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. Introduction 1 Systems biology models are used to understand complex biological and physiological 2 systems comprised of large numbers of individual elements that give rise to emergent 3 behaviours. These complex systems are dependent on both the properties of the whole 4 network and on the individual elements [1]. This inherent complexity within the models 5 can lead to difficulties in determining how best to interpret information obtained 6 through their use.7At University College London, the family of BrainSignals models (and the 8 BRAINCIRC model on which they are based) are used to understand the brain's 9 dynamics via a systems biology approach. They bring together a number of 10 mathematical models relating to different aspects of blood circulation, oxygen transport 11 and oxygen metabolism within the brain in order to develop a more complete model that 12 can be used alongside experimental data to simulate physiological phenomena of the 13 brain, such as autoregulation and neural activation. This allows us to understand how 14 our measurements are linked to specific brain physiological and metabolic mechanisms. 15 All of the models were developed to reproduce broadband near-infrared spectroscopy 16 (NIRS) measurements of brain tissue concentration changes of haemoglobin (oxygenation 17 and haemodynamics) and cytochrome-c-oxidase (mitochondrial metabolism) and vary 18 in their complexity and scope. Table 1 compares the number of reactions, equations, 19 relations, reactions, variables and parameters in three different models. The first model 20 developed was the 'BRAINCIRC' model in 2005 [2]. This built on an earlier circulatory 21 model by Ursino and Lodi [3] and combined models for the biophysics of the circulatory 22 system, the brain metabolic biochemistry and the function of vascular smooth muscle.
23This model was succeeded by the 'BrainSignals' model [4], which simplified the previous 24 'BRAINCIRC' model and added a submodel of mitochondrial metabolism. A number of 25 additional versions were then developed from this, such as the 'BrainPiglet' model [5] 26 which was developed to to simulate the physiological and metabolic processes of the 27 piglet brain often used as the neonatal preclinical model. It involved modifying the 28 default values for 11 of the 107 parameters used and was extended to include simulated 29 measurements for magnetic resonance spectroscopy values that included brain tissue 30 lactate and ATP production, measurements of which are available in piglet studies. 31 This was extended in BrainPiglet v2 to incorporate the effects of ce...