Cell-level Models Research Articles

Utilizing Neural Networks for Optimizing the Performance of Solid Oxide Cell Stacks

Solid oxide cells (SOCs) are one of the promising energy conversion devices due to their high efficiency and relevance to many commercial and industrial applications. Much development progress has been made in the last 10-years improving the scale-up, degradation, and commercialization outlook globally. Further commercialization of the SOCs necessitates a deeper understanding of their complex internal processes. Experimental methods, albeit valuable, are constrained by cost and time and often cannot capture intricate details like distributions of species, current density, and temperature. Therefore, numerical analyses are essential as they offer a deeper understanding of the complex phenomena within SOCs. Yet, high-fidelity modeling SOCs is computationally expensive as it includes a multitude of physical and chemical phenomena spanning various layers and length scales. Even at the single-cell and repeating unit levels, 3D simulations are computationally costly due to the intricate interplay of mass, momentum, species transport, charges, and heat. Cell-level models, while useful, cannot capture all of the thermophysical behavior of SOC stacks accurately, particularly along the height of the stack. Full-stack models, while more comprehensive, come with significant computational costs. A breakthrough in addressing this challenge comes through a multi-scale modeling approach, leveraging homogenization techniques to transform the layered complexity of SOC stacks into computationally tractable representations [1,2]. By replacing the layered domains of the stacks with equivalent mediums and calculating effective modeling variables, this approach makes the stack-scale simulations feasible on standard computational computers/workstations.Even with homogenized models, the optimization at the stack scale is not feasible due to prolonged run times and high computational demands. To address this challenge, this study employs parametric studies on stack-scale models to train a neural network. The trained neural network correlates stack outputs such as voltage, outflow temperatures, and fuel utilization with operational parameters like load current, inlet temperatures, flow rates, and inlet fuel compositions. The neural network is utilized to optimize the stack performance under various conditions while ensuring adherence to manufacturer-defined limits. For instance, the neural network can be used to optimize stack output power under fuel cell mode while avoiding overheating or exceeding maximum current densities. In essence, this work combines the detailed physics of multi-scale stack models with the efficiency of neural networks, paving the way for faster and more comprehensive optimization of SOC stacks.

Interpretation of PEMFC Impedance Response Using Continuum Modeling

The proton-exchange-membrane fuel cell (PEMFC) is an energy conversion technology developed to assist in the decarbonization of our energy infrastructure. Oxygen and hydrogen are electrochemically reacted to produce electricity, which can be used to power industrial processes like transportation and manufacturing. For hydrogen viability in heavy-duty transportation applications, PEMFC stacks are required to operate over long times scales, which prompts the development of more durable PEMFCs. Improving the durability of PEMFCs relies on understanding process variables and parameters that cause degradation and performance loss. A common diagnostic tool for electrochemical characterization is electrochemical impedance spectroscopy (EIS), where the current—potential relationship of an electrochemical cell is probed using sinusoidal perturbations, which yields the transfer function known as impedance.Due to the complex physics and chemistry occurring within a PEMFC, meaningful interpretation of impedance spectra is often challenging and relies on assumed equivalent-circuit models. The objective of this work is the development of mathematical continuum first-principle cell-level models capable of providing insight on the relationship between cell properties and measured impedance spectra. The mathematical model is based on a non-isothermal multi-scale continuum model of a PEMFC that accounts for multi-phase transport, where the impedance response is simulated about a steady-state operational mode.The mathematical model was used to simulate experimental measurements obtained from accelerated-stress tests on a commercially available PEMFC membrane-electrode assembly, as shown in Figure 1. Kinetic parameters obtained from a single EIS measurement were generalized to estimate overall cell performance, which was in good agreement with experimental polarization curves. The mathematical model represents the development of descriptive diagnostic tools capable of providing insights into the underlying governing physics and chemistry. Acknowledgements This research is supported by DOE Hydrogen and Fuel Cell Technologies Office, through the Million Mile Fuel Cell Truck (M2FCT) Consortia. Figure 1

