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Physiological Model

As the capacity to monitor cerebral and systemic physiological parameters increases, so does the requirement for data interpretation methods for the extraction of relevant clinical information from multimodal signals. We are using mathematical models of brain physiology to address this issue.

A large brain circulation and metabolism (BCM) model termed the “BRAINCIRC” model [1] was initially constructed, combining submodels of brain tissue and vascular smooth muscle biochemistry, vascular biophysics, and haemodynamics from many sources (e.g. [2,3,4,5]). More recently we have constructed the simpler “BRAINSIGNALS” model [6] (Figure 1), which retains the keys physiological processes with a reduced size and number of free parameters. Despite the simple representations of physiology, and the lack of cellular or spatial heterogeneity, predictive capabilities of the BRAINSIGNALS model have been confirmed via a number of simulations involving measured data from our hypoxia [7] (e.g. Figure 2) and hypercapnia studies [8].

Brainsignals

Figure 1. An outline of the BRAINSIGNALS model. Pa is arterial blood pressure, SaO2 is arterial oxygen saturation level, PaCO2 is arterial CO2 level. Tissue oxygen saturation (TOS) is a measure of blood oxygen saturation, while ΔoxCCO represents the change in average level of oxidised CuA in cytochrome c oxidase. Both TOS and ΔoxCCO are NIRS signals.

Brainsignals_Output

Figure 2. The ability of the BRAINSIGNALS model to reproduce measured signals during a hypoxia challenge. Modelled (black) and measured (red) A) TOS and B) ΔoxCCO. The apparent noise in the model outputs reflects the real physiological data used as a model input.

Model Individualisation

In a clinical context a model must be able to inform not only on averaged behaviour, but also on the behaviour of individuals, who may display a wide range of natural physiological and pathophysiological variation. In order to maximise the ability of the model to describe the physiology of a particular individual a reparametrisation of the model is performed. Given prior knowledge of a subject the success of the reparametrisation is determined via its ability to reproduce new unseen data from the same individual. In this context we have presented work taking steps towards model individualisation using data from our hypoxia studies [9]. Part of an experimental data set is used to optimise the model such that the predictive capabilities of the model are improved for the remaining data (Figure 3).

Hypoxia_Challenge

Figure 3. Modelled and measured ΔHbdiff signals during a hypoxic challenge. The bold line is the optimised model output, grey line the unoptimised model while the dashed line is the measured data.

References

  1. Banaji M., Tachtsidis I., Delpy D., and Baigent S. "A physiological model of cerebral blood flow control," Mathematical Biosciences (2005) 194(2):125-173 [URL]

  2. Ursino M. and Lodi C.A. "Interaction among autoregulation, CO2 reactivity, and intracranial pressure: a mathematical model," American Journal of Physiology: Heart and CirculatoryPhysiology (1998) 274(5):H1715-H1728 [URL]

  3. Aubert A. and Costalat R. "A model of the coupling between brain electrical activity, metabolism, and hemodynamics: application to the interpretation of functional neuroimaging," NeuroImage (2002) 17(3):1162-1181 [URL]

  4. Cortassa S., Aon M.A., Marbán E., Winslow R.L., and O'Rourke, B. "An Integrated Model of Cardiac Mitochondrial Energy Metabolism and Calcium Dynamics," Biophysical Journal (2003) 84:2734-2755 [URL]

  5. Korzeniewski B. "Theoretical studies on the regulation of oxidative phosphorylation in intact tissues," Biochimica et Biophysica Acta (2001) 1504(1):31-45 [URL]

  6. Banaji M., Mallet A., Elwell C.E., Nicholls P., and Cooper C.E., "A model of brain circulation and metabolism: NIRS signal changes during physiological challenges," PLoS Computational Biology (2008) 4(11): e1000212 [URL]

  7. Banaji M., Mallet A., Elwell C.E., Nicholls P., Tachtsidis I., Smith M., and Cooper C.E., "Modelling of mitochondrial oxygen consumption and NIRS detection of cytochrome oxidase redox state," Advances in Experimental Medicine and Biology (2010) 662:285-291 [URL] [Poster]

  8. Tachtsidis I., Pritchard C., Tisdall M.M., Leung T.S., Elwell C.E., Smith, M., "Hypercapnea does not consistently increase the oxidation of cytochrome c oxidase in traumatic brain injury." Journal of Cerebral Blood Flow and Metabolism (2009) 29:S197 [URL] [Poster]

  9. Jelfs B., Banaji M., Tachtsidis I., Cooper C.E., and Elwell C.E. "Modelling Noninvasively Measured Cerebral Signals during a Hypoxemia Challenge: Steps towards Individualised Modelling." PLoS ONE (2012) 7(6): e38297 [URL] [Poster]

Papers

  • Banaji M., Tachtsidis I., Delpy D., Baigent S. "A physiological model of cerebral blood flow control," Mathematical Biosciences (2005) 194(2):125-173 [URL]
  • Banaji M., Mallet A., Elwell C.E., Nicholls P., and Cooper C.E., "A model of brain circulation and metabolism: NIRS signal changes during physiological challenges," PLoS Computational Biology (2008) 4(11): e1000212 [URL]
  • Jelfs B., Banaji M., Tachtsidis I., Cooper C.E., and Elwell C.E. "Modelling Noninvasively Measured Cerebral Signals during a Hypoxemia Challenge: Steps towards Individualised Modelling." PLoS ONE (2012) 7(6): e38297 [URL]

Posters

  • Individualised optimisation of modelled cerebral oxygenation near-infrared spectroscopy signals. Jelfs B, Panovska-Griffiths J, Tachtsidis I, Banaji M, Elwell C. Optical Society of America Biomedical Optics Topical Meeting 2012, Miami, USA (May 2012) [Poster]
  • Modelling of mitochondrial oxygen consumption and NIRS detection of cytochrome oxidase. Cooper CE, Mallet A, Elwell CE, Nicholls P, Tachtsidis I, Banaji M. Conference of the International Society of Oxygen Transport to Tissue 2008, Sapporo, Japan (Aug 2008) [Poster]
  • Modelling the Cerebral Circulation. Banaji M, Tachtsidis I, Donnell P, Delpy D, Baigent S. IRC Review Meeting 2007, London, UK, (April 2007) [Poster]
  • The Application of the BRAINCIRC Model in Clinical Scenarios. Tachtsidis I, Banaji M, Tisdall M, Smith M, Baigent S, Leung TS, Elwell CE, Delpy DT. IRC Review Meeting 2007, London, UK, (April 2007) [Poster]
  • The Application of a Model of Human Brain Circulation to Head Trauma Patients: A Computational Systems Biology Approach. Tachtsidis I, Banaji M, Tisdall M, Smith M, Baigent S, Elwell CE, Delpy DT. Gordon Conference 2006, Oxford, UK (Aug 2006) [Poster]
  • Multimodal modelling simulation of hypercapnoeic challenge in acutely brain injured adult patient. Tisdall M, Tachtsidis I, Banaji M, Delpy DT, Elwell CE, Smith M. IRC Meeting 2005, Manchester, UK (Nov 2005) [Poster]

Models

Our models have been created using the BRAINCIRC modelling environment:
http://braincirc.sourceforge.net

For details of our physiological model please see:
http://www.medphys.ucl.ac.uk/braincirc/index.html

Work currently being carried out within the Multimodal Spectroscopy Group has adapted and extended the above model to describe the neonatal brain:
http://www.ucl.ac.uk/~ucbptmo/index.html