Navigating Between Right, Wrong, and Relevant: The Use of Mathematical Modeling in Preclinical Decision Making

The goal of this mini-review is to summarize the collective experience of the authors for how modeling and simulation approaches have been used to inform various decision points from discovery to First-In-Human clinical trials. The article is divided into a high-level overview of the types of problems that are being aided by modeling and simulation approaches, followed by detailed case studies around drug design (Nektar Therapeutics, Genentech), feasibility analysis (Novartis Pharmaceuticals), improvement of preclinical drug design (Pfizer), and preclinical to clinical extrapolation (Merck, Takeda, and Amgen).

Predicting left ventricular contractile function via Gaussian process emulation in aortic-banded rats

Cardiac contraction is the result of integrated cellular, tissue and organ function. Biophysical in silico cardiac models offer a systematic approach for studying these multi-scale interactions. The computational cost of such models is high, due to their multi-parametric and nonlinear nature. This has so far made it difficult to perform model fitting and prevented global sensitivity analysis (GSA) studies. We propose a machine learning approach based on Gaussian process emulation of model simulations using probabilistic surrogate models, which enables model parameter inference via a Bayesian history matching (HM) technique and GSA on whole-organ mechanics. This framework is applied to model healthy and aortic-banded hypertensive rats, a commonly used animal model of heart failure disease. The obtained probabilistic surrogate models accurately predicted the left ventricular pump function (R² = 0.92 for ejection fraction). The HM technique allowed us to fit both the control and diseased virtual bi-ventricular rat heart models to magnetic resonance imaging and literature data, with model outputs from the constrained parameter space falling within 2 SD of the respective experimental values. The GSA identified Troponin C and cross-bridge kinetics as key parameters in determining both systolic and diastolic ventricular function. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Quantitative Systems Pharmacology: A Case for Disease Models

Quantitative systems pharmacology (QSP) has emerged as an innovative approach in model‐informed drug discovery and development, supporting program decisions from exploratory research through late‐stage clinical trials. In this commentary, we discuss the unique value of disease‐scale “platform” QSP models that are amenable to reuse and repurposing to support diverse clinical decisions in ways distinct from other pharmacometrics strategies.

GPS for QSP: A Summary of the ACoP6 Symposium on Quantitative Systems Pharmacology and a Stage for Near-Term Efforts in the Field

Quantitative Systems Pharmacology (QSP) is experiencing increased application in the drug discovery and development process. Like its older sibling, systems biology, the QSP field is comprised of a mix of established disciplines and methods, from molecular biology to engineering to pharmacometrics. As a result, there exist critical segments of the discipline that differ dramatically in approach and a need to bring these groups together toward a common goal.

Efficient Generation and Selection of Virtual Populations in Quantitative Systems Pharmacology Models

Quantitative systems pharmacology models mechanistically describe a biological system and the effect of drug treatment on system behavior. Because these models rarely are identifiable from the available data, the uncertainty in physiological parameters may be sampled to create alternative parameterizations of the model, sometimes termed "virtual patients." In order to reproduce the statistics of a clinical population, virtual patients are often weighted to form a virtual population that reflects the baseline characteristics of the clinical cohort. Here we introduce a novel technique to efficiently generate virtual patients and, from this ensemble, demonstrate how to select a virtual population that matches the observed data without the need for weighting. This approach improves confidence in model predictions by mitigating the risk that spurious virtual patients become overrepresented in virtual populations.

Fine particle deposition within human nasal airways

An original mathematical model describing particle diffusion in human nasal passages is presented. A unique feature of the model is that it combines effects of both turbulent and laminar flows. To account for turbulence, concentration equations written in cylindrical coordinates are first simplified by a scaling technique and then solved analytically based on momentum/mass transfer analogy. To describe laminar motion, the work of Martonen et al. (1995a) is modified for application to nasal passages. The predictions of the new model agree well with particle deposition data from experiments using human replica nasal casts over a wide range of flow rates (4-30 L/min) and particle sizes (0.001-0.1 micro m). The results of our study suggest that a complex fluid dynamics situation involving a natural transition from laminar to turbulent motion may exist within human nasal passages during inspiration. The model may be used to predict deposition efficiencies of inhaled particles for inhalation toxicology (e.g., the risk assessment of air pollutants) and aerosol therapy (e.g., the treatment of lung diseases) applications.

