SUMMARYThis work deals with the computational modeling of passive myocardial tissue within the framework of mixed, non-linear finite element methods. We consider a recently proposed, convex, anisotropic hyperelastic model that accounts for the locally orthotropic micro-structure of cardiac muscle. A coordinate-free representation of anisotropy is incorporated through physically relevant invariants of the Cauchy-Green deformation tensors and structural tensors of the corresponding material symmetry group. This model, which has originally been designed for exactly incompressible deformations, is extended towards entirely three-dimensional inhomogeneous deformations by additively decoupling the strain energy function into volumetric and isochoric parts along with the multiplicative split of the deformation gradient. This decoupled constitutive structure is then embedded in a mixed finite element formulation through a threefield Hu-Washizu functional whose simultaneous variation with respect to the independent pressure, dilatation, and placement fields results in the associated Euler-Lagrange equations, thereby minimizing the potential energy. This weak form is then consistently linearized for uniform-pressure elements within the framework of an implicit finite element method. To demonstrate the performance of the proposed approach, we present a three-dimensional finite element analysis of a generic biventricular heart model, subjected to physiological ventricular pressure. The parameters employed in the numerical analysis are identified by solving an optimization problem based on six simple shear experiments on explanted cardiac tissue.

The goal of this manuscript is to establish a novel computational model for stretch-induced skin growth during tissue expansion. Tissue expansion is a common surgical procedure to grow extra skin for reconstructing birth defects, burn injuries, or cancerous breasts. To model skin growth within the framework of nonlinear continuum mechanics, we adopt the multiplicative decomposition of the deformation gradient into an elastic and a growth part. Within this concept, we characterize growth as an irreversible, stretch-driven, transversely isotropic process parameterized in terms of a single scalar-valued growth multiplier, the in-plane area growth. To discretize its evolution in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To demonstrate the characteristic features of skin growth, we simulate the process of gradual tissue expander inflation. To visualize growth-induced residual stresses, we simulate a subsequent tissue expander deflation. In particular, we compare the spatio-temporal evolution of area growth, elastic strains, and residual stresses for four commonly available tissue expander geometries. We believe that predictive computational modeling can open new avenues in reconstructive surgery to rationalize and standardize clinical process parameters such as expander geometry, expander size, expander placement, and inflation timing.

The ability to stimulate mammalian cells with light has significantly changed our understanding of electrically excitable tissues in health and disease, paving the way toward various novel therapeutic applications. Here, we demonstrate the potential of optogenetic control in cardiac cells using a hybrid experimental/computational technique. Experimentally, we introduced channelrhodopsin-2 into undifferentiated human embryonic stem cells via a lentiviral vector, and sorted and expanded the genetically engineered cells. Via directed differentiation, we created channelrhodopsin-expressing cardiomyocytes, which we subjected to optical stimulation. To quantify the impact of photostimulation, we assessed electrical, biochemical, and mechanical signals using patch-clamping, multielectrode array recordings, and video microscopy. Computationally, we introduced channelrhodopsin-2 into a classic autorhythmic cardiac cell model via an additional photocurrent governed by a light-sensitive gating variable. Upon optical stimulation, the channel opens and allows sodium ions to enter the cell, inducing a fast upstroke of the transmembrane potential. We calibrated the channelrhodopsin-expressing cell model using single action potential readings for different photostimulation amplitudes, pulse widths, and frequencies. To illustrate the potential of the proposed approach, we virtually injected channelrhodopsin-expressing cells into different locations of a human heart, and explored its activation sequences upon optical stimulation. Our experimentally calibrated computational toolbox allows us to virtually probe landscapes of process parameters, and identify optimal photostimulation sequences toward pacing hearts with light.

Smoothly varying muscle fiber orientations in the heart are critical to its electrical and mechanical function. From detailed histological studies and diffusion tensor imaging, we now know that fiber orientations in humans vary gradually from approximately −70° in the outer wall to +80° in the inner wall. However, the creation of fiber orientation maps for computational analyses remains one of the most challenging problems in cardiac electrophysiology and cardiac mechanics. Here we show that Poisson interpolation generates smoothly varying vector fields that satisfy a set of user-defined constraints in arbitrary domains. Specifically, we enforce the Poisson interpolation in the weak sense using a standard linear finite element algorithm for scalar-valued second-order boundary value problems and introduce the feature to be interpolated as a global unknown. User-defined constraints are then simply enforced in the strong sense as Dirichlet boundary conditions. We demonstrate that the proposed concept is capable of generating smoothly varying fiber orientations, quickly, efficiently, and robustly, both in a generic bi-ventricular model and in a patient-specific human heart. Sensitivity analyses demonstrate that the underlying algorithm is conceptually able to handle both arbitrarily and uniformly distributed user-defined constraints; however the quality of the interpolation is best for uniformly distributed constraints. We anticipate our algorithm to be immediately transformative to experimental and clinical settings, where it will allow us to quickly and reliably create smooth interpolations of arbitrary fields from data sets, which are sparse but uniformly distributed.

