A Predictive Toxicokinetic Model for Nickel Leaching from Vascular Stents

In vitro testing methods offer valuable insights into the corrosion vulnerability of metal implants and enable prompt comparison between devices. However, they fall short in predicting the extent of leaching and the biodistribution of implant byproducts under in vivo conditions. Physiologically based toxicokinetic (PBTK) models are capable of quantitatively establishing such correlations and therefore provide a powerful tool in advancing nonclinical methods to test medical implants and assess patient exposure to implant debris. In this study, we present a multicompartment PBTK model and a simulation engine for toxicological risk assessment of vascular stents. The mathematical model consists of a detailed set of constitutive equations that describe the transfer of nickel ions from the device to peri-implant tissue and circulation and the nickel mass exchange between blood and the various tissues/organs and excreta. Model parameterization was performed using (1) in-house-produced data from immersion testing to compute the device-specific diffusion parameters and (2) full-scale animal in situ implantation studies to extract the mammalian-specific biokinetic functions that characterize the time-dependent biodistribution of the released ions. The PBTK model was put to the test using a simulation engine to estimate the concentration-time profiles, along with confidence intervals through probabilistic Monte Carlo, of nickel ions leaching from the implanted devices and determine if permissible exposure limits are exceeded. The model-derived output demonstrated prognostic conformity with reported experimental data, indicating that it may provide the basis for the broader use of modeling and simulation tools to guide the optimal design of implantable devices in compliance with exposure limits and other regulatory requirements.

On the development of physiologically based toxicokinetic (PBTK) models for cardiovascular implants

Local and systemic contamination caused by metal ions leaching from medical device materials is a significant and continuing health problem. The increasing need for verification and validation, and the imposition of stringent government regulations to ensure that the products comply with the quality, safety, and performance standards, have led regulatory bodies worldwide to strongly recommend the use of modeling and simulation tools to support medical device submissions. A previously published physiologically based toxicokinetic (PBTK) model, is here expanded and enriched by an additional separate tissue compartment to better resemble normal physiology and by the introduction of time-dependent functions to describe all biokinetic parameters. The new model is exercised in conjunction with state-of-the-art probabilistic, Monte Carlo methodology to calculate the predictions' confidence intervals and incorporate variability associated with toxicological biodistribution studies. The quantitative consistency of the model-derived predictions is validated against reported data following the implantation of nickel-containing cardiovascular devices in humans and minipigs. Finally, a new methodology for compartmental toxicological risk assessment is presented that can be used for forward or reverse dosimetry. Our work is aimed at providing a computational tool to optimize the device design characteristics and safeguard that the substances released do not exceed permissible exposure limits.

Predicting High-Density Polyethylene Melt Rheology Using a Multimode Tube Model Derived Using Non-Equilibrium Thermodynamics

Based on the Generalized bracket, or Beris-Edwards, formalism of non-equilibrium thermodynamics, we recently proposed a new differential constitutive model for the rheological study of entangled polymer melts and solutions. It amended the shortcomings of a previous model that was too strict regarding the values of the convective constraint release parameter for the model not to violate the second law of thermodynamics, and it has been shown capable of predicting a transient stress undershoot (following the overshoot) at high shear rates. In this study, we wish to further examine this model's capability to predict the rheological response of industrial polymer systems by extending it to its multiple-mode version. The comparison with industrial rheological data (High-Density Polyethylene resins), which was based on comparison with experimental data available in (a) Small Amplitude Oscillatory shear, (b) start-up shear, and (c) start-up uniaxial elongation, was noted to be good.

Correction: A constitutive hemorheological model addressing the deformability of red blood cells in Ringer solutions

Correction for 'A constitutive hemorheological model addressing the deformability of red blood cells in Ringer solutions' by Pavlos S. Stephanou et al., Soft Matter, 2020, 16, 7585-7597, https://doi.org/10.1039/D0SM00974A.

Elucidating the rheological implications of adding particles in blood

In the past few decades, nanotechnology has been employed to provide breakthroughs in the diagnosis and treatment of several diseases using drug-carrying particles (DCPs). In such an endeavor, the optimal design of DCPs is paramount, which necessitates the use of an accurate and trustworthy constitutive model in computational fluid dynamics (CFD) simulators. We herein introduce a continuum model for elaborating on the rheological implications of adding particles in blood. The model is developed using non-equilibrium thermodynamics to guarantee thermodynamic admissibility. Red blood cells are modeled as deformed droplets with a constant volume that are able to aggregate, whereas particles are considered rigid spheroids. The model predictions are compared favorably against rheological data for both spherical and non-spherical particles immersed in non-aggregating blood. It is expected that the use of this model will allow for the testing of DCPs in virtual patients and for their tailor-design in treating various diseases.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00397-021-01289-x.