Flow simulation in the human upper respiratory tract

Computer simulations of airflow patterns within the human upper respiratory tract (URT) are presented. The URT model includes airways of the head (nasal and oral), throat (pharyngeal and laryngeal), and lungs (trachea and main bronchi). The head and throat morphology was based on a cast of a medical school teaching model; tracheobronchial airways were defined mathematically. A body-fitted three-dimensional curvilinear grid system and a multiblock method were employed to graphically represent the surface geometries of the respective airways and to generate the corresponding mesh for computational fluid dynamics simulations. Our results suggest that for a prescribed phase of breath (i.e., inspiration or expiration), convective respiratory airflow patterns are highly dependent on flow rate values. Moreover, velocity profiles were quite different during inhalation and exhalation, both in terms of the sizes, strengths, and locations of localized features such as recirculation zones and air jets. Pressure losses during inhalation were 30-35% higher than for exhalation and were proportional to the square of the flow rate. Because particles are entrained and transported within airstreams, these results may have important applications to the targeted delivery of inhaled drugs.

Small- and large-scale biosimulation applied to drug discovery and development

Biosimulation uses mathematics to quantitatively represent the dynamics of biological systems and thereby analyze and predict system behavior. Biosimulations can be classified into two general categories: small-scale models designed to address a specific problem, and large-scale models of detailed regulatory mechanisms used to address a broad scope of questions. Both classes of biosimulations have been applied to problems important for drug discovery and development. Small-scale biosimulations have been particularly useful for interpreting clinical data and developing novel biomarkers. Large-scale biosimulations typically integrate a wide variety of data and can provide insights into how complex biological systems are regulated in both health and disease. Because large-scale biosimulations represent detailed regulatory mechanisms and their interactions, they can predict the overall clinical effect of modulating individual pathways or targets. In this mini-review, we describe several examples of how small- and large-scale biosimulations have been applied to problems important for drug development in diabetes, HIV, heart disease and asthma.

Three-dimensional computer modeling of the human upper respiratory tract

Computer simulations of airflow and particle-transport phenomena within the human respiratory system have important applications to aerosol therapy (e.g., the targeted delivery of inhaled drugs) and inhalation toxicology (e.g., the risk assessment of air pollutants). A detailed description of airway morphology is necessary for these simulations to accurately reflect conditions in vivo. Therefore, a three-dimensional (3D) physiologically realistic computer model of the human upper-respiratory tract (URT) has been developed. The URT morphological model consists of the extrathoracic (ET) region (nasal, oral, pharyngeal, and laryngeal passages) and upper airways (trachea and main bronchi) of the lung. The computer representation evolved from a silicone rubber impression of a medical school teaching model of the human head and throat. A mold of this ET system was sliced into 2-mm serial sections, scanned, and digitized. Numerical grids, for use in future computational fluid dynamics (CFD) simulations, were generated for each slice using commercially available software (CFX-F3D), AEA Technology, Harwell, UK. The meshed sections were subsequently aligned and connected to be consistent with the anatomical model. Finally, a 3D curvilinear grid and a multiblock method were employed to generate the complete computational mesh defined by the cross-sections. The computer reconstruction of the trachea and main bronchi was based on data from the literature (cited herein). The final unified 3D computer model may have significant applications to aerosol medicine and inhalation toxicology, and serve as a cornerstone for computer simulations of air flow and particle-transport processes in the human respiratory system.

A nonhuman primate aerosol deposition model for toxicological and pharmaceutical studies

Nonhuman primates may be used as human surrogates in inhalation exposure studies to assess either the (1) adverse health effects of airborne particulate matter or (2) therapeutic effects of aerosolized drugs and proteins. Mathematical models describing the behavior and fate of inhaled aerosols may be used to complement such laboratory investigations. For example, the optimal conditions, in terms of ventilatory parameters (e.g., breathing frequency and tidal volume) and aerosol characteristics (e.g., geometric size and density), necessary to target drug delivery to specific sites within the respiratory tract may be estimated a priori with models. In this work a mathematical description of the rhesus monkey (Macaca mulatta) lung is presented for use with an aerosol deposition model. Deposition patterns of 0.01- to 5-microm-diameter monodisperse aerosols within lungs were calculated for 3 monkey lung models (using different descriptions of alveolated regions) and compared to human lung results obtained using a previously validated mathematical model of deposition physics. Our findings suggest that there are significant differences between deposition patterns in monkeys and humans. The nonhuman primates had greater exposures to inhaled substances, particularly on the basis of deposition per unit airway surface area. However, the different alveolar volumes in the rhesus monkey models had only minor effects on aerosol dosimetry within those lungs. By being aware of such quantitative differences, investigators can employ the respective primate models (human and nonhuman) to more effectively design and interpret the results of future inhalation exposure experiments.

