Computational modelling of the piglet brain to simulate near-infrared spectroscopy and magnetic resonance spectroscopy data collected during oxygen deprivation

The influence of carbon dioxide on cerebral metabolism and oxygen consumption: combining multimodal monitoring with dynamic systems modelling

Hypercapnia increases cerebral blood flow. The effects on cerebral metabolism remain incompletely understood although studies show an oxidation of cytochrome c oxidase, Complex IV of the mitochondrial respiratory chain. Systems modelling was combined with previously published non-invasive measurements of cerebral tissue oxygenation, cerebral blood flow, and cytochrome c oxidase redox state to evaluate any metabolic effects of hypercapnia. Cerebral tissue oxygen saturation and cytochrome oxidase redox state were measured with broadband near infrared spectroscopy and cerebral blood flow velocity with transcranial Doppler ultrasound. Data collected during 5-min hypercapnia in awake human volunteers were analysed using a Fick model to determine changes in brain oxygen consumption and a mathematical model of cerebral hemodynamics and metabolism (BrainSignals) to inform on mechanisms. Either a decrease in metabolic substrate supply or an increase in metabolic demand modelled the cytochrome oxidation in hypercapnia. However, only the decrease in substrate supply explained both the enzyme redox state changes and the Fick-calculated drop in brain oxygen consumption. These modelled outputs are consistent with previous reports of CO2 inhibition of mitochondrial succinate dehydrogenase and isocitrate dehydrogenase. Hypercapnia may have physiologically significant effects suppressing oxidative metabolism in humans and perturbing mitochondrial signalling pathways in health and disease.

Computational analysis of cortical neuronal excitotoxicity in a large animal model of neonatal brain injury

BACKGROUND

Neonatal hypoxic brain injury is a major cause of intellectual and developmental disability. Hypoxia causes neuronal dysfunction and death in the developing cerebral cortex due to excitotoxic Ca²⁺-influx. In the translational piglet model of hypoxic encephalopathy, we have previously shown that hypoxia overactivates Ca²⁺/Calmodulin (CaM) signaling via Sarcoma (Src) kinase in cortical neurons, resulting in overexpression of proapoptotic genes. However, identifying the exact relationship between alterations in neuronal Ca²⁺-influx, molecular determinants of cell death, and the degree of hypoxia in a dynamic system represents a significant challenge.

METHODS

We used experimental and computational methods to identify molecular events critical to the onset of excitotoxicity-induced apoptosis in the cerebral cortex of newborn piglets. We used 2-3-day-old piglets (normoxic [Nx], hypoxic [Hx], and hypoxic + Src-inhibitor-treatment [Hx+PP2] groups) for biochemical analysis of ATP production, Ca²⁺-influx, and Ca²⁺/CaM-dependent protein kinase kinase 2 (CaMKK2) expression. We then used SimBiology to build a computational model of the Ca²⁺/CaM-Src-kinase signaling cascade, simulating Nx, Hx, and Hx+PP2 conditions. To evaluate our model, we used Sobol variance decomposition, multiparametric global sensitivity analysis, and parameter scanning.

RESULTS

Our model captures important molecular trends caused by hypoxia in the piglet brain. Incorporating the action of Src kinase inhibitor PP2 further validated our model and enabled predictive analysis of the effect of hypoxia on CaMKK2. We determined the impact of a feedback loop related to Src phosphorylation of NMDA receptors and activation kinetics of CaMKII. We also identified distinct modes of signaling wherein Ca²⁺ level alterations following Src kinase inhibition may not be a linear predictor of changes in Bax expression. Importantly, our model indicates that while pharmacological pre-treatment significantly reduces the onset of abnormal Ca²⁺-influx, there exists a window of intervention after hypoxia during which targeted modulation of Src-NMDAR interaction kinetics in combination with PP2 administration can reduce Ca²⁺-influx and Bax expression to similar levels as pre-treatment.

