Modeling plays a crucial role in pharmaceutical and medical applications by facilitating the comprehension and analysis of intricate biochemical processes and the design of optimal treatments. Particularly in pharmacokinetic and pharmacodynamic modeling, which investigates the absorption, distribution, metabolism, and effects of drugs, developing interpretable, precise, and robust models is paramount. However, modeling is a resource-intensive process that demands significant experties, time, data, and computational resources. Researchers often resort to pre-existing models with fixed coefficients that may not be tailored to their specific dataset due to its size or characteristics. This might lead to the creation of overly complex models, excessive parameterization, incorrect calibration, or even erroneous insights into underlying mechanisms. The advancement of automatic differentiation and machine learning has provided a data-driven alternatives to traditional modeling. Scientific machine learning, in particular, merges first order principles with adaptable algorithmic frameworks, offering semi-automated approaches to model discovery. In pharmacokinetic-pharmacodynamic (PKPD) systems, deep nonlinear mixed effect models enable the integration of universal approximators within fixed model architectures, allowing for the identification and extraction of previously unknown signals. This study delves into the utilization of deep nonlinear mixed effect models in conjunction with symbolic regression to explore data-driven alternatives to a conventional baseline model. Specifically, the objective is to substitute the feedback term in the classical Friberg model using a previously published dataset related to acute myeloid leukemia treatment with intermediate to high-dose cytarabine.

Over the last decade, bulk DNA-sequencing (DNA-seq) has allowed us to appreciate the sheer amount and diversity of the genomic changes associated with cancer development. More recently, advances in single-cell DNA-seq has enabled profiling of copy number aberrations (CNAs) at high resolution in thousands of cells, and has uncovered the level of intra-tumor chromosomal instability (CIN). These technologies promise quantitative measurements of tumor dynamics, and measurements of the rate of chromosomal aneuploidy, whole-genome duplications and replication errors in tumors. We have developed CINner, a state-of-the-art mathematical model and simulation algorithm for studying single-cell dynamics in a population of cells, incorporating clonal selection of somatic driver mutations and copy number aberrations (CNAs), as well as accumulation of neutral passenger mutations and CNAs. CINner follows population dynamics as input by the user, generates the clonal evolution forward in time, where clones are defined by their copy number and driver mutation profiles. The phylogeny of a sample is then computed backward in time. CINner is designed to be efficient for large cell populations while maintaining statistical accuracy in the sampled cells. The mathematical model and simulation method provide an efficient framework for modeling genomic changes during tumor growth, and are easily adaptable to accommodate newly uncovered genomic alterration mechanisms.

We present several applications of the simulator package. The first study uncovers the selection forces driving chromosomal CNAs, estimated from large bulk DNA-seq datasets. The inferred selection parameters can predict the prevalence of whole-genome duplication in each cancer type. Moreover, the selection parameters inferred from a pan-cancer dataset show a strong correlation with the chromosomal driver gene count and potency. Together, these observations prove the biological relevance of the uncovered selection parameters. The second part of this presentation delves into the development of an inference method for single-cell DNA-seq data, which holds great potentials for more accurate parameter estimation but also poses several distinct challenges over bulk data. Based on a novel implementation of random forests within the Approximate Bayesian Computation (ABC) framework, we developed an inference method to uncover both occurance rates and selection parameters driving specific CNA mechanisms in CINner. The inference recovers the parameters of interest well, even for datasets with small sample sizes. In combination, the width and depth of these studies showcase CINner’s applicability in analyzing current and upcoming DNA-seq data, toward the goal of reconstructing tumor history and predicting patient outcome.

With an overall 5-year relative survival rate of ~30\% Acute Myeloid Leukemia (AML) is a serious disease with a complex dynamic acting on the whole organism. Due to this complexity the treatment choices made by clinicians are crucial for the prospects of recovery of every single patient. Finding and researching new and promising improvements in treatment strategies for this deadly disease using clinical trials is therefore a very slow and tedious process. We aim to accelerate this process by using modelling, simulation, and optimization methods to find new treatment regimens that both improve the chance of survival and reduce the stress on the patients during these treatments.
In this talk we will discuss a pharmacokinetic and pharmacodynamic model of ordinary differential equations that allows to simulate both chemotherapy and immunostimulator intake at arbitrary points in time. Considering white blood cell measurements obtained during clinical trials we estimate sets of patient specific parameters for this model which serve us as digital twins allowing for detailed analysis of simulated drug response. With these digital twins we are able to reproduce clinically observed treatment responses strengthening the trust in our model. This validation allows us to expand the analysis upon yet unconsidered treatment combinations and gives insight into clinically hard to observe behaviours.