Computer simulations of particle deposition in the developing human lung

An age-dependent theoretical model has been developed to predict PM dosimetry in children's lungs. Computer codes have been written that describe the dimensions of individual airways and the geometry of branching airway networks within developing lungs. Breathing parameters have also been formulated as functions of subject age. Our computer simulations suggest that particle size, age, and activity level markedly affect deposition patterns of inhaled air pollutants. For example, the predicted lung deposition fraction is 38% in an adult but is nearly twice as high (73%) in a 7-month-old for 2-micron particles inhaled during heavy breathing. Tracheobronchial (TB) and pulmonary (or alveolated airways, P) deposition patterns may also be calculated using the model. Due to different clearance processes in the TB and P airways (i.e., mucociliary transport and macrophage action, respectively), the determination of compartmental dose is important for PM risk assessment analyses. Furthermore, the results of such simulations may aid in the setting of regulatory standards for air pollutants, as the data provide a scientific basis for estimating dose delivered to a designated sensitive subpopulation (children).

Lung models: strengths and limitations

The most widely used particle dosimetry models are those proposed by the National Council on Radiation Protection, International Commission for Radiological Protection, and the Netherlands National Institute of Public Health and the Environment (the RIVM model). Those models have inherent problems that may be regarded as serious drawbacks: for example, they are not physiologically realistic. They ignore the presence and commensurate effects of naturally occurring structural elements of lungs (eg, cartilaginous rings, carinal ridges), which have been demonstrated to affect the motion of inhaled air. Most importantly, the surface structures have been shown to influence the trajectories of inhaled particles transported by air streams. Thus, the model presented herein by Martonen et al may be perhaps the most appropriate for human lung dosimetry. In its present form, the model's major "strengths" are that it could be used for diverse purposes in medical research and practice, including: to target the delivery of drugs for diseases of the respiratory tract (eg, cystic fibrosis, asthma, bronchogenic carcinoma); to selectively deposit drugs for systemic distribution (eg, insulin); to design clinical studies; to interpret scintigraphy data from human subject exposures; to determine laboratory conditions for animal testing (ie, extrapolation modeling); and to aid in aerosolized drug delivery to children (pediatric medicine). Based on our research, we have found very good agreement between the predictions of our model and the experimental data of Heyder et al, and therefore advocate its use in the clinical arena. In closing, we would note that for the simulations reported herein the data entered into our computer program were the actual conditions of the Heyder et al experiments. However, the deposition model is more versatile and can simulate many aerosol therapy scenarios. For example, the core model has many computer subroutines that can be enlisted to simulate the effects of aerosol polydispersity, aerosol hygroscopicity, patient ventilation, patient lung morphology, patient age, and patient airway disease.

Importance of cloud motion on cigarette smoke deposition in lung airways

Deposition patterns of mainstream cigarette smoke were studied in casts of human extrathoracic and lung airways. The laboratory tests were designed to simulate smoking (i.e., the behavior of undiluted cigarette smoke in smokers' lungs), not secondary exposures to non-smokers. The experimental data revealed concentrated deposits at well-defined sites, particularly at bifurcations (most notably at inclusive carinal ridges) and certain segments of tubular airways. The measurements suggest the occurrence of cloud motion wherein particles are not deposited by their individual characteristics but behave as an entity. The observed behavior is consistent with the theory of Martonen (1992), where it was predicted that cigarette smoke could behave aerodynamically as a large cloud (e.g., 20 microns diameter) rather than as submicrometer constituent particles. The effects of cloud motion on deposition are pronounced. For example, an aerosol with a mass median aerodynamic diameter (MMAD) of 0.443 micron and geometric standard deviation (GSD) of 1.44 (i.e., published cigarette smoke values) will have the following deposition fractions: lung (TB + P) = 0.14, tracheobronchial (TB) = 0.03, and pulmonary (P) = 0.11. When cloud motion is simulated, total deposition increases to 0.99 and is concentrated in the TB compartment, especially the upper bronchi; pulmonary deposition is negligible. Cloud motion produces heterogeneous deposition resulting in increased exposures of underlying airway cells to toxic and carcinogenic substances. The deposition sites correlated with incidence of cancers in vivo. At present, cloud motion concentration effects per se are not addressed in federal regulatory standards. The experimental and theoretical data suggest that concentrations of particulate matter may be an important factor to be integrated into U.S. Environmental Protection Agency (EPA) risk assessment protocols.