CONCLUSIONS

Our model identifies new dynamics of critical components in the Ca²⁺/CaM-Src signaling pathway leading to neuronal injury and provides a feasible framework for drug efficacy studies in translational models of neonatal brain injury for the prevention of intellectual and developmental disabilities.

Hydrogen and therapeutic gases for neonatal hypoxic-ischemic encephalopathy: potential neuroprotective adjuncts in translational research

Numerous studies have examined the potential use of therapeutic gases for the treatment of various neurological disorders. Hydrogen gas, a promising neuroprotective agent, has been a focus of study due to its potent antioxidative properties. In translational research into adult diseases, hydrogen has been shown to be neuroprotective in disorders such as cerebral ischemia and traumatic brain injury, and in neurodegenerative diseases such as Alzheimer's disease. Animal and human studies have verified the safety and feasibility of molecular hydrogen. However, despite extensive research on its efficacy in adults, only a few studies have investigated its application in pediatric and neonatal medicine. Neonatal hypoxic-ischemic encephalopathy (HIE) is characterized by damage to neurons and other cells of the nervous system. One of the major contributing factors is excessive exposure to oxidative stress. Current research interest in HIE is shifting toward new neuroprotective agents, as single agents or as adjuncts to therapeutic hypothermia. Here, we review therapeutic gases, particularly hydrogen, and their potentials and limitations in the treatment of HIE in newborns. IMPACT: Translational animal models of neonatal HIE are a current focus of research into the therapeutic usefulness of various gases. Hydrogen ventilation as a single agent or in combination with therapeutic hypothermia shows short- and long-term neuroprotection in neonatal translational HIE models. The optimal target severity for therapeutic interventions should be well established to improve outcomes.

Systems Biology Model of Cerebral Oxygen Delivery and Metabolism During Therapeutic Hypothermia: Application to the Piglet Model

Hypoxic ischaemic encephalopathy (HIE) is a significant cause of death and disability. Therapeutic hypothermia (TH) is the only available standard of treatment, but 45-55% of cases still result in death or neurodevelopmental disability following TH. This work has focussed on developing a new brain tissue physiology and biochemistry systems biology model that includes temperature effects, as well as a Bayesian framework for analysis of model parameter estimation. Through this, we can simulate the effects of temperature on brain tissue oxygen delivery and metabolism, as well as analyse clinical and experimental data to identify mechanisms to explain differing behaviour and outcome. Presented here is an application of the model to data from two piglets treated with TH following hypoxic-ischaemic injury showing different responses and outcome following treatment. We identify the main mechanism for this difference as the Q10 temperature coefficient for metabolic reactions, with the severely injured piglet having a median posterior value of 0.133 as opposed to the mild injury value of 5.48. This work demonstrates the use of systems biology models to investigate underlying mechanisms behind the varying response to hypothermic treatment.

A Bayesian framework for the analysis of systems biology models of the brain

Systems biology models are used to understand complex biological and physiological systems. Interpretation of these models is an important part of developing this understanding. These models are often fit to experimental data in order to understand how the system has produced various phenomena or behaviour that are seen in the data. In this paper, we have outlined a framework that can be used to perform Bayesian analysis of complex systems biology models. In particular, we have focussed on analysing a systems biology of the brain using both simulated and measured data. By using a combination of sensitivity analysis and approximate Bayesian computation, we have shown that it is possible to obtain distributions of parameters that can better guard against misinterpretation of results, as compared to a maximum likelihood estimate based approach. This is done through analysis of simulated and experimental data. NIRS measurements were simulated using the same simulated systemic input data for the model in a ‘healthy’ and ‘impaired’ state. By analysing both of these datasets, we show that different parameter spaces can be distinguished and compared between different physiological states or conditions. Finally, we analyse experimental data using the new Bayesian framework and the previous maximum likelihood estimate approach, showing that the Bayesian approach provides a more complete understanding of the parameter space.

