Figure 1.
Summary of the main inputs, variables and processes in the model.
Model inputs are enclosed in solid ovals, while outputs are enclosed in dashed ovals. Pa is arterial blood pressure, SaO2 is arterial oxygen saturation level, PaCO2 is arterial CO2 level. TOS and ΔoxCCO are NIRS signals defined in the text.
Figure 2.
Schematic representation of the mitochondrial submodel.
The CuA centre is reduced by some reducing substrate, termed R. It in turn passes its electrons on to a terminal substrate, cyta3. Finally cyta3 is oxidised by oxygen. All processes can in general produce proton motive force Δp, by pumping protons out of the mitochondrial matrix. As a result, they are also inhibited by Δp. The rates of the three processes – initial reduction of CuA, electron transfer to cyta3 and final oxidation of cyta3, are termed f1, f2 and f3, respectively.
Figure 3.
Summary of the main variables and processes in the simplified model.
As in Figure 1, inputs are enclosed in solid ovals, while outputs are enclosed in dashed ovals. Components connected with blood flow have been removed from the model. O2 levels are now directly settable.
Figure 4.
The response of model steady state CBF to blood pressure and PaCO2 changes.
(A) Response to arterial blood pressure changes with data from [44] (red squares) and [45] (green triangles) for comparison. (B) Response to PaCO2 changes with data from [48] (with normal resting blood flow taken as 40 ml/min/100 g) for comparison.
Figure 5.
Model responses to a step up in demand.
(A) Change in CMRO2 (normalised). (B) Change in CBF (normalised). (C) Change in TOS (percent). (D) Change in ΔoxCCO (μM). All parameters are held at normal values apart from u which is stepped up from 1 to 1.2 for a ten second duration, giving rise to an approximately 3.5 percent increase in CMRO2 and an approximately 6 percent increase in blood flow. TOS increased by a little under 1 percent, and ΔoxCCO also increased by about 0.05 μM corresponding to an oxidation of just under 1 percent.
Figure 6.
Response of haemoglobin signals to a step up in demand.
The response in μM of ΔHbO2 (red), ΔHHb (green) and ΔHbt (black) to a step up in demand. The stimulus and parameter values are as in Figure 5. In (A) τu = 0.5 s (the default value). In (B) τu = 1 s. With the slower response time, there is more pronounced transient behaviour including a clear initial decrease in ΔHbO2 before it starts to increase.
Figure 7.
Response of CuA redox state in the simplified model to changes in u.
(A) The time course of oxidised CuA in response to functional activation. As in the in vivo simulations, u was changed from 1 to 1.2 for a ten second duration, resulting in an approximately 1 percent increase in CuA oxidation. (B) The steady state level of CuA oxidation in response to varying levels of activation. u was varied from 0.2 to 100 resulting in variation in CMRO2 from 80 to 170 percent of baseline. CuA oxidation increased steadily.
Figure 8.
Relationship between CMRO2 and mitochondrial oxygen levels during activation.
The full model was run with parameter Ru set to zero so that an increase in demand had no effect on blood flow. Increasing u allowed increases in CMRO2 up to approximately 145 percent of baseline. The three data points shown are calculated from Figure 2 of [55] in which predictions on how tissue oxygen levels in the “lethal corner” should vary with activation level during normoxia are presented.
Figure 9.
Comparison of experimentally measured and modelled CCO redox states.
(A) How the level of reduction of cytochrome c varies with oxygen concentration (redrawn from Figure 5A of [20]). (B) The equivalent data for CuA from model simulations is presented. For the simulation, the reducing substrate is set to be succinate, and the demand parameter u is set to be low (u = 0.4) to represent a high phosphorylation potential.
Figure 10.
The response of steady state CMRO2 to a drop in mitochondrial O2 level.
CMRO2 is in arbitrary units. (A) In coupled mitochondria. (B) Uncoupled mitochondria. As above, for both simulations, the reducing substrate is set to be succinate, so that input to the system is by electron transfer to ubiquinone, and the demand parameter u is set to be low (u = 0.4 in both simulations). For the uncoupled mitochondria, the parameter kunc is raised from its normal value of 1 to a value of 1000 giving an approximately four-fold increase in maximum CMRO2.
Figure 11.
Model response of TOS and ΔoxCCO to a step down in arterial oxygen saturation.
(A) Response of TOS (percent). (B) Response of ΔoxCCO (μM). A hyperaemic effect is seen in both signals.
Figure 12.
Relationship between ΔHbO2, ΔoxCCO and CMRO2 during changes in arterial oxygen saturation.
(A) The model was run with normal parameter values and an approximately linear relationship between ΔHbO2 and ΔoxCCO held. (B) At these same normal parameter values CMRO2 showed an approximately linear relationship with ΔoxCCO. (C) Baseline CMRO2 was lowered to about 60 percent of the normal model baseline, by setting u = 0.1, while normal CBF was also lowered by about the same amount by setting CBFn = 0.007 ml blood per ml brain tissue per second. A more clearly biphasic relationship between ΔHbO2 and ΔoxCCO was obtained. (D) Again, at the changed parameter values, CMRO2 had an approximately linear relationship with ΔoxCCO.
Figure 13.
Responses of measured and modelled TOS and ΔoxCCO during a hypoxia challenge.
Measured (red) and modelled (black) responses of (A) TOS (%) and (B) ΔoxCCO (μM) are shown. Details are given in the text.
Figure 14.
Responses of measured and modelled TOS during a hypercapnia challenge.
Measured (red) and modelled (black) responses of TOS: (A) For subject 1 without optimisation. (B) For subject 1 following optimisation of AVRn and RC, which gave values of AVRn = 1.28 and RC = 1.31. (C) For subject 2 without optimisation. (D) For subject 2 following optimisation of AVRn and RC, which gave values of AVRn = 0.286 and RC = 1.62.