Limits...
A program for solving the brain ischemia problem.

DeGracia DJ - Brain Sci (2013)

Bottom Line: We simulate measuring a neuroprotectant by time course analysis, which revealed emergent nonlinear effects that set dynamical limits on neuroprotection.Using over-simplified stroke geometry, we calculate a theoretical maximum protection of approximately 50% recovery.We also calculate what is likely to be obtained in practice and obtain 38% recovery; a number close to that often reported in the literature.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, Wayne State University, 4116 Scott Hall, 540 E. Canfield, Detroit, MI 48201, USA. ddegraci@med.wayne.edu.

ABSTRACT
Our recently described nonlinear dynamical model of cell injury is here applied to the problems of brain ischemia and neuroprotection. We discuss measurement of global brain ischemia injury dynamics by time course analysis. Solutions to proposed experiments are simulated using hypothetical values for the model parameters. The solutions solve the global brain ischemia problem in terms of "master bifurcation diagrams" that show all possible outcomes for arbitrary durations of all lethal cerebral blood flow (CBF) decrements. The global ischemia master bifurcation diagrams: (1) can map to a single focal ischemia insult, and (2) reveal all CBF decrements susceptible to neuroprotection. We simulate measuring a neuroprotectant by time course analysis, which revealed emergent nonlinear effects that set dynamical limits on neuroprotection. Using over-simplified stroke geometry, we calculate a theoretical maximum protection of approximately 50% recovery. We also calculate what is likely to be obtained in practice and obtain 38% recovery; a number close to that often reported in the literature. The hypothetical examples studied here illustrate the use of the nonlinear cell injury model as a fresh avenue of approach that has the potential, not only to solve the brain ischemia problem, but also to advance the technology of neuroprotection.

No MeSH data available.


Related in: MedlinePlus

Flow diagram outlining experimental design to measure global brain ischemia injury dynamics at lethal CBF values of 0%, 10%, 25% and 40%, each corresponding to a different value of cD. For each CBF decrement, multiple I values are sampled, giving injury courses. Finally, individual time courses are measured at each cD and I. The numbers used do not have real units because these are hypothetical values for the sake of example. ΔcD, ΔI, and Δt indicate which parameter/variable is being controlled. Finally, for each time point where D and S are sampled, the sample occurs from the same neuron populations. Therefore, with this protocol, cS and λS are maintained constant.
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brainsci-03-00460-f005: Flow diagram outlining experimental design to measure global brain ischemia injury dynamics at lethal CBF values of 0%, 10%, 25% and 40%, each corresponding to a different value of cD. For each CBF decrement, multiple I values are sampled, giving injury courses. Finally, individual time courses are measured at each cD and I. The numbers used do not have real units because these are hypothetical values for the sake of example. ΔcD, ΔI, and Δt indicate which parameter/variable is being controlled. Finally, for each time point where D and S are sampled, the sample occurs from the same neuron populations. Therefore, with this protocol, cS and λS are maintained constant.

Mentions: Because we can control: (a) the global CBF level, (b) the duration of any given CBF level, and (c) the cell type we sample from, we can design an experimental protocol that will allow us to measure D and S time courses by varying (a) and (b) and keeping (c) constant. This will result in a large number of measured D and S time courses from the same cell type. From these time courses, the model parameters can be estimated by nonlinear curve fitting to Equation (1). The following protocol turns out to be relatively straightforward in its design, but because we must measure the system while systematically varying parameters, the protocol is tedious, repetitious and laborious (Figure 5).


A program for solving the brain ischemia problem.

DeGracia DJ - Brain Sci (2013)

Flow diagram outlining experimental design to measure global brain ischemia injury dynamics at lethal CBF values of 0%, 10%, 25% and 40%, each corresponding to a different value of cD. For each CBF decrement, multiple I values are sampled, giving injury courses. Finally, individual time courses are measured at each cD and I. The numbers used do not have real units because these are hypothetical values for the sake of example. ΔcD, ΔI, and Δt indicate which parameter/variable is being controlled. Finally, for each time point where D and S are sampled, the sample occurs from the same neuron populations. Therefore, with this protocol, cS and λS are maintained constant.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4061849&req=5

brainsci-03-00460-f005: Flow diagram outlining experimental design to measure global brain ischemia injury dynamics at lethal CBF values of 0%, 10%, 25% and 40%, each corresponding to a different value of cD. For each CBF decrement, multiple I values are sampled, giving injury courses. Finally, individual time courses are measured at each cD and I. The numbers used do not have real units because these are hypothetical values for the sake of example. ΔcD, ΔI, and Δt indicate which parameter/variable is being controlled. Finally, for each time point where D and S are sampled, the sample occurs from the same neuron populations. Therefore, with this protocol, cS and λS are maintained constant.
Mentions: Because we can control: (a) the global CBF level, (b) the duration of any given CBF level, and (c) the cell type we sample from, we can design an experimental protocol that will allow us to measure D and S time courses by varying (a) and (b) and keeping (c) constant. This will result in a large number of measured D and S time courses from the same cell type. From these time courses, the model parameters can be estimated by nonlinear curve fitting to Equation (1). The following protocol turns out to be relatively straightforward in its design, but because we must measure the system while systematically varying parameters, the protocol is tedious, repetitious and laborious (Figure 5).

Bottom Line: We simulate measuring a neuroprotectant by time course analysis, which revealed emergent nonlinear effects that set dynamical limits on neuroprotection.Using over-simplified stroke geometry, we calculate a theoretical maximum protection of approximately 50% recovery.We also calculate what is likely to be obtained in practice and obtain 38% recovery; a number close to that often reported in the literature.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, Wayne State University, 4116 Scott Hall, 540 E. Canfield, Detroit, MI 48201, USA. ddegraci@med.wayne.edu.

ABSTRACT
Our recently described nonlinear dynamical model of cell injury is here applied to the problems of brain ischemia and neuroprotection. We discuss measurement of global brain ischemia injury dynamics by time course analysis. Solutions to proposed experiments are simulated using hypothetical values for the model parameters. The solutions solve the global brain ischemia problem in terms of "master bifurcation diagrams" that show all possible outcomes for arbitrary durations of all lethal cerebral blood flow (CBF) decrements. The global ischemia master bifurcation diagrams: (1) can map to a single focal ischemia insult, and (2) reveal all CBF decrements susceptible to neuroprotection. We simulate measuring a neuroprotectant by time course analysis, which revealed emergent nonlinear effects that set dynamical limits on neuroprotection. Using over-simplified stroke geometry, we calculate a theoretical maximum protection of approximately 50% recovery. We also calculate what is likely to be obtained in practice and obtain 38% recovery; a number close to that often reported in the literature. The hypothetical examples studied here illustrate the use of the nonlinear cell injury model as a fresh avenue of approach that has the potential, not only to solve the brain ischemia problem, but also to advance the technology of neuroprotection.

No MeSH data available.


Related in: MedlinePlus