Systems biology models are mathematical representations of biological processes that reproduce the overall behaviour of a biological system. They are comprised by a number of parameters representing biological information. We use them to understand the behaviour of biological systems, such as the brain. We do this by fitting the model’s parameter to observed or simulated data; and by looking at how these values change during the fitting process we investigate the behaviour of our system. We are interested in understanding differences between a healthy and an injured brain. Here we outline a statistical framework that uses a Bayesian approach during the fitting process that can provide us with a distribution of parameters rather than single parameter number. We apply this method when simulating the physiological responses between a healthy and a vascular compromised brain to a drop in oxygenation. We then use experimental data that demonstrates the healthy brain response to an increase in arterial CO2 and fit our brain model predictions to the measurements. In both instances we show that our approach provides more information about the overlap between healthy and unhealthy brain states than a fitting process that provides a single value parameter estimate.

WeBCMD: A cross-platform interface for the BCMD modelling framework

Multimodal monitoring of the brain generates a great quantity of data, providing the potential for great insight into both healthy and injured cerebral dynamics. In particular, near-infrared spectroscopy can be used to measure various physiological variables of interest, such as haemoglobin oxygenation and the redox state of cytochrome-c-oxidase, alongside systemic signals, such as blood pressure. Interpreting these measurements is a complex endeavour, and much work has been done to develop mathematical models that can help to provide understanding of the underlying processes that contribute to the overall dynamics. BCMD is a software framework that was developed to run such models. However, obtaining, installing and running this software is no simple task. Here we present WeBCMD, an online environment that attempts to make the process simpler and much more accessible. By leveraging modern web technologies, an extensible and cross-platform package has been created that can also be accessed remotely from the cloud. WeBCMD is available as a Docker image and an online service.

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.

BrainSignals Revisited: Simplifying a Computational Model of Cerebral Physiology

Multimodal monitoring of brain state is important both for the investigation of healthy cerebral physiology and to inform clinical decision making in conditions of injury and disease. Near-infrared spectroscopy is an instrument modality that allows non-invasive measurement of several physiological variables of clinical interest, notably haemoglobin oxygenation and the redox state of the metabolic enzyme cytochrome c oxidase. Interpreting such measurements requires the integration of multiple signals from different sources to try to understand the physiological states giving rise to them. We have previously published several computational models to assist with such interpretation. Like many models in the realm of Systems Biology, these are complex and dependent on many parameters that can be difficult or impossible to measure precisely. Taking one such model, BrainSignals, as a starting point, we have developed several variant models in which specific regions of complexity are substituted with much simpler linear approximations. We demonstrate that model behaviour can be maintained whilst achieving a significant reduction in complexity, provided that the linearity assumptions hold. The simplified models have been tested for applicability with simulated data and experimental data from healthy adults undergoing a hypercapnia challenge, but relevance to different physiological and pathophysiological conditions will require specific testing. In conditions where the simplified models are applicable, their greater efficiency has potential to allow their use at the bedside to help interpret clinical data in near real-time.

Investigation of cerebral autoregulation in the newborn piglet during anaesthesia and surgery

The relationship between cerebral autoregulation (CA) and the neurotoxic effects of anaesthesia with and without surgery is investigated. Newborn piglets were randomly assigned to receive either 6 h of anaesthesia (isoflurane) or the same with an additional hour of minor surgery. The effect of the spontaneous changes in mean arterial blood pressure (MABP) on the cerebral haemodynamics (oxy- and deoxy-haemoglobin, HbO2 and Hb) was measured using transverse broadband near-infrared spectroscopy (NIRS). A marker for impaired CA, concordance between MABP and intravascular oxygenation (HbD = HbO2 - Hb) in the ultra-low frequency domain (0.0018-0.0083 Hz), was assessed using coherence analysis. Presence of CA impairment was not significant but found to increase with surgical exacerbation. The impairment did not correlate with histological outcome (presence of cell death, apoptosis and microglial activation in the brain).

