Trajectory Landscapes for Therapeutic Strategy Design in Agent-Based Tumor Microenvironment Models

Abstract

Multiplex tissue imaging (MTI) enables high- dimensional, spatially resolved measurements of the tumor microenvironment (TME), but most clinical datasets are tempo- rally undersampled and longitudinally limited, restricting direct inference of underlying spatiotemporal dynamics and effective intervention timing. Agent-based models (ABMs) provide mech- anistic, stochastic simulators of TME evolution; yet their high- dimensional state space and uncertain parameterization make direct control design challenging. This work presents a reduced- order, simulation-driven framework for therapeutic strategy design using ABM-derived trajectory ensembles. Starting from a nominal ABM, we systematically perturb biologically plausible parameters to generate a set of simulated trajectories and construct a low-dimensional trajectory landscape describing TME evolution. From time series of spatial summary statistics extracted from the simulations, we learn a probabilistic Markov State Model (MSM) that captures metastable states and the transitions between them. To connect simulation dynamics with clinical observations, we map patient MTI snapshots onto the landscape and assess concordance with observed spatial phenotypes and clinical outcomes. We further show that conditioning the MSM on dominant governing parameters yields group-specific transition models to formulate a finite-horizon Markov Decision Process (MDP) for treatment scheduling. The resulting framework enables simulation-grounded therapeutic policy design for partially observed biological systems without requiring longitudinal patient measurements.

Figures (7)

• Figure 1: Agent-based TME signaling architecture. The model encodes seven cell types and the signaling interactions governing their transitions; the T-cell exhaustion rate $r_{\mathrm{exh}}$ is the primary control-relevant parameter. T-cell exhaustion ($r_{\mathrm{exh}}$) is a state transition rate governing the progressive loss of effector function in tumor-infiltrating T cells; immunotherapeutic interventions such as checkpoint blockade act in part by reducing this rate.
• Figure 2: Simulation-to-embedding pipeline. (1) Latin hypercube sampling of the parameter space yields $N$ parameter vectors $\mathbf{p}^i$. (2) Each vector seeds a PhysiCell simulation producing a cell-configuration trajectory. (3) Spatial statistics $u_k^i \in \mathbb{R}^M$ are extracted at each step $k = 1,\ldots,K$. (4) Delay-coordinate embedding stacks a window of $w$ consecutive observations, reconstructing latent dynamical structure from the scalar spatial-statistic time series.
• Figure 3: ABM Simulation Trajectory Landscape. The vector field indicates the mean intra-window displacement in UMAP space. Contours show the density of each metastable TME state ($S_1$--$S_6$). Trajectories diverge from a shared early origin toward terminal attractors.
• Figure 4: UMAP landscape colored by relative cell-type population levels: (A) $c_{\mathrm{tum}}$, (B) $c_{\mathrm{T_{eff}}}$, (C) $c_{\mathrm{T_{exh}}}$. Each point is a delay-embedded simulation window. $c_{\mathrm{tum}}$ is elevated in the immune-escape region, $c_{\mathrm{T_{eff}}}$ concentrates near $S_1$, and $c_{\mathrm{T_{exh}}}$ accumulates toward $S_4$ and $S_6$.
• Figure 5: Clinical validation in the MIBI cohort (Keren et al., 2018; $n=38$ patients, 360 ROIs). (A) Distribution of MIBI ROIs across TME states $S_1$--$S_6$; $S_4$ receives zero clinical ROIs. (B) Kaplan-Meier survival curves stratified by log-rank-optimized $S_1$ and $S_6$ proportion cutoffs.