Non-equilibrium thermal models of lithium batteries

Temperature fluctuations impact battery performance, safety, and health. Industry-standard cell-level models of these phenomena ignore thermal gradients within the electrodes’ active material, i.e., assume the latter to be in “thermal equilibrium”. We present a “non-equilibrium” thermal model that explicitly accounts for spatial variability of temperature with the active material (and the carbon-binder domain). We investigate the conditions, expressed in terms of the heat-generation rate and the thermal properties of a cell’s liquid (electrolyte) and solid (active material and CBD) phases, under which the thermal equilibrium assumption breaks down and our model should be used instead. The differences between these two thermal models are investigated further by coupling them with an industry-standard electrochemical model. The resulting thermal–electrochemical model demonstrates the importance of thermal gradients within the active material at high C-rates (discharge current densities) and for large grain sizes. Under these conditions, the equilibrium assumption underestimates internal temperature by as much as 50%. These two thermal models are then applied to a commercial NMC battery with multiple units. Our non-equilibrium model predicts the battery surface temperature that is in good agreement with measurements, while the equilibrium model underestimates the observed temperature.

Validation and Implementation in the Cloud of Cell-Level Models of a Digital Twin Simulation Platform

The monitoring and modelling of the Li-Ion Batteries behaviour is still a major technical challenge due to the non-linearities and coupled phenomena that determine their operation. These Li-Ion Batteries can consist of thousands of cells with series/parallel connections, which suffer from operating and degradation deviations. The pursuit of new, increasingly intelligent and heavier state estimation algorithms requires a significant amount of data and computational power, which can be challenging to deploy in current Battery Management System solutions. To solve this problem, this paper proposes a Digital Twin Simulation Platform that considers all the individual cells based on the Cloud to extend the computational power and data storage capacity. This work presents validated cell models, a module-level modelling approach, and an experimental validation platform is suggested. In addition, the first results obtained when implementing the Digital Twin Simulation Platform in the Cloud are presented.

Resonating with Cellular Pathways: Transcriptome Insights into Nonthermal Bioeffects of Middle Infrared Light Stimulation and Vibrational Strong Coupling on Cell Proliferation and Migration.

Middle infrared stimulation (MIRS) and vibrational strong coupling (VSC) have been separately applied to physically regulate biological systems but scarcely compared with each other, especially at identical vibrational frequencies, though they both involve resonant mechanism. Taking cell proliferation and migration as typical cell-level models, herein, we comparatively studied the nonthermal bioeffects of MIRS and VSC with selecting the identical frequency (53.5 THz) of the carbonyl vibration. We found that both MIRS and VSC can notably increase the proliferation rate and migration capacity of fibroblasts. Transcriptome sequencing results reflected the differential expression of genes related to the corresponding cellular pathways. This work not only sheds light on the synergistic nonthermal bioeffects from the molecular level to the cell level but also provides new evidence and insights for modifying bioreactions, further applying MIRS and VSC to the future medicine of frequencies.

Proposing a Caputo-Land System for active tension. Capturing variable viscoelasticity

Accurate cell-level active tension modeling for cardiomyocytes is critical to understanding cardiac functionality on a subject-specific basis. However, cell-level models in the literature fail to account for viscoelasticity and inter-subject variations in active tension, which are relevant to disease diagnostics and drug screening, e.g., for cardiotoxicity. Thus, we propose a fractional order system to model cell-level active tension by extending Land's state-of-the-art model of cardiac contraction. Our approach features the (left) Caputo derivative of six state variables that identify the mechanistic origins of viscoelasticity in a myocardial cell in terms of the thin filament, thick filament, and length-dependent interactions. This proposed CLS is the first of its kind for active tension modeling in cells and demonstrates notable subject-specificity, with smaller mean square errors than the reference model relative to cell-level experiments across subjects, promising greater clinical relevance than its counterparts in the literature by highlighting the contribution of different cellular mechanisms to apparent viscoelastic cell behavior, and how it could vary with disease.