Brain mitochondrial oxidative metabolism during and after cerebral hypoxia-ischemia studied by simultaneous phosphorus magnetic-resonance and broadband near-infrared spectroscopy

BACKGROUND

Multimodal measurements combining broadband near-infrared spectroscopy (NIRS) and phosphorus magnetic resonance spectroscopy ((31)P MRS) assessed associations between changes in the oxidation state of cerebral mitochondrial cytochrome-c-oxidase (Δ[oxCCO]) and (31)P metabolite peak-area ratios during and after transient cerebral hypoxia-ischemia (HI) in the newborn piglet.

METHODS

Twenty-four piglets (aged<24 h) underwent transient HI (inspired oxygen fraction 9% and bilateral carotid artery occlusion for ~20 min). Whole-brain (31)P MRS and NIRS data were acquired every minute. Inorganic phosphate (Pi)/epp, phosphocreatine (PCr)/epp, and total nucleotide triphosphate (NTP)/epp were measured by (31)P MRS and were plotted against Δ[oxCCO] during HI and recovery (epp=exchangeable phosphate pool=Pi+PCr+2γ-NTP+β-NTP).

RESULTS

During HI Δ[oxCCO], PCr/epp and NTP/epp declined and Pi/epp increased. Significant correlations were seen between (31)P ratios and Δ[oxCCO]; during HI a threshold point was identified where the relationship between Δ[oxCCO] and both NTP/epp and Pi/epp changed significantly. Outcome at 48 h related to recovery of Δ[oxCCO] and (31)P ratios 1h post-HI (survived: 1-h NTP/epp 0.22 ± 0.02, Δ[oxCCO] -0.29 ± 0.50 μM; died: 1-h NTP/epp 0.10 ± 0.04, Δ[oxCCO] -2.41 ± 1.48 μM).

CONCLUSIONS

Both lowered Δ[oxCCO] and NTP/epp 1h post-HI indicated mitochondrial impairment. Animals dying before 48 h had slower recovery of both Δ[oxCCO] and (31)P ratios by 1 h after HI.

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.

Maturation of the mitochondrial redox response to profound asphyxia in fetal sheep

Fetal susceptibility to hypoxic brain injury increases over the last third of gestation. This study examined the hypothesis that this is associated with impaired mitochondrial adaptation, as measured by more rapid oxidation of cytochrome oxidase (CytOx) during profound asphyxia. Methods: Chronically instrumented fetal sheep at 0.6, 0.7, and 0.85 gestation were subjected to either 30 min (0.6 gestational age (ga), n = 6), 25 min (0.7 ga, n = 27) or 15 min (0.85 ga, n = 17) of complete umbilical cord occlusion. Fetal EEG, cerebral impedance (to measure brain swelling) and near-infrared spectroscopy-derived intra-cerebral oxygenation (ΔHb = HbO₂ – Hb), total hemoglobin (THb) and CytOx redox state were monitored continuously. Occlusion was associated with profound, rapid fall in ΔHb in all groups to a plateau from 6 min, greatest at 0.85 ga compared to 0.6 and 0.7 ga (p<0.05). THb initially increased at all ages, with the greatest rise at 0.85 ga (p<0.05), followed by a progressive fall from 7 min in all groups. CytOx initially increased in all groups with the greatest rise at 0.85 ga (p<0.05), followed by a further, delayed increase in preterm fetuses, but a striking fall in the 0.85 group after 6 min of occlusion. Cerebral impedance (a measure of cytotoxic edema) increased earlier and more rapidly with greater gestation. In conclusion, the more rapid rise in CytOx and cortical impedance during profound asphyxia with greater maturation is consistent with increasing dependence on oxidative metabolism leading to earlier onset of neural energy failure before the onset of systemic hypotension.