ECMSim: Cardiac ECM Remodeling Simulator

• ECMSim is a web-based platform that simulates cardiac extracellular matrix remodeling by integrating intracellular signaling with spatially resolved molecular diffusion.
• It leverages a high-performance C++/WebAssembly codebase to solve over 1.3 million coupled equations in real time, ensuring interactive simulation and visualization.
• The platform offers features such as brush-style cell selection and live parameter tuning, enabling precise mechanistic hypothesis testing in cardiac fibrosis research.

ECMSim refers to a high-performance, web-based computational platform specifically developed for simulating cardiac extracellular matrix (ECM) remodeling via the explicit integration of large-scale intracellular signaling dynamics with spatially resolved molecular diffusion. The platform is designed to address the mechanistic complexity of ECM regulation in cardiac fibroblasts, emphasizing the coupling of molecular-scale reactions, paracrine feedback, and tissue-level heterogeneity. ECMSim achieves highly interactive, real-time simulation and visualization of over 1.3 million coupled equations using a modern C++/WebAssembly codebase, enabling direct user manipulation and scenario testing within a standard browser environment (Hays et al., 14 Oct 2025).

1. Mathematical Framework and Underlying Model

At the algorithmic core, ECMSim models the biochemical and biophysical events of ECM remodeling with a system of ordinary differential equations (ODEs) per cell, each describing the time evolution of molecular concentrations as a function of production, degradation, activation, and inhibition:

$$\frac{dX_i}{dt} = \sum_j k_j^{\text{prod}} \prod_k X_k^{(\text{activators})} - \sum_l k_l^{\text{inhib}} X_i \prod_m X_m^{(\text{inhibitors})} - k_i^{\text{deg}} X_i$$

where $X_i$ denotes the dimensionless abundance (clamped to [0, 1]) of molecular species $i$, $k$ values represent kinetic rate constants, and the products run over designated network activators or inhibitors for each reaction.

This ODE system is tightly coupled to a reaction-diffusion module for extracellular molecules that mediate intercellular feedback. For a diffusible species $k$, concentration $C^k_{i, j}$ in cell at lattice position $(i, j)$ evolves as

$$\frac{dC^k_{i, j}}{dt} = D_k \sum_{(m,n) \in \mathcal{N}_{i,j}} \left(C^k_{m, n} - C^k_{i,j} \right) + P^k_{i,j} - \lambda_k C^k_{i,j}$$

where $D_k$ denotes the diffusion coefficient, $P^k_{i,j}$ the local production (from network output), $\lambda_k$ the degradation rate, and the sum is over all eight lattice neighbors using an eight-connected Laplacian (periodic BCs). Integration is performed using forward Euler with adaptive time stepping for stability and efficiency in high-dimensional spaces (Hays et al., 14 Oct 2025).

2. Biological and Biophysical Scope

The modeled system comprises a $100 \times 100$ square lattice, with each of the 10,000 cells carrying an identical but independent ODE network for cardiac fibroblast intracellular signaling. The molecular network per cell encompasses:

• $>$125 molecular species (nodes)
• $>$200 regulatory interactions (edges) encompassing receptor activation, second messenger cascades, MAPK pathways, transcriptional control, ECM protein synthesis, and paracrine feedback loops

By modulating ligand inputs (e.g., TGF‑β, cytokines) and matrix-related feedback, ECMSim recovers both micro-scale (single cell) dynamics and emergent macro-scale (tissue) heterogeneity, including fibrotic scar formation, propagation of pathological signals, and spatial transitions between healthy and diseased states—a fundamental challenge in post-infarction cardiac remodeling (Hays et al., 14 Oct 2025).

3. Simulation Performance and Technology Stack

Real-time integration of $>$1.3 million ODEs plus $\sim$40,000 reaction-diffusion equations is achieved by:

• Implementing the solver and data structures in C++, using cache-optimized memory layouts and aggressive compiler-level loop transformations.
• Compiling to WebAssembly (WASM) via Emscripten, resulting in $\sim$20% of native C++ performance on in-browser execution.
• Employing direct WebAssembly-to-JavaScript memory interfaces to communicate simulation state efficiently to visualization layers, with no serialization overhead.

Browser-based deployment is fully self-contained, requiring no client installation or native backend. Adaptive time-stepping ensures numeric stability and responsiveness to user-driven parameter changes (Hays et al., 14 Oct 2025).