(Invited) Challenges and Opportunities for the Computational Analysis of Electrochemical Energy Systems

Electrochemical systems are challenging to analyze and design due to their multi-dimensional, time-dependent, and multi-physics nature. For this reason, many computational electrochemical system models have been developed in the past three decades, some of which can now be found in commercial software packages, e.g., COMSOL or ANSYS Fluent. These models however: i) are based on simplifying assumptions, e.g., reduced dimensionality, infinite dilution, Tafel kinetics; ii) contain uncertain input parameters, e.g., effective transport properties and kinetic parameters; and, iii) are only validated with a limited number of experiments, e.g., polarization curves. These limitations, understandable at the time due to limited computational resources, characterization techniques, and material understanding and stability, are difficult to justify today that parallel programming and computer clusters enable scientists to perform large multi-dimensional simulations; electrochemical testing has expanded to include segmented cell testing, impedance spectroscopy, water flux estimation, and in-operando visualization; and, characterization tools and techniques have been developed to, for example, easily measure adsorption isotherms, effective proton conductivity and, within a given resolution, visualize the three-dimensional microstructure of the electrodes.Scientists working on computational analysis of electrochemical systems must acknowledge that further model development is still needed and must take advantage of new resources to improve the robustness and accuracy of cell-level models. The path is long and crooked, but it is very likely that the opportunity for a truly useful computational model, one that can be used for design, is beyond simplistic implementations and polarization curves. The effort is great, but it can be minimized by concurrent software development, as well as, by careful experimental work dedicated to parameter estimation and model validation.This presentation aims at outlining the limitations of state-of-the-art models, the challenges and opportunities of concurrent development and maintenance of a multi-scale, transient electrochemical energy system software, such as the open-source fuel cell simulation toolbox (OpenFCST) [1], and the new opportunities provided by combining advanced characterization tools with computational analysis. As an example, the development and validation of the transient, two-phase fuel cell and electrolyzer cell-level models in OpenFCST will be discussed [2]. The use of a hydrogen-pump model to study the effect of an active catalyst in CL effective proton conductivity measurements will also be discussed as an example of concurrent experimental/model design [3].

(Invited) Mixed Conduction in Ceramic Electrolytes For Intermediate-Temperature Fuel Cells and Electrolyzers

High-temperature fuel cells and electrolyzers (e.g., T > 700 ˚C) rely on oxide electrolytes such as stabilized cubic zirconia that conduct a single defect, oxygen vacancies. Intermediate-temperature electrochemical cells (e.g., T < 650 ˚C) utilize mixed conducting ceramic electrolytes, that conduct multiple defects. Operating at T < 600 ˚C facilitates lower-cost interconnect materials and balance-of-plant components, but the mixed conductor behavior can reduce fuel cell voltages and lower electrolyzer faradaic efficiencies. Predicting behavior of these mixed conductors, even at open-circuit voltage, requires modeling the coupled transport of the multiple conducting defects in the electrolyte. Detailed models of mixed conductors coupled to porous electrode models can simulate cell performance over a broad range of operating conditions. This presentation highlights models of two types of cells with mixed conducting oxide electrolytes. Firstly, gadolinium-doped ceria (GDC) primarily conducts oxygen vacancies but also some electrons via a reduced-ceria small polaron, but it performs well in intermediate temperature solid-oxide fuel cells [1]. Secondly, yttrium-doped barium zirconates (BZY) primarily conducts protons but also oxygen vacancies and small polarons, which contribute to electronic leakage. Variants of BZY electrolytes perform well in fuel cells and electrolyzers [2-4]. This paper focuses on cell-level models of these mixed-conductors and how to identify favorable regions for high performance in fuel cells and electrolyzers. Zhu, A. Ashar, R.J. Kee, R.J. Braun, G.S. Jackson, “Physics-based model to represent the membrane-electrode assemblies of solid-oxide fuel cells based on gadolinium-doped ceria,” J. Electrochem. Soc., Under revision, 2023.J. Kee, S. Ricote, H. Zhu, R.J. Braun, G. Carins, J.E. Persky, “Perspectives on technical challenges and scaling considerations for tubular protonic-ceramic electrolysis cells and stacks ,” J. Electrochem. Soc. 169:054525 (2022).Zhu, Y. Shin, S. Ricote, R.J. Kee, “Defect incorporation and transport in dense BaZr0.8Y0.2O3-d membranes and their impact on hydrogen separation and compression,” J. Electrochem. Soc., Under revision, 2023.Zhu, S. Ricote, R.J. Kee, “Thermodynamics, transport, and electrochemistry in proton-conducting ceramic electrolysis cells,” in High Temperature Electrolysis, W. Sitte and R. Merkle, Editors, IOP Publishing, 2023.

