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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.


Related in: MedlinePlus

Simulation results showing outcomes of transplant surgery with placement of allo-Ag graft for various degrees of apparent mismatch (i.e., α > 0). The initial condition used in Figure 3G [i.e., (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0)] was also used here but now various values of the apparent mismatch factor parameter, α, were explored to observe the effects of initial host and graft tissue damage from IRI in conjunction with allo-recognition. (A) With low mismatch factor (α = 0–0.03), graft tolerance is seen. (B) Within a higher range (α = 0.04–0.25), damped oscillations in graft functionality appear but resolve to greater than 95% functionality in the long term with values of α on the higher end of the range taking months to resolve and stabilize. (C) Within the next highest interval (α = 0.29–0.5), undamped oscillations are apparent. This indicates a regime where graft function is affected by chronic inflammation driven by T cells that flares up and subsides periodically. (D) The last interval (α = 0.55–1.0) displays acute graft failure within 400 h for α values near the minimum of this range and within 125 h near the maximum of this range.
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Figure 4: Simulation results showing outcomes of transplant surgery with placement of allo-Ag graft for various degrees of apparent mismatch (i.e., α > 0). The initial condition used in Figure 3G [i.e., (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0)] was also used here but now various values of the apparent mismatch factor parameter, α, were explored to observe the effects of initial host and graft tissue damage from IRI in conjunction with allo-recognition. (A) With low mismatch factor (α = 0–0.03), graft tolerance is seen. (B) Within a higher range (α = 0.04–0.25), damped oscillations in graft functionality appear but resolve to greater than 95% functionality in the long term with values of α on the higher end of the range taking months to resolve and stabilize. (C) Within the next highest interval (α = 0.29–0.5), undamped oscillations are apparent. This indicates a regime where graft function is affected by chronic inflammation driven by T cells that flares up and subsides periodically. (D) The last interval (α = 0.55–1.0) displays acute graft failure within 400 h for α values near the minimum of this range and within 125 h near the maximum of this range.

Mentions: In this next simulation set, we consider varying levels of host–graft mismatch, and thus the interactions shown in Figure 1 involving allo-recognition come into play. We use the initial condition (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0) as in Figure 3G, and set α to different values within the interval [0,1] in the multiple simulation runs. Figures 4A–D display four qualitatively different outcome scenarios corresponding to ranges of the mismatch parameter, α. Each figure panel displays the graft functionality results of multiple simulation runs for values of α within the specified ranges. In these various scenarios, we observe outcomes corresponding to the clinical scenarios mentioned earlier at the beginning of Section “Results.” Clinical quiescence is represented in Figure 4A, where there is little or no graft damage and full or nearly full graft functionality is achieved and retained. Acute clinical rejection is represented in Figure 4D, where poor graft functionality is seen very early after the simulation is initiated (i.e., after the transplant is completed), and failure is predicted to occur within less than a month’s time. The subclinical inflammation outcome is represented in Figures 4B,C. In Figure 4B, we interpret the smaller oscillations as subclinical chronic inflammation predicted to resolve on the order of 1–3 months (shown for up to 1000 h ~ 42 days), since the recovery behavior is different from, and takes longer than, the graft tolerance recovery scenario of Figure 4A. Furthermore, since in Figure 4B the damped oscillations are such that (1) graft health does not decrease too often nor too greatly below the original graft health level; and (2) an acceptable recovery is seen eventually (i.e., graft health is greater than 95%), we interpret this behavior as subclinical. In other words, the graft is in comparable or better condition than when it was first transplanted, but it is not maintaining optimal function until much later. Note that Figure 4A could also be classified as subclinical, but the length of time in which graft health is not ideal is much shorter relative to the scenarios in Figure 4B. Thus, we do not classify Figure 4A as a chronic scenario. In Figure 4C, the oscillations are larger and do not resolve as in Figure 4B. We equate this outcome with long-term rejection since a high and steady level of graft function is never observed as T cells cause inflammation and subsequent damage to flare up and subside repeatedly. This prediction points to a scenario leading to graft failure, even though there are times when there is only subclinical inflammation, and a good level of graft function is observed.


