The UCL brain models

The Biomedical Optics Research Laboratory (BORL) at UCL’s department of Medical Physics lays claim to a number of mathematical and compu-tational models of brain metabolism and circulation. This work spans al-most a decade to date, and runs alongside an extensive research effort into non-invasive clinical measurement techniques, including near infrared spec-troscopy. These measurement techniques are detailed more thoroughly in the next chapter.

4.3.1 History of model development at UCL

The models presented in this thesis are derived from a number of previously published brain models – a timeline of which is illustrated in Table 4.3. A brief history and description of these models is summarised below.

BrainCirc

The first model, an elaborate adult brain model, was published in 2005 by Banaji et al (Banaji et al. 2005). Three preexisting models of circulation, brain biochemistry and vascular smooth muscle function were united in one.

Thus, a physiological approach was used and the model was constructed in a modular way so as to enable easy modification.

The model encompasses three ’sites’: blood vessels, brain tissue and vascular smooth muscle. Each of these are further divided into different components:

arteries, arterioles, capillaries and veins in the vascular system, extracellular, intracellular, cytoplasmic and mitochondrial compartments in brain tissue, and vascular smooth muscle in the proximal and distal arterial segments.

Biochemical reactions are represented as mass action or Michaelis Menten equations. Other equations included are those representing the biomechan-ics of vessel walls and circulation, and volume balance equations between different compartments derived from conservation laws.

BrainCirc is the largest of all the models in this series, including a vast number of variables and parameters. In order to manage and run such a large and complex model, the BRAINCIRC modelling environment was built. This software focuses on the biological processes (eg. chemical reac-tions) that are central to the model. These can be input into the interface

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Figure 4.16: Main processes and compartments of the Braincirc model(Banaji et al.

2005).

and the environment then converts them into differential equations (Banaji 2005).

BrainSignals

Technical developments allowed the measurement of oxidised CCO concen-tration using NIRS. In order to better understand and interpret these mea-surements, the model was extended to simulate them. The BrainCirc model was first greatly simplified in order to maintain the possibility of optimis-ing parameters for each individual patient. The BrainSignals model was then used to successfully simulate ∆oxCCO and tissue oxygen saturation (TOS) measurements from patients undergoing hypoxia and hypercapnia challenges (Banaji et al. 2008). The model was later also shown to predict data from a hypoxemia challenge (low blood oxygen levels) (Jelfs et al. 2012).

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Figure 4.17: Schematic of the BrainSignals model (Banaji et al. 2008).

BrainPiglet

Following the commencement of hypoxia-ischaemia experiments in piglets by a collaborating research group, in 2012 Moroz et al. published the first version of the BrainPiglet model. This is an adaptation and extension of the BrainSignals model (Moroz et al. 2012). 11 of the 107 parameters were altered to suit the piglet brain. The model was also extended to simulate magnetic resonance spectroscopy (MRS) measurements - ATP, PCr, Pi and

lactate - which were recorded simultaneously during the experiments. The next section details this model.

Comparison

The general differences between the BrainCirc, BrainSignals and BrainPiglet v1.0 models are detailed in Table 4.2. Compartments included are volume compartments in reactions and do not include blood compartments. The number of parameters include those that are explicitly set as well as those that are derived from other parameters.

Table 4.2: A comparison of the three models.

BrainCirc BrainSignals BrainPiglet v1.0

Compartments 4 1 2

Reactions 81 5 16

Differential equations 5 5 5

Algebraic relations 72 3 3

Variables 168 12 30

Parameters 697 196 270

Computational environments

With the development of the first model BrainCirc, the team also created a similarly named interface BRAINCIRC to compile the model. The mod-els are encoded as a combination of reactions, differential equations and algebraic relations. However, this interface was ridden with many issues -exasperated further by a lack of proper documentation. A new simpler in-terface has been recently developed by Matthew Caldwell, called BCMD – Table 4.3 Timeline of models of cerebral metabolism produced at UCL

2005 • Braincirc 2008 • BrainSignals 2012 • BrainPiglet v1.0 2013 • BrainPiglet v2.0 2014 • BrainPiglet v2.1

• Brainsignals neonatal

• Baby Brain

Brain/Circulation Model Developer (Figure 4.18). BCMD retains the same logical basis of model construction – the model is described in reactions and differential equations – and uses the same RADAU5 solver, but offers a much better understanding of model behaviour. The interface software and all model definitions are freely available from http://tinyurl.com/ucl-bcmd.

Unlike BRAINCIRC which only runs in a Linux environment, BCMD is also compatible with Windows and Mac environments.

BCMD is mainly written in Python 2.7, however models are translated into C and linked against a Fortran library. It uses the RADAU 5 DAE solver by Hairer and Wanner (1996) – an implicit Runge-Kutta method of order 5 for integrating stiff systems of differential-algebraic equations. BCMD offers a number of functions. In model compilation and running, the graphical user interface (GUI) is able to outline any errors. Initial values of model param-eters can be altered, artificial inputs can be generated (including noise), and outputs can be plotted. The software enables sensitivity analysis (including the morris method used in this thesis) and can generate relevant heatmaps.

It also allows for optimisation of parameter values to better simulate known outputs, using the particle swarming method used in this thesis. BCMD can further be used to create dependency graphs of model variables and parameters such as those presented in the discussion in Chapter 5.

As discussed earlier in this chapter, several other modelling environments are used in systems biology. The systems biology markup language (SBML) (Hucka et al. 2003) and CellML (Cuellar et al. 2003) are the most popular languages for model specification. Both are based on XML and enable the computational representation of biological processes, which must be com-piled using suitable software. Commonly, these software environments do not support the use of time series data, and we have not identified one that does. The models encoded are often perturbed from steady state by altering parameter values, the effect of which may be observed over time.

These environments are hence not compatible with the objective of the UCL metabolism models.

The early BRAINCIRC interface does facilitate the import and export of SBML models. The metabolism models are thus available in SBML format, although their functionality is significantly reduced by the environment.

The BCMD interface may also include a similar feature in the future. MAT-LAB is another popular environment for systems biology models. While

it useful (and has been used) for signal processing of measurements and plotting results, confining the model to MATLAB restricts access to those who have license to use the software. BRAINCIRC and BCMD on the other hand are open-source, and freely available. They also compile the model first before it is run, unlike MATLAB, and so have a lower computational cost.

Figure 4.18: The BRAINCIRC and BCMD modelling environenments.