Dynamic modelling and evaluation of preclinical trials in acute leukaemia

TL;DR

The paper addresses how to detect growth-inhibiting effects of gene knockouts in preclinical acute leukaemia trials by replacing single-time-point tests with dynamic population models. It compares exponential and logistic growth forms, linking measured fractions to two interacting cell populations via an observable and a log-normal measurement error model, and uses maximum likelihood with profile likelihoods to estimate parameters and quantify uncertainty. The exponential model consistently provides more reliable identification of true effects and clearer parameter inference than the logistic model, while also competing with endpoint paired t-tests for sufficiently large samples. The findings support using time-resolved, mechanistic modelling to optimize experimental design in PDX leukaemia studies, potentially reducing animal use and improving inference about gene-therapy targets.

Abstract

Dynamic models are widely used to mathematically describe biological phenomena that evolve over time. One important area of application is leukaemia research, where leukaemia cells are genetically modified in preclinical studies to explore new therapeutic targets for reducing leukaemic burden. In advanced experiments, these studies are often conducted in mice and generate time-resolved data, the analysis of which may reveal growth-inhibiting effects of the investigated gene modifications. However, the experimental data is often times evaluated using statistical tests which compare measurements from only two different time points. This approach does not only reduce the time series to two instances but also neglects biological knowledge about cell mechanisms. Such knowledge, translated into mathematical models, expands the power to investigate and understand effects of modifications on underlying mechanisms based on experimental data. We utilise two population growth models -- an exponential and a logistic growth model -- to capture cell dynamics over the whole experimental time horizon and to consider all measurement times jointly. This approach enables us to derive modification effects from estimated model parameters. We demonstrate that the exponential growth model recognises simulated scenarios more reliably than the other candidate model and than a statistical test. Moreover, we apply the population growth models to evaluate the efficacy of candidate gene knockouts in patient-derived xenograft (PDX) models of acute leukaemia.

Figures (14)

• Figure 1: Schematic workflow of gene modification experiments, here a CRISPR-Cas9 knockout experiment, exploring new therapeutic targets for acute leukaemia (AL). First, patient cells are engrafted into mice to generate PDX cells. These cells are genetically modified and again engrafted into mice together with an untreated cell population providing PDX models. The output measurements, i. e. the concentrations of the modified population in the bone marrow of mice at an advanced stage of leukaemia, are compared with the input measurements, i. e. the concentration that is injected, to assess a possible growth-inhibiting effect on the modified cell population
• Figure 2: Trajectories of the exponential growth model with exemplary values for $\beta_1$ and $\beta_2$ with $x_1(0)=x_2(0)=10^4$. (a) Both populations grow, as $\beta_1,\beta_2>0$, but Population 1 grows less strongly than Population 2. (b) Population 1 shrinks and Population 2 grows, as $\beta_1<0$ and $\beta_2>0$
• Figure 3: Trajectories of the logistic growth model with exemplary values for $\lambda_1$ and $\lambda_2$ with $K=10^9$ and $x_1(0)=x_2(0)=10^4$. (a) Both populations grow, as $\lambda_1,\lambda_2>0$, but Population 1 grows less strongly than Population 2. (b) Population 1 shrinks and Population 2 grows, as $\lambda_1<0$ and $\lambda_2>0$
• Figure 4: Trajectories of the observable $\eta(t)$ for (a) the exponential and (b) the logistic growth model with $x_1(0)=x_2(0)=10^4$ and $K=10^9$. The other parameter values correspond to those in Figures \ref{['models:fig_exp_traj1']} and \ref{['models:fig_logistic_traj1']}
• Figure 5: Detection results for simulated data via five evaluation methods: paired $t$-tests for two different end days, the exponential growth model (once with quantile $\Delta_{0.05}^{\chi_1^2}=3.84$, once with adapted threshold $\Delta_{0.05}^{\text{Cant}}=7.16$ for profile likelihood-based $95$ % confidence intervals of $\theta_1^{(e)}$), and the logistic growth model based on $95$ % bootstrapping confidence intervals for $\theta_2^{(l)}-\theta_1^{(l)}$. The data stems from four simulated scenarios and four sample size settings. Dashed parts represent the proportion of confidence intervals for the corresponding evaluation quantity which are a subset of $\mathbb{R}_{-}$, indicating a growth-enhancing rather than growth-inhibiting effect. Light blue and light yellow bars represent the numbers of detected modification effects of a corresponding scenario for the next larger sample size for paired $t$-tests of day $14$ measurements and endpoint measurements, respectively. Figure \ref{['appendix:heat_map_simulation']} in Appendix \ref{['sec:appendix_figures']} provides a detailed visualisation of detection results per dataset, revealing individual (dis-)agreement between evaluation methods