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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 of the inflammatory cascade following transplant surgery and non-allo-Ag graft placement (i.e., α = 0). Combined initial host and graft IRI can synergize to incite an inflammatory response that (A–D) cannot resolve, causing graft failure or (E–H) transiently decrease graft function significantly. (A–C) present a series of simulations in which (A) a moderate level of initial surgical IRI in the host is considered with no corresponding graft IRI associated with the placement, (B) no initial surgical IRI in the host is considered with a low level of initial graft IRI, or (C) the moderate level of initial surgical IRI in the host of simulation (A) is coupled with the low level of initial graft IRI of simulation (B). In (D), the graft functionality curves corresponding to simulations (A–C) are shown. The “Graft function for C” time course in (D) displays the synergy to severely affect graft function such that the graft fails, shown as functionality decreasing to and remaining at 12%. Similarly, panels (E–G) display outcomes for (E) a low/moderate level of initial surgical IRI in the host with no corresponding graft IRI associated with the placement, (F) no initial surgical IRI in the host with a corresponding moderate level of initial graft IRI, or (G) the combination of the low/moderate initial level of surgical IRI in the host from simulation (E) with the moderate level of initial graft IRI from simulation (F). In (H), the graft functionality curves corresponding with (E–G) are shown. The “Graft function for G” time course in (H) displays the synergy to significantly affect graft function, but only transiently after which the graft functionality fully recovers. Initial conditions for (C): (I0, D0, A0, DG0, TP0, TA0) = (0, 3, 0.5, 0.125, 0, 0); initial conditions for (G): (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0).
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Figure 3: Simulation results of the inflammatory cascade following transplant surgery and non-allo-Ag graft placement (i.e., α = 0). Combined initial host and graft IRI can synergize to incite an inflammatory response that (A–D) cannot resolve, causing graft failure or (E–H) transiently decrease graft function significantly. (A–C) present a series of simulations in which (A) a moderate level of initial surgical IRI in the host is considered with no corresponding graft IRI associated with the placement, (B) no initial surgical IRI in the host is considered with a low level of initial graft IRI, or (C) the moderate level of initial surgical IRI in the host of simulation (A) is coupled with the low level of initial graft IRI of simulation (B). In (D), the graft functionality curves corresponding to simulations (A–C) are shown. The “Graft function for C” time course in (D) displays the synergy to severely affect graft function such that the graft fails, shown as functionality decreasing to and remaining at 12%. Similarly, panels (E–G) display outcomes for (E) a low/moderate level of initial surgical IRI in the host with no corresponding graft IRI associated with the placement, (F) no initial surgical IRI in the host with a corresponding moderate level of initial graft IRI, or (G) the combination of the low/moderate initial level of surgical IRI in the host from simulation (E) with the moderate level of initial graft IRI from simulation (F). In (H), the graft functionality curves corresponding with (E–G) are shown. The “Graft function for G” time course in (H) displays the synergy to significantly affect graft function, but only transiently after which the graft functionality fully recovers. Initial conditions for (C): (I0, D0, A0, DG0, TP0, TA0) = (0, 3, 0.5, 0.125, 0, 0); initial conditions for (G): (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0).

Mentions: On the other hand, an unhealthy outcome is presumed if the departure away from the healthy equilibrium is not transient but instead causes the variables to approach a different equilibrium that has elevated levels of the variable states. The unhealthy equilibrium implies host health failure and, when a graft is considered, graft failure as well. Alternatively, one could define a level of cumulative damage that could be considered as irreparable, rather than defining non-recovery only by the system’s long-term behavior; we did not explore this possibility in the present study. Figures 2E–H display a basic unhealthy outcome scenario in terms of host health. When a graft placement is considered (with and without apparent mismatch), outcomes also include the percent graft functionality, where a steady-state graft functionality value of 12% represents outright graft failure. See Figures 3A–D, for instance.