A constitutive hemorheological model addressing the deformability of red blood cells in Ringer solutions

Red blood cells (RBCs) can deform substantially, a feature that allows them to pass through capillaries that are narrower than the largest dimension of an undeformed RBC. Clearly, to understand how they transport through our microcirculation, we need a constitutive model able of accurately predicting the deformability of RBCs, which seems currently unavailable. To address this void, we herein propose a new model that accounts for the deformability of RBCs by modeling them as deformed droplets with a constant volume. To make sure the model is by construction thermodynamically admissible we employ non-equilibrium thermodynamics as our tool. Since RBCs are merely droplets with the inner fluid exhibiting a higher viscosity than that of the outer one, RBCs are described by a conformation tensor constrained to have a constant determinant (volume). The model predicts the second normal stress coefficient in steady-state simple shear flow to first shear thicken and then shear thin, which is an unexpected behavior; however, we cannot judge whether such a prediction is aphysical or not due to unavailable experimental rheological data in the literature. We show that the new model is capable of addressing the deformability of isolated (very low hematocrit) RBCs in simple shear and the shear viscosity of non-aggregating blood. As derived the model addresses only non-aggregating blood, but can very easily be generalized to account for aggregating blood.

Assessment of the Tumbling-Snake Model against Linear and Nonlinear Rheological Data of Bidisperse Polymer Blends

We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the academic case of a monodisperse sample. Here, we extend these studies and provide the stationary solutions of the tumbling-snake model both analytically, for small shear rates, and via Brownian dynamics simulations, for a bidisperse sample over a wide range of shear rates and model parameters. We further show that the tumbling-snake model bears the necessary capacity to compare well with available linear and non-linear rheological data for bidisperse systems. This capacity is added to the already documented ability of the model to accurately predict the shear rheology of monodisperse systems.

A nonequilibrium thermodynamics perspective of thixotropy

We propose a new description of elasto-viscoplastic fluids by relating the notion of thixotropy directly to internal viscoelasticity and network structures through a general, thermodynamically consistent approach. By means of non-equilibrium thermodynamics, a thermodynamically admissible elasto-viscoplastic model is derived which introduces self-consistently and effortlessly thixotropic effects and reproduces at both low and high shear rates experimental data usually fitted with empirical constitutive equations, such as the Bingham and Herschel-Bulkley models. The predictions of the new model are in very good agreement with available steady-state shear rheological data for soft colloidal pastes and blood, i.e., systems exhibiting a yield stress, and with time-dependent rheological data for blood, i.e., during a triangular time-dependent change in the shear rate, exhibiting a hysteresis. The proposed approach is expected to provide the means to improve our understanding of thixotropic fluids.

From intermediate anisotropic to isotropic friction at large strain rates to account for viscosity thickening in polymer solutions

The steady-state extensional viscosity of dense polymeric liquids in elongational flows is known to be peculiar in the sense that for entangled polymer melts it monotonically decreases-whereas for concentrated polymer solutions it increases-with increasing strain rate beyond the inverse Rouse time. To shed light on this issue, we solve the kinetic theory model for concentrated polymer solutions and entangled melts proposed by Curtiss and Bird, also known as the tumbling-snake model, supplemented by a variable link tension coefficient that we relate to the uniaxial nematic order parameter of the polymer. As a result, the friction tensor is increasingly becoming isotropic at large strain rates as the polymer concentration decreases, and the model is seen to capture the experimentally observed behavior. Additional refinements may supplement the present model to capture very strong flows. We furthermore derive analytic expressions for small rates and the linear viscoelastic behavior. This work builds upon our earlier work on the use of the tumbling-snake model under shear and demonstrates its capacity to improve our microscopic understanding of the rheology of entangled polymer melts and concentrated polymer solutions.

Tumbling-Snake Model for Polymeric Liquids Subjected to Biaxial Elongational Flows with a Focus on Planar Elongation

We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.

How the flow affects the phase behaviour and microstructure of polymer nanocomposites

We address the issue of flow effects on the phase behaviour of polymer nanocomposite melts by making use of a recently reported Hamiltonian set of evolution equations developed on principles of non-equilibrium thermodynamics. To this end, we calculate the spinodal curve, by computing values for the nanoparticle radius as a function of the polymer radius-of-gyration for which the second derivative of the generalized free energy of the system becomes zero. Under equilibrium conditions, we recover the phase diagram predicted by Mackay et al. [Science 311, 1740 (2006)]. Under non-equilibrium conditions, we account for the extra terms in the free energy due to changes in the conformations of polymer chains by the shear flow. Overall, our model predicts that flow enhances miscibility, since the corresponding miscibility window opens up for non-zero shear rate values.