The dynamic properties of suspensions of rodlike cellulose microcrystallites (whiskers) are investigated using polarized and depolarized dynamic light scattering (DLS, DDLS) and transient electric birefringence (TEB). The whiskers were prepared by controlled sulfuric acid hydrolysis from cotton and tunicate cellulose fibers. Translational (D) and rotational (Θ) diffusion coefficients in dilute suspensions were measured. For the cotton system, D ) 5.5 × 10 -8 cm 2 /s, ΘDDLS ) 552 s -1 , and ΘTEB ) 536 s -1 . With the use of Broersma's relations, the rotational and translational diffusion coefficients lead to values of the length L ) 255 nm and the cross-section diameter d ) 15 nm. For the tunicate-derived whiskers, D ) 1.5 × 10 -8 cm 2 /s, ΘDDLS ) 11 s -1 , and ΘTEB ) 14 s -1 . These values and Broersma's relations give L ) 1160 nm and d ) 16 nm. The DDLS and TEB techniques are in good agreement for the rotational diffusion coefficients, especially for the cotton whiskers. These results provide validation for using DDLS to study the dynamics of cellulose whisker systems in both simple suspensions and complex environments. Cellulose whiskers may thus be used as model rigid rods dispersible in aqueous suspensions the structure and dynamics of which may be readily studied by widely available techniques.

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BackgroundGlypican-3 (GPC-3) is an oncofetal protein that is highly expressed in various solid tumors, but rarely expressed in healthy adult tissues and represents a rational target of particular relevance in hepatocellular carcinoma (HCC). Autologous chimeric antigen receptor (CAR) αβ T cell therapies have established significant clinical benefit in hematologic malignancies, although efficacy in solid tumors has been limited due to several challenges including T cell homing, target antigen heterogeneity, and immunosuppressive tumor microenvironments. Gamma delta (γδ) T cells are highly cytolytic effectors that can recognize and kill tumor cells through major histocompatibility complex (MHC)-independent antigens upregulated under stress. The Vδ1 subset is preferentially localized in peripheral tissue and engineering with CARs to further enhance intrinsic antitumor activity represents an attractive approach to overcome challenges for conventional T cell therapies in solid tumors. Allogeneic Vδ1 CAR T cell therapy may also overcome other hurdles faced by allogeneic αβ T cell therapy, including graft-versus-host disease (GvHD).MethodsWe developed the first example of allogeneic CAR Vδ1 T cells that have been expanded from peripheral blood mononuclear cells (PBMCs) and genetically modified to express a 4-1BB/CD3z CAR against GPC-3. The CAR construct (GPC-3.CAR/secreted interleukin-15 (sIL)-15) additionally encodes a constitutively-secreted form of IL-15, which we hypothesized could sustain proliferation and antitumor activity of intratumoral Vδ1 T cells expressing GPC-3.CAR.ResultsGPC-3.CAR/sIL-15 Vδ1 T cells expanded from PBMCs on average 20,000-fold and routinely reached >80% purity. Expanded Vδ1 T cells showed a primarily naïve-like memory phenotype with limited exhaustion marker expression and displayed robust in vitro proliferation, cytokine production, and cytotoxic activity against HCC cell lines expressing low (PLC/PRF/5) and high (HepG2) GPC-3 levels. In a subcutaneous HepG2 mouse model in immunodeficient NSG mice, GPC-3.CAR/sIL-15 Vδ1 T cells primarily accumulated and proliferated in the tumor, and a single dose efficiently controlled tumor growth without evidence of xenogeneic GvHD. Importantly, compared with GPC-3.CAR Vδ1 T cells lacking sIL-15, GPC-3.CAR/sIL-15 Vδ1 T cells displayed greater proliferation and resulted in enhanced therapeutic activity.ConclusionsExpanded Vδ1 T cells engineered with a GPC-3 CAR and sIL-15 represent a promising platform warranting further clinical evaluation as an off-the-shelf treatment of HCC and potentially other GPC-3-expressing solid tumors.

This manuscript proposes a novel, efficient finite element solution technique for the computational simulation of cardiac electrophysiology. We apply a two-parameter model that is characterized through a fast action potential and a slow recovery variable. The former is introduced globally as a nodal degree of freedom, whereas the latter is treated locally as internal variable on the integration point level. This particular discretization is extremely efficient and highly modular since different cardiac cell models can be incorporated straightforwardly through only minor local modifications on the integration point level. In this manuscript, we illustrate the algorithm in terms of the Aliev-Panfilov model for cardiomyocytes. To ensure unconditional stability, a backward Euler scheme is applied to discretize the evolution equation for both the action potential and the recovery variable in time. To increase robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme and illustrate the consistent linearization of the weak form of the excitation problem. The proposed algorithm is illustrated by means of two-and three-dimensional examples of re-entrant spiral and scroll waves characteristic of cardiac arrhythmias in atrial and ventricular fibrillation.