Mathematical modeling of intratumoral immunotherapy yields strategies to improve the treatment outcomes

Abstract

Intratumoral injection of immunotherapy aims to maximize its activity within the tumor. However, cytokines are cleared via tumor vessels and escape from the tumor periphery into the host-tissue, reducing efficacy and causing toxicity. Thus, understanding the determinants of the tumor and immune response to intratumoral immunotherapy should lead to better treatment outcomes. In this study, we developed a mechanistic mathematical model to determine the efficacy of intratumorally-injected conjugated-cytokines, accounting for properties of the tumor microenvironment and the conjugated-cytokines. The model explicitly incorporates i) the tumor vascular density and permeability and the tumor hydraulic conductivity, ii) conjugated-cytokines size and binding affinity as well as their clearance via the blood vessels and the surrounding tissue, and iii) immune cells-cancer cells interactions. Model simulations show how the properties of the tumor and of the conjugated-cytokines determine treatment outcomes and how selection of proper parameters can optimize therapy. A high tumor tissue hydraulic permeability allows for the uniform distribution of the cytokines into the tumor, whereas uniform tumor perfusion is required for sufficient access and activation of immune cells. The permeability of the tumor vessels affects the blood clearance of the cytokines and optimal values depend on the size of the conjugates. A size >5 nm in radius was found to be optimal, whereas the binding of conjugates should be high enough to prevent clearance from the tumor into the surrounding tissue. In conclusion, development of strategies to improve vessel perfusion and tissue hydraulic conductivity by reprogramming the microenvironment along with optimal design of conjugated-cytokines can enhance intratumoral immunotherapy.

Fig 1. Model methodology.

(a) Shcematic of various transport mechanisms considered in the model. The conjugated-cytokines are injected in the tumor region and can be transported via convection and diffusion to the host tissue and across the tumor vessel walls. Hyperpermeability of the tumor blood vessels and the lack of functional lymphatic vessels elevates interstitial fluid pressuse, inducing pressure gradients at the tumor periphery that drive transport of the conjugated-cytokines from the tumor to the host tissue via convection. The injected conjugated-cytokines can bind and unbind to the target (e.g., collagen fibers) in both tumor and host tissue. Cytokines produced by the immune cells can disperse via convection and difusion as well. Also immune cells can migrate (i.e., diffuse) from the tumor tissue to the host tissue and the reverse depending on the concentration gradients. (b) Model components of the immune system: IN represents the innate immune cells that induce cytolysis and produce antigen, e.g., Natural Killer cells. Immature APCs are the immature antigen presenting cells that can become antigen presenting cells (APCs). CD4 and CD8 represent effector CD4+ and CD8+ T cells. Production and activation of immune cells are affected by cytokines. The immune cells also produce cytokines. Oxygen supply increases cancer cells’ proliferation and tumor growth and decreases the apoptosis rate of the immune cells. Created with BioRender.com.

Fig 2. Experimental data (circles) of tumor growth and model predictions (solid line) for control tumors (blue) and tumors treated with intratumoral injection of conjugated-cytokines (red) by Momin et al. [17] and Agarwal et al. [35].

Fig 3. Results for the total amount of cytokines and the bound conjugated-cytokines for various time points for each study.

The plots represent the distribution in the radial direction. The value 0 in the x axis corresponds to the tumor center. As we move along the x axis, we move away from the tumor center towards the host tissue. Plots include both the tumor region and host tissue that surrounds the tumor. The vertical dashed lines show the tumor boundary at the given time points.

Fig 4. Results at various time points for each optimization case.

The plots represent the distribution in the radial direction. The value 0 in the x axis corresponds to the tumor center. As we move along the x axis, we move away from the tumor center towards the host tissue. Plots include both the tumor region and host tissue that surrounds the tumor. The vertical dashed lines represent the tumor boundary.

Fig 5. The impact of various model components to tumor growth by varying a single parameter.

Figure presents the tumor growth through time and the number of innate cells that induce cytolysis (NK cells), antigen presenting cells and effector CD8+ T cells when varying: the injected conjugate radius, the conjugate binding rate constant, the vascular density inside the tumor region, the vessel wall pore radius inside tumor, and the hydraulic conductivity inside the tumor region. The baseline values of the parameters for these simulations are: rs = 3.85[nm], kon = 100 [m³/mol/s], Sv = 50[1/cm], r₀ = 100 [nm], kh = 4.13e-8 [cm²/mmHg/s].

Fig 6. Diagrams of the efficacy of conjugated-cytokines injection as a function of tumor physiological properties and conjugate radius and binding affinity.

Each point in the diagrams represents the tumor volume of a different simulation. The tumor volume is measured either at the end of the simulations (day 10) or at the time point where at least one of the simulations reached complete cure (i.e., tumor volume becomes zero). For each simulation only the parameters shown in the two axes were varied. (a) The hydraulic conductivity in the tumor region was varied relative to the binding of the injected conjugate (day 7.5) and (b) the conjugate radius (day 5.2). (c) The tumor vessel wall pore radius was varied relative to the binding of the injected conjugate (day 10) and (d) the conjugate radius (day 6.0). (e) The tumor vascular density was varied relative to the binding of the injected conjugate (day 3.2) and (f) the conjugate radius (day 2.9).