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 showing outcomes of transplant surgery with placement of allo-Ag graft for various degrees of apparent mismatch (i.e., α > 0). The initial condition used in Figure 3G [i.e., (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0)] was also used here but now various values of the apparent mismatch factor parameter, α, were explored to observe the effects of initial host and graft tissue damage from IRI in conjunction with allo-recognition. (A) With low mismatch factor (α = 0–0.03), graft tolerance is seen. (B) Within a higher range (α = 0.04–0.25), damped oscillations in graft functionality appear but resolve to greater than 95% functionality in the long term with values of α on the higher end of the range taking months to resolve and stabilize. (C) Within the next highest interval (α = 0.29–0.5), undamped oscillations are apparent. This indicates a regime where graft function is affected by chronic inflammation driven by T cells that flares up and subsides periodically. (D) The last interval (α = 0.55–1.0) displays acute graft failure within 400 h for α values near the minimum of this range and within 125 h near the maximum of this range.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4585194&req=5

Figure 4: Simulation results showing outcomes of transplant surgery with placement of allo-Ag graft for various degrees of apparent mismatch (i.e., α > 0). The initial condition used in Figure 3G [i.e., (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0)] was also used here but now various values of the apparent mismatch factor parameter, α, were explored to observe the effects of initial host and graft tissue damage from IRI in conjunction with allo-recognition. (A) With low mismatch factor (α = 0–0.03), graft tolerance is seen. (B) Within a higher range (α = 0.04–0.25), damped oscillations in graft functionality appear but resolve to greater than 95% functionality in the long term with values of α on the higher end of the range taking months to resolve and stabilize. (C) Within the next highest interval (α = 0.29–0.5), undamped oscillations are apparent. This indicates a regime where graft function is affected by chronic inflammation driven by T cells that flares up and subsides periodically. (D) The last interval (α = 0.55–1.0) displays acute graft failure within 400 h for α values near the minimum of this range and within 125 h near the maximum of this range.
Mentions: In this next simulation set, we consider varying levels of host–graft mismatch, and thus the interactions shown in Figure 1 involving allo-recognition come into play. We use the initial condition (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0) as in Figure 3G, and set α to different values within the interval [0,1] in the multiple simulation runs. Figures 4A–D display four qualitatively different outcome scenarios corresponding to ranges of the mismatch parameter, α. Each figure panel displays the graft functionality results of multiple simulation runs for values of α within the specified ranges. In these various scenarios, we observe outcomes corresponding to the clinical scenarios mentioned earlier at the beginning of Section “Results.” Clinical quiescence is represented in Figure 4A, where there is little or no graft damage and full or nearly full graft functionality is achieved and retained. Acute clinical rejection is represented in Figure 4D, where poor graft functionality is seen very early after the simulation is initiated (i.e., after the transplant is completed), and failure is predicted to occur within less than a month’s time. The subclinical inflammation outcome is represented in Figures 4B,C. In Figure 4B, we interpret the smaller oscillations as subclinical chronic inflammation predicted to resolve on the order of 1–3 months (shown for up to 1000 h ~ 42 days), since the recovery behavior is different from, and takes longer than, the graft tolerance recovery scenario of Figure 4A. Furthermore, since in Figure 4B the damped oscillations are such that (1) graft health does not decrease too often nor too greatly below the original graft health level; and (2) an acceptable recovery is seen eventually (i.e., graft health is greater than 95%), we interpret this behavior as subclinical. In other words, the graft is in comparable or better condition than when it was first transplanted, but it is not maintaining optimal function until much later. Note that Figure 4A could also be classified as subclinical, but the length of time in which graft health is not ideal is much shorter relative to the scenarios in Figure 4B. Thus, we do not classify Figure 4A as a chronic scenario. In Figure 4C, the oscillations are larger and do not resolve as in Figure 4B. We equate this outcome with long-term rejection since a high and steady level of graft function is never observed as T cells cause inflammation and subsequent damage to flare up and subside repeatedly. This prediction points to a scenario leading to graft failure, even though there are times when there is only subclinical inflammation, and a good level of graft function is observed.

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