Data-driven learning how oncogenic gene expression locally alters heterocellular networks

Developing drugs increasingly relies on mechanistic modeling and simulation. Models that capture causal relations among genetic drivers of oncogenesis, functional plasticity, and host immunity complement wet experiments. Unfortunately, formulating such mechanistic cell-level models currently relies on hand curation, which can bias how data is interpreted or the priority of drug targets. In modeling molecular-level networks, rules and algorithms are employed to limit a priori biases in formulating mechanistic models. Here we combine digital cytometry with Bayesian network inference to generate causal models of cell-level networks linking an increase in gene expression associated with oncogenesis with alterations in stromal and immune cell subsets from bulk transcriptomic datasets. We predict how increased Cell Communication Network factor 4, a secreted matricellular protein, alters the tumor microenvironment using data from patients diagnosed with breast cancer and melanoma. Predictions are then tested using two immunocompetent mouse models for melanoma, which provide consistent experimental results.

Mol* Viewer: modern web app for 3D visualization and analysis of large biomolecular structures.

Large biomolecular structures are being determined experimentally on a daily basis using established techniques such as crystallography and electron microscopy. In addition, emerging integrative or hybrid methods (I/HM) are producing structural models of huge macromolecular machines and assemblies, sometimes containing 100s of millions of non-hydrogen atoms. The performance requirements for visualization and analysis tools delivering these data are increasing rapidly. Significant progress in developing online, web-native three-dimensional (3D) visualization tools was previously accomplished with the introduction of the LiteMol suite and NGL Viewers. Thereafter, Mol* development was jointly initiated by PDBe and RCSB PDB to combine and build on the strengths of LiteMol (developed by PDBe) and NGL (developed by RCSB PDB). The web-native Mol* Viewer enables 3D visualization and streaming of macromolecular coordinate and experimental data, together with capabilities for displaying structure quality, functional, or biological context annotations. High-performance graphics and data management allows users to simultaneously visualise up to hundreds of (superimposed) protein structures, stream molecular dynamics simulation trajectories, render cell-level models, or display huge I/HM structures. It is the primary 3D structure viewer used by PDBe and RCSB PDB. It can be easily integrated into third-party services. Mol* Viewer is open source and freely available at https://molstar.org/.

Combined Two-phase Co-flow and Counter-flow in a Gas Channel/Porous Transport Layer Assembly

Polymer electrolyte fuel cells and electrolyzers are low temperature devices whereby both gases and liquids intermingle within the porous transport layers and open channels. The flow of the liquid and gas is of paramount importance to the functioning of the unit. This motion is poorly understood. Cell-level models typically employ volume-averaging techniques to describe the motion of the flowing reactants and products. Until recently, detailed analysis of the two-phase liquid gas mixture, employing front-tracking methods has proved too computationally prohibitive. Previous work [1,2] has considered the motion of liquid drops in gas channels, it being assumed the drops are formed at specific nucleation sites on the sides of the channels. The present work considers a detailed numerical analysis of combined liquid-gas co-flow in a gas channel with liquid-gas counter-flow in a porous transport layer (PTL). The geometry considered is a ‘T-shape’ with the porous transport layer in the form of a thin rectangular prism of dimensions 0.5×0.5×0.1 mm3 located at the base of the ‘T’, and the gas flowing across the top channel, as shown in Fig. 1. The PTL is reproduced by digital reconstruction of nano-computer tomography images of a Freudenberg H2315 PTL as a stereolithography file*, see Figure 2(a). From this, the domain is tessellated with an unstructured castellated, or octree, type mesh, Fig. 2(b). Liquid water is introduced at an electrode at the base of the PTL and gaseous oxygen is simultaneously removed by electrochemical reduction; the resulting liquid-gas counter-flow in the porous transport layer effects liquid droplets being entrained in co-flow in the gas channel and being convected downstream, thereafter.The equations of mass and momentum are solved by means of the open source software library OpenFOAM. A volume-of-fluid approach based on the multidimensional universal limiter for explicit solution was employed. At t = 0, the channel is presumed to be filled with gas, and the PTL partially saturated with liquid water. Gas is introduced at the inlet at a given velocity. Water is added and gas removed at the electrode (counter-flow), whereas both water and gas are removed at the outlet (co-flow). At the channel walls and on the PTL fibres, the static contact angle is fixed.Some results are shown in Fig. 3(a-d). It can be seen that the location and size of the drops shed varies somewhat in space and time, i.e., there is a stochastic component to the motion of the fluid, due to the spatial distribution of the fibres in the PTL, the transient shedding process, and the merging of liquid streams flowing into the gas channel. Nonetheless a definite periodicity is observed, with drops being injected into the channel at a fairly regular rate. Some relatively minor switching with time is observed within the PTL due to the random packing of fibres, but these transients are relatively quiescent. In addition to providing important new information about flow and pressure losses in electrochemical cells as a function of current density and stoichiometry, the present model may be also used to enumerate properties such as relative permeability which can subsequently be employed in cell-scale models.* The authors wish to thank Mr. Eugen Hoppe for constructing a stereolithography file of the porous material used in this study.[1] Andersson, M., Beale, S.B., Reimer, U., Lehnert, W., Stolten, D., Int. J. Hydrog. Energy, 2018, 43(5): 2961-2976.[2] Andersson, M., Mularczyk, A., Lamibrac, A., Beale, S.B., Eller, J., Lehnert, W., Büchi, F.N., J. Power Sources, 2018. 404: 159-171. Figure 1

