneous fat, the anisotropic skeletal muscle (with the degree of anisotropy equal to 7:1), and the lungs have larger average impacts on the body surface potential distributions than other elements of the model (with values of 14.9, 12.6, and 11.7% RE, respectively). The results also show that the size of the effect depended strongly on the distribution of epicardial potentials. The results of this study suggest that accurate representation of tissue inhomogeneity has a significant effect on the accuracy of the forward solution, with regions near the torso surface playing a larger role, in general, than those near the heart.

Estimation of the Effective Self-Diffusion Tensor from the NMR Spin Echo

The diagonal and off-diagonal elements of the effective self-diffusion tensor, Deff, are related to the echo intensity in an NMR spin-echo experiment. This relationship is used to design experiments from which Deff is estimated. This estimate is validated using isotropic and anisotropic media, i.e., water and skeletal muscle. It is shown that significant errors are made in diffusion NMR spectroscopy and imaging of anisotropic skeletal muscle when off-diagonal elements of Deff are ignored, most notably the loss of information needed to determine fiber orientation. Estimation of Deff provides the theoretical basis for a new MRI modality, diffusion tensor imaging, which provides information about tissue microstructure and its physiologic state not contained in scalar quantities such as T1, T2, proton density, or the scalar apparent diffusion constant.

Finite element models of thoracic conductive anatomy: sensitivity to changes in inhomogeneity and anisotropy.

A moderately detailed 3-D finite element model of the conductive anatomy of a canine thorax was used to examine the sensitivity of the results obtained during simulated transthoracic defibrillation to variations in skeletal muscle anisotropy and differing degrees of model inhomogeneity. Our results suggest that the myocardial current density distribution is not particularly sensitive to the method used to model skeletal muscle anisotropy. However, anisotropy variations caused defibrillation parameters such as paddle to paddle impedance and threshold current to change by as much as 50%. We found a greater sensitivity in the myocardial current density and the defibrillation parameters to variations in model inhomogeneity. The changes observed in both depended substantially on paddle placement. This sensitivity to paddle placement highlights the difficulty in predicting how a reduction in anatomical detail will affect the myocardial current density distribution. In general, we found the defibrillation parameters to be more sensitive than the myocardial current density distribution to the variations in anatomical detail we examined.

The volume conductor effects of anisotropic muscle on body surface potentials using an eccentric spheres model

The purpose of this paper is to determine the volume conductor effects of muscle anisotropy on body surface potentials using an eccentric spheres model with a uniform double layer source configuration. Previous eccentric spheres work assumed that cardiac muscle anisotropy was small and that skeletal muscle effects could be accounted for by boundary extension, i.e., by scaling the conductivities and dimensions. However, in this paper, anisotropy for both the myocardium and the skeletal muscle is explicitly incorporated into the eccentric spheres volume conductor model. The anisotropy is treated as having uniform orthogonal components in the radial and tangential directions for both the skeletal muscle and myocardium. The solution for Laplace's equation is written in a series expansion of appropriate basis functions for each region. In the isotropic regions spherical harmonics with integer radial dependence and Legendre polynomial azimuthal dependence are utilized. For the anisotropic regions, Legendre polynomials are still appropriate for the azimuthal dependence, but noninteger powers of radial dependence are required. The approximate representation for anisotropy, i.e., the boundary extension method for the skeletal muscle and a scaled homogeneous conductivity without boundary extension for the myocardium are compared with explicit representations for the two regions. Two basic conclusions are drawn from the results. First, the treatment of skeletal muscle anisotropy by the boundary extension method is a valid and useful simplification which yields errors of 2% for the peak body surface potential. The second conclusion drawn from this study is that myocardial anisotropy has a significant effect on the magnitude of body surface potentials.(ABSTRACT TRUNCATED AT 250 WORDS)

An assessment of variable thickness and fiber orientation of the skeletal muscle layer on electrocardiographic calculations

This paper assesses the effectiveness of including variable thickness and fiber orientation characteristics of the skeletal muscle layer in calculations relating epicardial and torso potentials. A realistic model of a canine torso which includes extensive detail about skeletal muscle layer thickness and fiber orientation is compared with two other uniformly anisotropic models: one of constant thickness and the other of variable thickness. First, transfer coefficients are calculated from the model data. Then torso potentials for each model are calculated from the transfer coefficients and measured epicardial potentials. The comparison of calculated and observed torso potentials indicates that a simple model consisting of a uniformly anisotropic skeletal muscle layer of 1.0-1.5 cm constant thickness significantly improves the model. However, if photographic slices of the canine torso are used to introduce more detailed data about the variation in skeletal muscle thickness and fiber orientation into the model, the agreement and between calculated and measured torso potentials decreased, although a finite element mesh of over 5000 nodes was used to describe the skeletal muscle in the more detailed model. One source of error increase was considered to be due to numerical discretization and could be reduced with a much finer mesh or by utilizing higher order polynomials to represent the potential distribution within each finite element. However, the results presented in this paper show that high precision computation (64-bit word length) on the mainframe IBM 3081 with an attached FPS-164 gives a slow rate of improvement with reduced discretization intervals and that utilizing higher order polynomials within each finite element gives an even slower rate of improvement.(ABSTRACT TRUNCATED AT 250 WORDS)

The effects of thoracic inhomogeneities on the relationship between epicardial and torso potentials.

This study examines the effects of the lungs, spine, sternum, and the anisotropic skeletal muscle layer on the relationship between torso and epicardial potentials. Boundary integral equations representing potentials on the epicardial surface, the torso surface, and the internal conductivity interfaces were solved yielding a set of transfer coefficients valid for any source inside the epicardium and for any conductivity configuration outside the epicardial surface. These transfer coefficients relate potentials on the torso to potentials on the epicardial surface. Calculated torso potentials are generated via the transfer coefficients and measured epicardial potentials for comparison to measured torso potentials. This comparison indicates whether including the thoracic inhomogeneities improves attainable accuracy in calculations relating torso potentials to epicardial potentials.