The Lafata Laboratory focuses on the theory, development, and application of computational oncology. The lab interrogates cancer at different length-scales of its biological organization via high-performance computing, multiscale modeling, advanced imaging technology, and the applied analysis of stochastic partial differential equations. Current research interests include tumor topology, cellular dynamics, tumor immune microenvironment, drivers of radiation resistance and immune dysregulation, molecular insight into tissue heterogeneity, and biologically-guided adaptative treatment strategies.

## Modeling high-dimensional feature spaces as dynamical systems

Figure 1. (Left) A self-consistent potential function, V(x), is constructed directly from data. When V(x) has several distinct minima, if we propagate the trajectories starting from the data points of a given data set, with a high probability, those trajectories will aggregate into several groups within a short time. Further, if the profile of the potential function intrinsically indicates the density distribution of the data, the data points that end up in the neighborhood of the same minima of V (q) after O(1) time can be considered to be in the same cluster. While the forces from the potential surface push data points towards potential minima, corresponding Brownian fluctuations allow them to jump small potential barriers and escape saddle points into locations of the potential surface otherwise forbidden. (Top Right) Numerical verification of ergodic sampling at critical temperature (dynamics on left). Data are shown to be more localized at sub-critical temperature due to non-ergodic dynamical behavior, and do not fully sample the potential landscape (dynamics on right). (Bottom Right) A 2D projection of Hilbert space demonstrating ergodic behavior at critical temperature (dynamics on left) and self-organization of data at sub-critical temperature (dynamics on right). (DETAILED PUBLICATION).

## Modeling tumor time evolution via non-equilibrium thermodynamics

Figure 2. (Top) Images before and after treatment are interpreted as no-flux boundary conditions of the Fokker-Planck equation, where the initial condition is an excited state and the final condition is an equilibrium state. To simulate the time dynamics as an estimate of disease progression, each voxel is propagated according to the Fokker-Planck equation. The time evolution of different tumors demonstrates differences in non-linear dynamics, which can capture aspects of treatment resistance. (Bottom) This transformation is driven by an underlying potential force uniquely determined by the equilibrium state, resulting in a 4th order spatial-temporal manifold.

## Image-based high-throughput tumor phenotyping

Figure 3. (Top) High-dimensional imaging signatures (i.e., radiomic expression) are linked to treatment outcome in patients with head and neck cancer. (Bottom) Disecting clustering mechanics: illustrating example comparing PET images and radiomic expression patterns of two different patients demonstrating the importance of metabolic heterogeneity to treatment resistance.

## Computational interrogation of immune microenvironments

Figure 4. Computational characterization of the lymphocytic microenvironment on digital pathology. The left column shows the H&E image provided as input to a deep learning model tasked with identifying lymphocytes. The center column shows the model prediction, where lymphocytes are detected and color-coded as blue relative to other cell types, which are color-coded as yellow. The right column shows corresponding single-cell resolution immunohistochemistry stained with antibodies against CD3/CD20, where brown indicates positive staining for lymphocytes.

## Computational radiation biology

Figure 5. Measuring immune response in genetically engineered mice. (Left) The violin plots depict the distribution of lymphocyte density measured via deep learning in mouse spleens. Rag2-/- genetic knockout mice demonstrated an average lymphocyte density of 16.2%, which was significantly smaller compared to the Rag2+/- experimental control mouse of >90% (p<0.0001, ANOVA). These experimental data suggest that deep learning can capture basic aspects of lymphocytic immune response. (Right) Example of stromal inflammation and tumor infiltrating lymphocytes in a Rag2+/- control mouse after radiation.