Modelling Blood Flow and Metabolism in the Piglet Brain During Hypoxia-Ischaemia: Simulating pH Changes

We describe the extension of a computational model of blood flow and metabolism in the piglet brain to investigate changes in neonatal intracellular brain pH during hypoxia-ischemia (HI). The model is able to simulate near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS) measurements obtained from HI experiments conducted in piglets. We adopt a method of using (31)P-MRS data to estimate of intracellular pH and compare measured pH and oxygenation with their modelled counterparts. We show that both NIRS and MRS measurements are predicted well in the new version of the model

Modelling Blood Flow and Metabolism in the Preclinical Neonatal Brain during and Following Hypoxic-Ischaemia

Hypoxia-ischaemia (HI) is a major cause of neonatal brain injury, often leading to long-term damage or death. In order to improve understanding and test new treatments, piglets are used as preclinical models for human neonates. We have extended an earlier computational model of piglet cerebral physiology for application to multimodal experimental data recorded during episodes of induced HI. The data include monitoring with near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS), and the model simulates the circulatory and metabolic processes that give rise to the measured signals. Model extensions include simulation of the carotid arterial occlusion used to induce HI, inclusion of cytoplasmic pH, and loss of metabolic function due to cell death. Model behaviour is compared to data from two piglets, one of which recovered following HI while the other did not. Behaviourally-important model parameters are identified via sensitivity analysis, and these are optimised to simulate the experimental data. For the non-recovering piglet, we investigate several state changes that might explain why some MRS and NIRS signals do not return to their baseline values following the HI insult. We discover that the model can explain this failure better when we include, among other factors such as mitochondrial uncoupling and poor cerebral blood flow restoration, the death of around 40% of the brain tissue. Copyright

Comparing behaviour of simplified metabolic submodels to BrainSignals.

<p><b>A</b> Steady state simulations of CMRO₂ for different levels of arterial blood pressure (<i>P_a</i>), oxygen saturation (<i>S_aO₂</i>) and partial pressure of carbon dioxide (<i>P_aCO₂</i>). Model variants M1 and M2 reproduce the BrainSignals behaviour closely, whereas M3 exhibits substantial deviations. <b>B</b> Time courses of model outputs driven by real experimental data. The three plots show values simulated from the same adult hypercapnia data as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126695#pone.0126695.g007" target="_blank">Fig 7</a>. For estimation of some output values, such as CBF (bottom), behaviour is dominated by the blood flow submodel and the impact of swapping the metabolic submodels is negligible. More metabolically-relevant outputs such as CMRO₂ and ΔoxCCO again show good correspondence for variants M1 and M2, while M3’s behaviour is very poor. (Average output distances for simulations from all experimental subjects are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126695#pone.0126695.t003" target="_blank">Table 3</a>.)</p

Simplifying the metabolic submodel.

<p><b>A</b> The main structure of the BrainSignals metabolic submodel, with parameters omitted. Although the number of species is small and the reactions apparently simple, the reaction rates are governed by a complex network of interactions. <b>B, C, D, E</b> Progressively simplified submodel variants M0–M3, corresponding to Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126695#pone.0126695.e023" target="_blank">M0.1</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126695#pone.0126695.e033" target="_blank">M3.2</a> in the text.</p

The modelled part of the mitochondrial electron transport chain.

<p>The electron transfer is indicated by red arrows, while the grey arrows show corresponding species changes. Quantities enclosed in unfilled circles are not explicitly modelled. The CCO Cu_A and a₃ centres are assumed present at constant concentration, so any change in the oxidised form implies an opposite change in the reduced form. The initial reducing substrate (denoted CC) is neglected on the assumption that O₂ and H⁺ are limiting, and the H₂O product vanishes into an effectively-infinite background. Protons are exported from the matrix by each electron transport step, returning at rate <i>L</i>, and the membrane potential <i>ψ</i> is affected by the net proton flux.</p

Comparing submodel combinations.

<p><b>A</b> Steady state simulations of CMRO₂ for different levels of arterial blood pressure (<i>P_a</i>), oxygen saturation (<i>S_aO₂</i>) and partial pressure of carbon dioxide (<i>P_aCO₂</i>). Behaviour is dominated by the blood flow submodel, with different metabolic submodels producing no discernible effect. As in the isolated tests, variant B1 is clearly superior for <i>P_a</i> autoregulation. <b>B</b> Time courses of model outputs driven by real experimental data. The three plots show values simulated from the same adult hypercapnia data as in previous figures. All models produce rather similar dynamic results. CBF and CMRO₂ are both largely determined by blood flow. ΔoxCCO varies also with choice of metabolic submodel, although the deviations are generally small. (Average output distances for simulations from all experimental subjects are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126695#pone.0126695.t003" target="_blank">Table 3</a>.)</p

Overall structure shared by BrainSignals and the simplified models.

<p>Systemic measurements of mean arterial blood pressure, arterial oxygen saturation and partial pressure of CO₂, together with a parameter specifying the relative demand, serve as model inputs. A blood flow submodel represents the delivery of oxygenated blood from the arteries through the capillary bed to the veins, and an oxygen transport submodel estimates diffusion of dissolved O₂ from the capillary blood to the brain tissue. Delivered oxygen is utilised by a metabolic submodel, with an external dependence on the demand. Finally, a measurement submodel translates the internal states of the blood flow and metabolic submodels into observable outputs. Circles within each submodel indicate the local state variables—note that the measurement submodel has no state of its own.</p

Dependencies between the reaction rate constants and variables in the metabolic submodel.

<p>All rate constants exhibit a very nearly linear relationship to the model variables on which they are primarily dependent, suggesting that a good approximation can be obtained with a linear model. However, the relationships are also very highly correlated, implying the model is overdetermined and further reduction is required.</p

Relative sizes of the different variants of the blood flow submodel.

<p>Relative sizes of the different variants of the blood flow submodel.</p