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function.

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

A contraction–reaction–diffusion model: Integrating biomechanics and biochemistry in cell migration

Cell migration is a fundamental biological process involved in many physiological and pathological processes. To understand how cell migration works at the whole cell level, biomechanical and biochemical models have been developed but were mainly independent of each other. In this work, we developed a mechanobiochemical model for cell migration at the whole-cell scale. In the model, mechanics of cytoskeleton contraction generates distributed forces for the cell to sense the mechanical properties of itself and its microenvironment. The mechanosensing is coupled with the signaling network of reaction–diffusion of biomolecules in the cell. The computational results show that the model can simulate cell polarization (head-to-tail formation) and shape-dependent localization of the protrusion signal. Furthermore, this dynamic model of cell migration can recapitulate durotaxis in silicon and simulate cellular morphogenesis.

On the existence–uniqueness and computation of solution of a class of cardiac electric activity models

In this study, we consider a system of coupled PDEs–ODEs which govern the electric activity in heart with a diffusion term modeling the potential in the surrounding tissue and the nonlinear ionic model proposed by the different reduced cell level models. We prove the existence and uniqueness of the bidomain model with the Morris and Lecar ionic model. The global existence of solution is established based on regularization argument using Fedo–Galerkin/compactness approach. The uniqueness of the solution is shown based on Gronwell’s lemma upon some special treatment of nonlinear terms. The computational realization of the monodomain model with different reduced ionic test models is presented. Also, the coupled parabolic PDE and ODE system modeling the cardiac electric activity in a monodomain system representation of cardiac tissue with different ionic models (at cell level), viz. FitzHugh–Nagumo model, Roger–McCulloch model (RMM), Aliev–Panfilov model and Mitchell–Schaeffer model (MSM), is numerically analyzed by Galerkin linear finite elements in space and the backward Euler method in time. Simulations are done using FreeFem++ open source, and the evolution pattern of the solution has been investigated. MSM and RMM models are unconditionally stable with respect to applied stimulus and initial state, although other models are conditionally stable.

Transitions of lithium occupation in graphite: A physically informed model in the dilute lithium occupation limit supported by electrochemical and thermodynamic measurements

Understanding the role of the phase transitions during lithiation and delithiation of graphite remains a problem of fundamental importance, but also practical relevance owing to its widespread use as the anode material in most commercial lithium-ion cells. Previously performed density functional theory (DFT) calculations show a rapid change in the lithium-carbon interaction at low occupation, due to partial charge transfer from Li to C. We integrate this effect in our previously developed two level mean field model, which describes the Stage I – Stage II transition in graphite. The modified model additionally describes the most predominant transition that occurs at low Li content in graphite, which results in a previously unexplained feature in voltage and dQ/dV profiles, and thermodynamic measurements of partial molar enthalpy. In contrast with the Stage I-Stage II transition, this extra feature is not associated with observable features in the partial molar entropy and our model demonstrates why. There is a sharp change in the open circuit voltage at very low Li occupation, followed by a transition to a voltage plateau (peak in dQ/dV). The behaviour arises due to the contrasting effects of the partial molar entropy and enthalpy terms on the partial molar Gibbs energy and hence cell voltage. Hence the voltage profile and phase transitions can be approximated for all lithium occupations, potentially allowing a predictive capability in cell level models.

