Patrick Joyce1, Professor Mike Chappell1, Professor James Yates2
1University of Warwick, 2GSK
Introduction: Antibody Drug Conjugates (ADCs) represent a novel therapeutic modality which are currently mainly used for the treatment of cancer. ADCs combine the specificity of monoclonal antibodies with potent cytotoxic agents, producing a mechanism for the selective delivery of the cytotoxic agent directly to malignant cells whilst minimising toxicity to healthy cells. One of the main issues with ADCs is achieving a uniform distribution within solid tumours due to the typical complex tumour physiology. The binding site barrier (BSB) also complicates ADC delivery, as high-affinity antibodies bind rapidly to antigens nearer the blood vessels, limiting deeper penetration within the tumour resulting in a reduced therapeutic efficacy. This study aims to develop and compare two types of target-mediated drug disposition (TMDD) models for an antibody, incorporating the BSB and assuming a spherical tumour geometry: one model using ordinary differential equations (ODEs) to simulate a discrete number of layers within the tumour geometry, each with equal thickness, derived from [1], and a second model using partial differential equations (PDEs) to model a tumour with a continuous spatial resolution, derived from [2]. Objectives: •Develop an ODE model to simulate the distribution of antibodies within the tumour with n discretised layers representing a spherical tumour geometry. •Develop a PDE model to simulate the distribution of antibodies within the tumour with a continuous spatial resolution •Perform structural identifiability analysis (SIA) on both models to determine identifiability or otherwise of the unknown model parameters. Methods: TMDD models were developed to describe the pharmacokinetics and pharmacodynamics of a typical monoclonal antibody and the distribution of the concentration of antibodies within the tumour. Both models were constructed using published parameter values obtained from literature and simulated in MATLAB [3] . The ‘ode45’ function was used to numerically solve the ODEs in MATLAB allowing for the simulation of the distribution of monoclonal antibodies across multiple discrete layers of the tumour. The ‘pdepe’ function in MATLAB was used to simulate the PDE model, enabling simulation of the continuous spatial resolution of the distribution of monoclonal antibodies within the tumour. To ensure model validity and subsequent robust parameter estimation, SIA was performed on the ODE model using the Exact Arithmetic Ranking Approach in Mathematica. For the PDE model, structural identifiability was assessed in Maple via the input-output method for PDE models [4]. Results: Preliminary findings indicate significant differences in the predictions of the distribution of the concentration of monoclonal antibodies between the ODE and PDE models when the number of discrete layers in the ODE model is minimal (n=2,3), due to the continuous nature of the PDE model. As the number of tumour layers simulated within the ODE model increases and therefore the thickness of the tumour layer decreases, the concentration profile within the tumour begins to converge towards that of the PDE model. However, the implementation of additional layers significantly increases the model complexity of the ODE system. The ODE model, and the corresponding number of layers, was deemed satisfactory if there was less than a 10% difference between the concentration at the layer’s boundary in comparison to the concentration determined from the PDE model at the same tumour depth. It has been ascertained that the ODE model is structurally identifiable, irrespective of the number of layers, whereas, at present, the PDE model rendered SIA intractable due to memory limitations within Maple. Conclusion: The results demonstrate the value of both ODE and PDE approaches in understanding the impact of the binding site barrier on antibody distribution. However, the advantage of the PDE model is that it can capture the intricacies of the concentration in different tumour layers with relatively low model complexity without the need to build additional compartments that would be required for the ODE model. While the PDE model cannot currently be proven structurally identifiable, future work will investigate alternative methods in proving structural identifiability to ensure reliability in parameter estimation.
[1] B. M. Bordeau, L. Abuqayyas, T. D. Nguyen, P. Chen and J. P. Balthasar, “Development and Evaluation of Competitive Inhibitors of Trastuzumab-HER2 Binding to Bypass the Binding-Site Barrier,” frontiers in Pharmacology, vol. 13, 2022. [2] G. M. Thurber, S. C. Zajic and K. D. Wittrup, “Theoretic Criteria for Antibody Penetration into Solid Tumours and Micometastases,” Journal of Nuclear Medicine, vol. 48, no. 6, pp. 995-999, 2007. [3] T. M. Inc., MATLAB Version: 9.14.0.2306882 (R2023a), Natick, Massachusetts, United States. [4] H. M. Byrne, H. A. Harrington, A. Ovchinnikov, G. Pogudin, H. Rahkooy and P. Soto, “Algebraic Identifiability of Partial Differential Equations Models,” Quantitative Biology, 2024.
Reference: PAGE 33 (2025) Abstr 11487 [www.page-meeting.org/?abstract=11487]
Poster: Drug/Disease Modelling - Oncology