4. User Interface and Interactive Features

ECMSim is designed around real-time human-in-the-loop hypothesis testing via several interactive mechanisms:

• Brush-style Cell Selection: Users can apply localized increases or decreases in any modeled input (e.g., ligand concentration) by painting across arbitrary grid regions to mimic focal injury, paracrine stimulation, or therapeutic intervention.
• Sliders for Parameter Adjustment: Eight primary kinetic parameters (inputs, production rates, degradation constants, diffusion coefficients, etc.) can be tuned live, updating all state variables and visual output instantaneously.
• Coupled Visualizations: Multi-scale outputs are shown as grid heatmaps (2D fields of species concentration, ECM protein abundance, or diffusible factor gradients) and as single-cell temporal traces for specified network components.

This interactive scheme allows rapid prototyping of experimental scenarios, digital “virtual experiments,” and side-by-side comparison of micro- and macro-level responses to shifts in signaling regimes or environmental stimuli (Hays et al., 14 Oct 2025).

5. Applications and Research Use Cases

ECMSim’s capabilities are tailored to a spectrum of translational and basic research applications:

• Cardiac Fibrosis Pathophysiology: Enabling simulation of scar tissue formation, spatial heterogeneity in ECM remodeling, and propagation of fibrotic signaling following infarct or chronic heart failure.
• Drug Targeting and Combinatorial Therapy: In silico testing of antagonists, agonists, or multi-target drugs, including spatially patterned application reflecting localized delivery technologies.
• Mechanistic Hypothesis Testing: Exploration of “what-if” scenarios such as targeted blockade of paracrine loops, altered mechanical signaling, or network node knockouts.
• Tissue Engineering, Cancer Microenvironment, Wound Healing: By modifying the underlying molecular interaction network, the framework can be adapted to address ECM remodeling in systems beyond the heart (this suggests extensibility to other organ systems).
• Educational Visualization: By coupling detailed network models with real-time feedback and visual outputs, ECMSim functions as an advanced teaching and demonstration tool for signaling, feedback, and tissue-level patterning in morphogenesis and pathology.

A plausible implication is that ECMSim can accelerate the translation of complex mechanistic models into accessible, interactive research and training environments (Hays et al., 14 Oct 2025).

6. Visual Output and Data Analysis

ECMSim visualizes simulation results via:

• Spatial Heatmaps: Real-time, color-mapped representations of species concentrations, ECM component levels, or signaling molecule gradients over the $100 \times 100$ tissue lattice.
• Temporal Dynamics: On-demand, single-cell time series for any molecular species to analyze transient versus steady-state behaviors, oscillations, or network bifurcations.
• Diffusion and Feedback Propagation: Visualization modules for dynamic spread of diffusible paracrine factors, clearly displaying feedback-initiated “waves” or boundaries in tissue.
• Immediate Visual Feedback on Intervention: Upon user interaction, all visualizations update synchronously with the changed simulation state, exposing system sensitivity and emergent properties.

This high level of visual coupling supports not only hypothesis generation but also rapid identification of features such as signal amplification, spatial confinement, or paradoxical responses under multi-factorial perturbations (Hays et al., 14 Oct 2025).

7. Limitations and Extensibility

All claims of simulation fidelity, scalability, and interactivity are contingent on the discrete ODE and diffusion formulations employed in the published version (Hays et al., 14 Oct 2025). The present implementation is specialized to cardiac fibrosis; adaptation to other biological contexts is plausible but would require model reparameterization and network redefinition. The system’s real-time constraint assumes browser environments with adequate computational resources and favorable WebAssembly support.

A plausible implication is that future versions could support alternative tissue dimensions, heterogeneous cell types, or user-imported signaling networks, further expanding the platform’s generality and research utility, within the constraint of web-delivered computational resources.

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In summary, ECMSim is a high-performance, massively parallel web tool for simulating ECM remodeling, integrating a detailed ODE-based cardiac fibroblast network with tissue-scale diffusion, real-time user interaction, and multi-scale visual analytic feedback. Its deployment in browser-native technologies and explicit focus on interactive mechanistic modeling render it a unique resource for cardiac fibrosis research and education, and potentially a template for similar simulation platforms in diverse biomedical domains (Hays et al., 14 Oct 2025).