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 and non-allo-Ag graft placement (i.e., α = 0). Combined initial host and graft IRI can synergize to incite an inflammatory response that (A–D) cannot resolve, causing graft failure or (E–H) transiently decrease graft function significantly. (A–C) present a series of simulations in which (A) a moderate level of initial surgical IRI in the host is considered with no corresponding graft IRI associated with the placement, (B) no initial surgical IRI in the host is considered with a low level of initial graft IRI, or (C) the moderate level of initial surgical IRI in the host of simulation (A) is coupled with the low level of initial graft IRI of simulation (B). In (D), the graft functionality curves corresponding to simulations (A–C) are shown. The “Graft function for C” time course in (D) displays the synergy to severely affect graft function such that the graft fails, shown as functionality decreasing to and remaining at 12%. Similarly, panels (E–G) display outcomes for (E) a low/moderate level of initial surgical IRI in the host with no corresponding graft IRI associated with the placement, (F) no initial surgical IRI in the host with a corresponding moderate level of initial graft IRI, or (G) the combination of the low/moderate initial level of surgical IRI in the host from simulation (E) with the moderate level of initial graft IRI from simulation (F). In (H), the graft functionality curves corresponding with (E–G) are shown. The “Graft function for G” time course in (H) displays the synergy to significantly affect graft function, but only transiently after which the graft functionality fully recovers. Initial conditions for (C): (I0, D0, A0, DG0, TP0, TA0) = (0, 3, 0.5, 0.125, 0, 0); initial conditions for (G): (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0).
© Copyright Policy
Related In: Results  -  Collection

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

Figure 3: Simulation results of the inflammatory cascade following transplant surgery and non-allo-Ag graft placement (i.e., α = 0). Combined initial host and graft IRI can synergize to incite an inflammatory response that (A–D) cannot resolve, causing graft failure or (E–H) transiently decrease graft function significantly. (A–C) present a series of simulations in which (A) a moderate level of initial surgical IRI in the host is considered with no corresponding graft IRI associated with the placement, (B) no initial surgical IRI in the host is considered with a low level of initial graft IRI, or (C) the moderate level of initial surgical IRI in the host of simulation (A) is coupled with the low level of initial graft IRI of simulation (B). In (D), the graft functionality curves corresponding to simulations (A–C) are shown. The “Graft function for C” time course in (D) displays the synergy to severely affect graft function such that the graft fails, shown as functionality decreasing to and remaining at 12%. Similarly, panels (E–G) display outcomes for (E) a low/moderate level of initial surgical IRI in the host with no corresponding graft IRI associated with the placement, (F) no initial surgical IRI in the host with a corresponding moderate level of initial graft IRI, or (G) the combination of the low/moderate initial level of surgical IRI in the host from simulation (E) with the moderate level of initial graft IRI from simulation (F). In (H), the graft functionality curves corresponding with (E–G) are shown. The “Graft function for G” time course in (H) displays the synergy to significantly affect graft function, but only transiently after which the graft functionality fully recovers. Initial conditions for (C): (I0, D0, A0, DG0, TP0, TA0) = (0, 3, 0.5, 0.125, 0, 0); initial conditions for (G): (I0, D0, A0, DG0, TP0, TA0) = (0, 2, 1, 0.125, 0, 0).
Mentions: On the other hand, an unhealthy outcome is presumed if the departure away from the healthy equilibrium is not transient but instead causes the variables to approach a different equilibrium that has elevated levels of the variable states. The unhealthy equilibrium implies host health failure and, when a graft is considered, graft failure as well. Alternatively, one could define a level of cumulative damage that could be considered as irreparable, rather than defining non-recovery only by the system’s long-term behavior; we did not explore this possibility in the present study. Figures 2E–H display a basic unhealthy outcome scenario in terms of host health. When a graft placement is considered (with and without apparent mismatch), outcomes also include the percent graft functionality, where a steady-state graft functionality value of 12% represents outright graft failure. See Figures 3A–D, for instance.

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