@article{lagergren_flores_gilman_tsynkov_2021, title={Deep Learning Approach to the Detection of Scattering Delay in Radar Images}, volume={15}, ISSN={["1559-8616"]}, DOI={10.1007/s42519-020-00149-w}, number={1}, journal={JOURNAL OF STATISTICAL THEORY AND PRACTICE}, author={Lagergren, John and Flores, Kevin and Gilman, Mikhail and Tsynkov, Semyon}, year={2021}, month={Mar} }
 @misc{everett_flores_henscheid_lagergren_larripa_li_nardini_nguyen_pitman_rutter_2020, title={A tutorial review of mathematical techniques for quantifying tumor heterogeneity}, volume={17}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2020207}, abstractNote={Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at https://github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Everett, Rebecca and Flores, Kevin B. and Henscheid, Nick and Lagergren, John and Larripa, Kamila and Li, Ding and Nardini, John T. and Nguyen, Phuong T. T. and Pitman, E. Bruce and Rutter, Erica M.}, year={2020}, pages={3660–3709} }
 @article{lagergren_nardini_baker_simpson_flores_2020, title={Biologically-informed neural networks guide mechanistic modeling from sparse experimental data}, volume={16}, ISSN={["1553-7358"]}, DOI={10.1371/journal.pcbi.1008462}, abstractNote={Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE). By allowing the diffusion and reaction terms to be multilayer perceptrons (MLPs), the nonlinear forms of these terms can be learned while simultaneously converging to the solution of the governing PDE. Further, the trained MLPs are used to guide the selection of biologically interpretable mechanistic forms of the PDE terms which provides new insights into the biological and physical mechanisms that govern the dynamics of the observed system. The method is evaluated on sparse real-world data from wound healing assays with varying initial cell densities [2].}, number={12}, journal={PLOS COMPUTATIONAL BIOLOGY}, author={Lagergren, John H. and Nardini, John T. and Baker, Ruth E. and Simpson, Matthew J. and Flores, Kevin B.}, year={2020}, month={Dec} }
 @article{nardini_lagergren_hawkins-daarud_curtin_morris_rutter_swanson_flores_2020, title={Learning Equations from Biological Data with Limited Time Samples}, volume={82}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-020-00794-z}, abstractNote={Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets; however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data are sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions.}, number={9}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Nardini, John T. and Lagergren, John H. and Hawkins-Daarud, Andrea and Curtin, Lee and Morris, Bethan and Rutter, Erica M. and Swanson, Kristin R. and Flores, Kevin B.}, year={2020}, month={Sep} }
 @article{lagergren_nardini_michael lavigne_rutter_flores_2020, title={Learning partial differential equations for biological transport models from noisy spatio-temporal data}, volume={476}, ISSN={["1471-2946"]}, DOI={10.1098/rspa.2019.0800}, abstractNote={We investigate methods for learning partial differential equation (PDE) models from spatio-temporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select candidate terms from a denoised set of data, including approximated partial derivatives. We analyse the performance in using previous methods to denoise data for the task of discovering the governing system of PDEs. We also develop a novel methodology that uses artificial neural networks (ANNs) to denoise data and approximate partial derivatives. We test the methodology on three PDE models for biological transport, i.e. the advection–diffusion, classical Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) and nonlinear Fisher–KPP equations. We show that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.}, number={2234}, journal={PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, author={Lagergren, John H. and Nardini, John T. and Michael Lavigne, G. and Rutter, Erica M. and Flores, Kevin B.}, year={2020}, month={Feb} }
 @article{rutter_lagergren_flores_2018, title={Automated Object Tracing for Biomedical Image Segmentation Using a Deep Convolutional Neural Network}, volume={11073}, ISBN={["978-3-030-00936-6"]}, ISSN={["1611-3349"]}, DOI={10.1007/978-3-030-00937-3_78}, abstractNote={Convolutional neural networks (CNNs) have been used for fast and accurate segmentation of medical images. In this paper, we present a novel methodology that uses CNNs for segmentation by mimicking the human task of tracing object boundaries. The architecture takes as input a patch of an image with an overlay of previously traced pixels and the output predicts the coordinates of the next m pixels to be traced. We also consider a CNN architecture that leverages the output from another semantic segmentation CNN, e.g., U-net, as an auxiliary image channel. To initialize the trace path in an image, we use either locations identified as object boundaries with high confidence from a semantic segmentation CNN or a short manually traced path. By iterating the CNN output, our method continues the trace until it intersects with the beginning of the path. We show that our network is more accurate than the state-of-the-art semantic segmentation CNN on microscopy images from the ISBI cell tracking challenge. Moreover, our methodology provides a natural platform for performing human-in-the-loop segmentation that is more accurate than CNNs alone and orders of magnitude faster than manual segmentation.}, journal={MEDICAL IMAGE COMPUTING AND COMPUTER ASSISTED INTERVENTION - MICCAI 2018, PT IV}, author={Rutter, Erica M. and Lagergren, John H. and Flores, Kevin B.}, year={2018}, pages={686–694} }
 @article{lagergren_reeder_hamilton_smith_flores_2018, title={Forecasting and Uncertainty Quantification Using a Hybrid of Mechanistic and Non-mechanistic Models for an Age-Structured Population Model}, volume={80}, ISSN={0092-8240 1522-9602}, url={http://dx.doi.org/10.1007/s11538-018-0421-7}, DOI={10.1007/s11538-018-0421-7}, abstractNote={In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set. The data come from cannibalistic flour beetles, in which it is observed that the adults preying on the eggs and pupae result in non-equilibrium population dynamics. Uncertainty quantification methods for the hybrid models are outlined and illustrated for these data. We perform an analysis of the results from Bayesian inference for the mechanistic model and hybrid models to suggest reasons why hybrid modeling methodology may enable more accurate forecasts of multivariate systems than traditional approaches.}, number={6}, journal={Bulletin of Mathematical Biology}, publisher={Springer Nature}, author={Lagergren, John and Reeder, Amanda and Hamilton, Franz and Smith, Ralph C. and Flores, Kevin B.}, year={2018}, month={Apr}, pages={1578–1595} }