The impact of cardiac tissue anisotropy on spiral wave superseding: A simulation study using ionic cell models

Several types of dangerous cardiac arrhythmias, such as paroxysmal tachycardia and fibrillation, are linked with the spiral waves of electrical excitation in the heart muscle. In many cases, these diseases must be cured immediately after their diagnosis. Low-voltage defibrillation and cardioversion are modern treatment methods. Electrotherapy is based on spiral wave superseding by a high-frequency pacing from an electrode. In the present work, we study the influence of the anisotropic myocardial structure and cell-level model on cardioversion results. We use long line and point electrodes. Intervals of effective stimulation periods are determined and compared for two ionic cell-level models. Of all the considered factors, the cell-level model appears to play the greatest role in the results.

Mechanobiological modelling of tendons: Review and future opportunities.

Tendons are adapted to carry large, repeated loads and are clinically important for the maintenance of musculoskeletal health in an increasing, actively ageing population, as well as in elite athletes. Tendons are known to adapt to mechanical loading. Also, their healing and disease processes are highly sensitive to mechanical load. Computational modelling approaches developed to capture this mechanobiological adaptation in tendons and other tissues have successfully addressed many important scientific and clinical issues. The aim of this review is to identify techniques and approaches that could be further developed to address tendon-related problems. Biomechanical models are identified that capture the multi-level aspects of tendon mechanics. Continuum whole tendon models, both phenomenological and microstructurally motivated, are important to estimate forces during locomotion activities. Fibril-level microstructural models are documented that can use these estimated forces to detail local mechanical parameters relevant to cell mechanotransduction. Cell-level models able to predict the response to such parameters are also described. A selection of updatable mechanobiological models is presented. These use mechanical signals, often continuum tissue level, along with rules for tissue change and have been applied successfully in many tissues to predict in vivo and in vitro outcomes. Signals may include scalars derived from the stress or strain tensors, or in poroelasticity also fluid velocity, while adaptation may be represented by changes to elastic modulus, permeability, fibril density or orientation. So far, only simple analytical approaches have been applied to tendon mechanobiology. With the development of sophisticated computational mechanobiological models in parallel with reporting more quantitative data from in vivo or clinical mechanobiological studies, for example, appropriate imaging, biochemical and histological data, this field offers huge potential for future development towards clinical applications.

Simulation of Overdrive Pacing in 2D Phenomenological Models of Anisotropic Myocardium

Spiral waves in the heart underlie dangerous cardiac arrhythmias such as fibrillation. Low-voltage defibrillation and cardioversion are modern methods to treat such pathologies. This type of electrotherapy is based on the phenomenon of superseding spiral waves by a high-frequency source of excitation. In this paper, we numerically simulated the superseding process in a thin layer of the cardiac muscle. We captured the case of a sole spiral wave with a stable core at the centre of a square. We used different cell-level models as well as a variety of electrode configurations and studied the induced drift of the spiral wave. Regimes of the external stimulation were classified based on whether they provide an effective and safe, that is without break-up, way to shift the spiral toward the boundary.

Altered architecture and cell populations affect bone marrow mechanobiology in the osteoporotic human femur.

Age-related increases in trabecular bone porosity, as seen in osteoporosis, not only affect the strength and stiffness, but also potentially the mechanobiological response of bone. The mechanical interaction between trabecular bone and bone marrow is one source of mechanobiological signaling, as many cell populations in marrow are mechanosensitive. However, measuring the mechanics of this interaction is difficult, due to the length scales and geometric complexity of trabecular bone. In this study, a multi-scale computational scheme incorporating high-resolution, tissue-level, fluid-structure interaction simulations with discrete cell-level models was applied to characterize the potential effects of trabecular porosity and marrow composition on marrow mechanobiology in human femoral bone. First, four tissue-level models with different volume fractions (BV/TV) were subjected to cyclic compression to determine the continuum level shear stress in the marrow. The calculated stress was applied to three detailed models incorporating individual cells and having differing adipocyte fractions. At the tissue level, compression of the bone along its principal mechanical axis induced shear stress in the marrow ranging from 2.0 to 5.6 Pa, which increased with bone volume fraction and strain rate. The shear stress was amplified at the cell level, with over 90% of non-adipocyte cells experiencing higher shear stress than the applied tissue-level stress. The maximum shear stress decreased by 20% when the adipocyte volume fraction (AVF) increased from 30%, as seen in young healthy marrow, to 45 or 60% AVF typically found in osteoporotic patients. The results suggest that increasing AVF has similar effects on the mechanobiological signaling in bone marrow as decreased volume fraction.

