Modeling Adoptive Cell Transfer in Heart Transplants

By Lina Sorg

In 2019, nearly 40,000 organ transplants occurred in the U.S. A wide variety of organs—including the heart, kidneys, lungs, and skin—are candidates for transplantation. However, the immune system registers a transplant as a foreign entity and attempts to destroy it; transplantation therefore requires some type of intervention to prevent the patient’s body from rejecting the new organ. To discourage rejection, doctors commonly administer immunosuppressive drugs on a long-term basis. Unfortunately, these drugs leave patients at a heightened risk for infection and increase the chance of hypertension, diabetes, opportunistic infections, and even cancer.

Researchers are thus interested in exploring alternative strategies with the therapeutic potential to prevent transplant rejection. “Can we use modeling to try to understand other types of interventions?” Julia Arciero of Indiana University – Purdue University Indianapolis asked. During a minisymposium presentation at the 2020 SIAM Conference on the Life Sciences, which took place virtually last month, she presented an experimentally-based mathematical model that examines the feasibility of adoptive cell transfer (ACT) in heart transplant cases. “There are a lot of things that we can easily simulate with a mathematical model without having to do everything separately in a lab,” she said.

T cells are a type of white blood cell that control and shape the body’s immune response. Arciero encouraged the audience to think of immune response as an up and down regulation. Up-regulators include effector T cells, helper T cells, and pro-inflammatory cytokines, all of which boost immune response and attack antigens. Down-regulators comprise regulatory T cells (Tregs) and anti-inflammatory cytokines, which maintain balance and attempt to keep the up-regulators in check.

If the antigen in question is a virus, up-regulators’ destruction of the toxin is desirable. But if it is a transplant, down-regulators work to reduce the immune response. In the case of the latter, Arciero seeks to determine whether ACT can boost the performance of down-regulators to minimize attacks on a transplanted organ and increase its chance of survival.

ACT is the transfer of cells into a patient with the ultimate goal of improving immune functionality. Tregs are removed from the patient, undergo genetic modification, and are then returned to the body to trigger an enhanced immune response. Arciero began with a basic compartmental model of transplant rejection that assumes a constant supply of naïve T cells. The graft (organ transplant) and lymphoid tissue comprise the two compartments, and their interactions provide much trackable information.

Antigen-presenting cells (APCs) activate the naïve helper T cells in the lymph node. Interactions commence after activation, and the activated T cells seek out the graft—in this case, the transplant—and become graft populations. As they attack and destroy the graft, Tregs inhibit the destruction. “Tregs have three important ways in which they regulate the response,” Arciero said. In addition to inhibiting the attack, they prevent the activation of inflammatory APCs and maturation of APCs. When ACT places a large amount of Tregs into the graft, it thus promotes graft survival.

To determine whether these actions are sufficient, Arciero introduced an ordinary differential equation model and presented a sample equation to track the number of Tregs in the graft. Variables include Tregs in the graft, Tregs in the lymph node, helper T cells in the graft, and effector T cells in the lymph node. She broke the associated equation into various sections, such as entry, natural decay, and dosing function. Arciero focused on dosing function and identified the following possible dosing strategies:

• Single dose: Varying the time and dosing rate of a single dose of Tregs
• Multiple doses: Varying the dosing rate and the number of days on which the dose is administered
• Fractional delivery: Varying the fraction of Tregs that go directly into the graft and lymph node 
• Size of dose and timing of delivery: Varying the magnitude of Tregs injected and/or the day of dosing. 

The goal of these strategies is to ultimately guarantee transplant survival. Arciero used an existing study to quantify heart transplant rejection at a 75 percent reduction of function. She then worked with a statistician to apply parameter estimation and sensitivity analysis techniques to her model. After pinpointing the most sensitive parameters for estimation, Arciero engaged model calibration.

She began the presentation of results with a model of graft rejection in the absence of ACT. Arciero depicted graft cells as a function of time, then simulated ACT by varying the following factors:

• Treg delivery site (graft or lymph node)
• Activation status of Tregs (activated or naïve)
• Dosing rate
• Timing of dose
• Dose frequency (single dose versus multiple doses)

She found that simply returning modified Tregs to the body delayed the transplant’s failure but did not prevent its ultimate death. So Arciero instead varied the dosing rate and learned that the optimal day of delivery is dependent on this rate. In this case, day 1 or 2 was optimal for a reasonable dose, as a slight delay allows some Tregs to build up in the lymph node; immediately injecting Tregs into the graft inhibits the APC maturation process. Waiting a few days allows for the impact of both directly-injected Tregs and additional cells that arrive from the lymph nodes. Finally, the optimal therapeutic strategy is to administer 14 doses of Tregs beginning on day 0, as delivering one dose over multiple days yields a more defensive effect than administering the same dose in a single day.

Arciero’s modeling efforts identified two key results that are particularly useful to transplant immunologists. Identifying the ideal window of opportunity for ACT is critical, as is predicting Tregs’ capabilities based on their distribution. But ACT alone does not successfully protect a transplant, and Arciero plans to extend her model to include the complexities of immunosuppression. Nevertheless, theoretical simulations remain an invaluable tool for revealing and experimentally validating treatment strategies for transplant patients.

Lina Sorg is the managing editor of SIAM News.