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Mathematical Modeling of Early Cellular Innate and Adaptive Immune Responses to Ischemia/Reperfusion Injury and Solid Organ Allotransplantation.

Day JD, Metes DM, Vodovotz Y - Front Immunol (2015)

Bottom Line: We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft.These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response.An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Tennessee , Knoxville, TN , USA ; National Institute for Mathematical and Biological Synthesis , Knoxville, TN , USA.

ABSTRACT
A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient's (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression.

No MeSH data available.


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Simulation results of the inflammatory cascade following transplant surgery only without graft placement (i.e., G = 0). (A–D) Below a certain threshold, initial host tissue damage caused by IRI incites an inflammatory response that resolves to baseline levels. Initial condition for this simulation was (I0, D0, A0, DG0, TP0, TA0) = (0, 3, 0, 0.125, 0, 0) with parameters as given in Table 4. For D < 4, this outcome is possible. (E–H) Above a certain threshold, initial host tissue damage caused by IRI incites an inflammatory response that does not resolve and results in host health failure. Note that this scenario is not the one we would consider for transplant conditions, but demonstrate the scope of the model dynamics to produce theoretically possible outcomes of traumatic injury. Initial condition for this simulation was (I0, D0, A0, DG0, TP0, TA0) = (0, 4, 0, 0.125, 0, 0) with parameters as given in Table 4. For D ≥ 4, this outcome is possible.
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Figure 2: Simulation results of the inflammatory cascade following transplant surgery only without graft placement (i.e., G = 0). (A–D) Below a certain threshold, initial host tissue damage caused by IRI incites an inflammatory response that resolves to baseline levels. Initial condition for this simulation was (I0, D0, A0, DG0, TP0, TA0) = (0, 3, 0, 0.125, 0, 0) with parameters as given in Table 4. For D < 4, this outcome is possible. (E–H) Above a certain threshold, initial host tissue damage caused by IRI incites an inflammatory response that does not resolve and results in host health failure. Note that this scenario is not the one we would consider for transplant conditions, but demonstrate the scope of the model dynamics to produce theoretically possible outcomes of traumatic injury. Initial condition for this simulation was (I0, D0, A0, DG0, TP0, TA0) = (0, 4, 0, 0.125, 0, 0) with parameters as given in Table 4. For D ≥ 4, this outcome is possible.

Mentions: In the Section “Materials and Methods,” the construction of the model is discussed and the full model is given by Eqs 1–6, with the model parameter descriptions and values used in the simulations given in Table 4. The equations are solved numerically to produce time courses of each of the system variables or states (see Materials and Methods). These resulting time courses are translated to clinical outcomes in the following manner. In general, we define a pre-surgery initial condition for the model variables as (I0, D0, A0, DG0, TP0, TA0) = (0, 0, 0.125, 0, 0, 0), which indicate that all system components are at their background values. This state is referred to as the baseline equilibrium. This setting assumes that there are no underlying immune conditions prior to transplant surgery, which is typically not realistic in the case of transplant recipients. Future iterations of the model could incorporate prior host health conditions. The system can be perturbed from this baseline state, for instance, by setting a non-zero initial condition for D and/or DG, which indicates the presence of damaged tissue to host and/or graft, respectively, due to IRI. The rates at which system variables change as a function of time are governed by the Eqs 1–6. A simulation in which the variables’ time courses return to the background levels, after a brief transient increase away from this state due to perturbation, is translated as a healthy outcome. Figures 2A–D display a basic healthy outcome scenario in terms of host health.


Mathematical Modeling of Early Cellular Innate and Adaptive Immune Responses to Ischemia/Reperfusion Injury and Solid Organ Allotransplantation.

Day JD, Metes DM, Vodovotz Y - Front Immunol (2015)

Simulation results of the inflammatory cascade following transplant surgery only without graft placement (i.e., G = 0). (A–D) Below a certain threshold, initial host tissue damage caused by IRI incites an inflammatory response that resolves to baseline levels. Initial condition for this simulation was (I0, D0, A0, DG0, TP0, TA0) = (0, 3, 0, 0.125, 0, 0) with parameters as given in Table 4. For D < 4, this outcome is possible. (E–H) Above a certain threshold, initial host tissue damage caused by IRI incites an inflammatory response that does not resolve and results in host health failure. Note that this scenario is not the one we would consider for transplant conditions, but demonstrate the scope of the model dynamics to produce theoretically possible outcomes of traumatic injury. Initial condition for this simulation was (I0, D0, A0, DG0, TP0, TA0) = (0, 4, 0, 0.125, 0, 0) with parameters as given in Table 4. For D ≥ 4, this outcome is possible.
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Figure 2: Simulation results of the inflammatory cascade following transplant surgery only without graft placement (i.e., G = 0). (A–D) Below a certain threshold, initial host tissue damage caused by IRI incites an inflammatory response that resolves to baseline levels. Initial condition for this simulation was (I0, D0, A0, DG0, TP0, TA0) = (0, 3, 0, 0.125, 0, 0) with parameters as given in Table 4. For D < 4, this outcome is possible. (E–H) Above a certain threshold, initial host tissue damage caused by IRI incites an inflammatory response that does not resolve and results in host health failure. Note that this scenario is not the one we would consider for transplant conditions, but demonstrate the scope of the model dynamics to produce theoretically possible outcomes of traumatic injury. Initial condition for this simulation was (I0, D0, A0, DG0, TP0, TA0) = (0, 4, 0, 0.125, 0, 0) with parameters as given in Table 4. For D ≥ 4, this outcome is possible.
Mentions: In the Section “Materials and Methods,” the construction of the model is discussed and the full model is given by Eqs 1–6, with the model parameter descriptions and values used in the simulations given in Table 4. The equations are solved numerically to produce time courses of each of the system variables or states (see Materials and Methods). These resulting time courses are translated to clinical outcomes in the following manner. In general, we define a pre-surgery initial condition for the model variables as (I0, D0, A0, DG0, TP0, TA0) = (0, 0, 0.125, 0, 0, 0), which indicate that all system components are at their background values. This state is referred to as the baseline equilibrium. This setting assumes that there are no underlying immune conditions prior to transplant surgery, which is typically not realistic in the case of transplant recipients. Future iterations of the model could incorporate prior host health conditions. The system can be perturbed from this baseline state, for instance, by setting a non-zero initial condition for D and/or DG, which indicates the presence of damaged tissue to host and/or graft, respectively, due to IRI. The rates at which system variables change as a function of time are governed by the Eqs 1–6. A simulation in which the variables’ time courses return to the background levels, after a brief transient increase away from this state due to perturbation, is translated as a healthy outcome. Figures 2A–D display a basic healthy outcome scenario in terms of host health.

Bottom Line: We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft.These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response.An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Tennessee , Knoxville, TN , USA ; National Institute for Mathematical and Biological Synthesis , Knoxville, TN , USA.

ABSTRACT
A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient's (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression.

No MeSH data available.


Related in: MedlinePlus