Elucidating Li/O2 Battery Performance By Comparing Cell-Level Models with Experiments

Elucidating Li/O2 Battery Performance by Comparing Cell-Level Models with Experiments Jing Liu, Lucas D. Griffith, and Charles W. MonroeChemical Engineering Department, University of Michigan A viable rechargeable lithium/oxygen battery would impact transportation markets dramatically, by expediting the development of highway-capable full-electric vehicles with ranges comparable to gasoline-powered automobiles. Even conservative estimates show that Li/O2 electrochemistry could support batteries with energy densities four times greater than present-day lithium-ion technology [1]. This talk will focus on theoretical and experimental research we have undertaken to elucidate design factors and reaction mechanisms that control the rate capabilities and energy capacities of Li/O2 cells. In a metal/oxygen battery cell, the positive electrode comprises a liquid-permeated, electronically conductive porous solid, which poses many of the main barriers that limit its performance. During discharge, lithium ions and dissolved O2 diffuse through the liquid phase to meet at the solid surface, where they receive an electron and precipitate the Li2O2 discharge product. We have performed systematic experiments to illustrate how Li/O2 cell capacities, voltage responses, and discharge-product morphologies vary with respect to discharge current. Some representative first-discharge voltage vs. capacity data is shown in Figure 1; scanning electron microscopy and X-ray diffraction were also performed to provide more detailed characterization. Experimental results suggest several possible mechanisms that could limit capacity and affect the rate capability of the system. For instance, discharge-product formation may shrink – or even block – liquid-filled pores, decrease the surface area available for charge transfer, or introduce interfacial resistances to charge (electronic) or material (ionic/molecular) exchange. The relative importance of hypothesized performance-limiting processes can be illustrated by multicomponent, multiphase transport modeling. We therefore developed a PDE-based cell model that accounts for the three distinct phases comprising the positive electrode, as well as the individual components that constitute each phase. Figure 1 shows that simulations can produce discharge-voltage curves that agree both qualitatively and quantitatively with experiments, displaying a ‘voltage plateau’ before ‘sudden death’ of the cell. The oxygen, porosity and reaction distributions in the positive electrode at various discharge levels reveal key characteristics of electrodes and electrolytes that could be tailored to improve the capacities and power capabilities of Li/O2 batteries. The model is used to probe three hypothetical reaction mechanisms, which involve distinct product morphologies and electron-transfer sites. To achieve consistency with experimental data, it appears that the discharge-product layer must have electronic conductivity several orders of magnitude higher than bulk lithium peroxide, supporting the notion that the discharge product does not wholly prevent electrons from reaching dissolved reactants [2]. The product also appears to allow charge transport over length scales longer than the proposed electron-tunneling mechanism [3] permits. At high rates, the ‘sudden death’ of voltage in Li/O2 cells is explained by macroscopic oxygen-diffusion limitations in the positive electrode; at low rates, sudden death occurs as a consequence of pore clogging by the discharge product. [1] J. Christensen, P. Albertus, R.S. Sanchez-Carrera, T. Lohmann, B. Kozinsky, R. Liedtke, J. Ahmed, and A. Kojic, Journal of the Electrochemical Society 159 (2011) R1-R30. [2] M.D. Radin and D.J. Siegel, Energy & Environmental Science 6 (2013), 2370-2379. [3] V. Viswanathan, K.S. Thygesen, J.S. Hummelshøj, J.K. Nørskov, G. Girishkumar, B.D. McCloskey, and A.C. Luntz, The Journal of Physical Chemistry Letters 4 (2013), 556-560. Figure 1