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Tumors exhibit high molecular, phenotypic, and physiological heterogeneity. In this effort, we employ quantitative magnetic resonance imaging (MRI) data to capture this heterogeneity through imaging-based subregions or “habitats” in a murine model of glioma. We then demonstrate the ability to model and predict the growth of the habitats using coupled ordinary differential equations (ODEs) in the presence and absence of radiotherapy. Female Wistar rats (N = 21) were inoculated intracranially with 10⁶C6 glioma cells, a subset of which received 20 Gy (N = 5) or 40 Gy (N = 8) of radiation. All rats underwent diffusion-weighted and dynamic contrast-enhanced MRI at up to seven time points. All MRI data at each visit were subsequently clustered usingk-means to identify physiological tumor habitats. A family of four models consisting of three coupled ODEs were developed and calibrated to the habitat time series of control and treated rats and evaluated for predictive capability. The Akaike Information Criterion was used for model selection, and the normalized sum-of-square-error (SSE) was used to evaluate goodness-of-fit in model calibration and prediction. Three tumor habitats with significantly different imaging data characteristics (p < 0.05) were identified: high-vascularity high-cellularity, low-vascularity high-cellularity, and low-vascularity low-cellularity. Model selection resulted in a five-parameter model whose predictions of habitat dynamics yielded SSEs that were similar to the SSEs from the calibrated model. It is thus feasible to mathematically describe habitat dynamics in a preclinical model of glioma using biology-based ODEs, showing promise for forecasting heterogeneous tumor behavior.

 

In additive manufacturing (AM), the surface roughness of the deposited parts remains significantly higher than the admissible range for most applications. Additionally, the surface topography of AM parts exhibits waviness profiles between tracks and layers. Therefore, post-processing is indispensable to improve surface quality. Laser-aided machining and polishing can be effective surface improvement processes that can be used due to their availability as the primary energy sources in many metal AM processes. While the initial roughness and waviness of the surface of most AM parts are very high, to achieve dimensional accuracy and minimize roughness, a high input energy density is required during machining and polishing processes although such high energy density may induce process defects and escalate the phenomenon of wavelength asperities. In this paper, we propose a systematic approach to eliminate waviness and reduce surface roughness with the combination of laser-aided machining, macro-polishing, and micro-polishing processes. While machining reduces the initial waviness, low energy density during polishing can minimize this further. The average roughness (Ra=1.11μm) achieved in this study with optimized process parameters for both machining and polishing demonstrates a greater than 97% reduction in roughness when compared to the as-built part.