# Brains Trust Research (BRATS)

### Research Group Summary

The group investogates advanced mathematical and numerical models of blood flow in the cerebral tissue and cerebro-vasculature.

It utilises massively parallel architectures such as the Blue Gene/P and Blue Gene/L supercomputers access via the UC HPC supercomputing unit.

We are happy to accept applications from potential interns anywhere in the world.

### Key Contact

### Members - UC Staff

- Timothy David: Group Leader; UC High Performance Computing
- Rua Murray: Researcher; Mathematics and Statistics
- Michael Plank: Researcher; Mathematics and Statistics
- David Wall: Researcher; Mathematics and Statistics
- Constantine Zakkaroff: Researcher; UC High Performance Computing

### Members - UC Students

- Katharina Dormanns
- Christine French
- Jaijus Pallippadan Johny
- Elshin Mathias
- Ealasukanthan Thavanayagam
- Michelle Goodman

### Subject Area: Disciplines

- Science & Technology: Science & Technology

### Relevant funding bodies

- Neurological Foundation of New Zealand
- Royal Society of New Zealand - Marsden Te Apārangi
- National Heart Foundation of New Zealand
- Lottery Health Research Te Tahua Rangahau Hauoratanga

### Research Projects

#### Katharina Dormanns, PhD candidate

Hello, my name is Katharina Dormanns and I am a PhD student at UC HPC. My background is in Biomimetics (also Bionics), a relatively new interdisciplinary science that has the aim to investigate nature’s magnificent inventions and incorporate them into technical solutions. My PhD research focuses on the understanding of neurovascular coupling, i.e. the ability of the vasculature to regulate cerebral perfusion. Recent research suggests that impaired neurovascular coupling is associated with several pathologies such as hypertension, Alzheimer’s Disease and stroke. However, little is known of the complete pathway for this phenomenon and only limited experimental data is available. Nitric oxide from both neuronal activity and endothelial production has been shown to play an important role as a major vasodilator whilst impaired production is associated with Alzheimer’s Disease.

Our research group has developed a numerical model (implemented in a parallel environment) able to describe the process of neurovascular coupling from neuronal activation to vascular response and hence bloodflow regulation. A number of neurovascular units, consisting of astrocytes, smooth muscle cells and endothelial cells lining arterioles, are globally coupled through a space filling H-tree (directed acyclic graph) simulating a vascular tree that is spatially embedded in cerebral tissue and bifurcates into a fine capillary bed.

We show that the model is able to regulate the bloodflow in response to neuronal activity by widening or narrowing of the arteries in a 2-dimensional tissue “slice” of width and depth of the order of millimetres culminating in the dynamic simulation of several million cells. With this spatial model we are able to show the importance of fast diffusing messenger molecules such as nitric oxide that can be locally released by neurons or endothelial cells as a response to increased wall shear stress but also the complex relationship between parallel chemical pathways that make up neurovascular coupling. The model thus allows us to study a number of important pathological scenarios.

##### Publications and Presentations

Dormanns, K.; van Disseldorp, E. J.; Brown, R. G. and David, T. (2014): Neurovascular coupling and the influence of luminal agonists via the endothelium. Journal of Theoretical Biology. http://dx.doi.org/10.1016/j.jtbi.2014.08.029i

Dormanns, K.; Brown, R. G. and David, T. (2014): Dynamic Parallel Simulation of Neurovascular Coupling. Presented at WCB 2014.

Dormanns, K.; Brown, R. G. and David, T. (2014): From experiments to differential equations - Possibilities and limitations of mathematical modelling and simulation of neurovascular coupling. Presented at AWCBR 2014.

Dormanns, K.; Brown, R. G. and David, T. (2013): Say ”NO” to Alzheimer’s! - The importance of an uncommon messenger molecule shown in computational simulations. Presented at AWCBR 2013.

#### Christine French, PhD candidate

**Affects of Changing Terminal Resistance on Blood Flow Through the Circle of Willis**

The primary purpose of the circle of Willis (CW) is to distribute blood to brain tissue in the event of high stenosis or occlusion of one of the main feeding arteries as well as supplying local metabolic demands. Blood flow is influenced by the resistance and compliance of the distal vessels perfusing the cortical tissue. Resistance is inversely proportional to the 4th power of radius and varies depending on metabolic demands. Increased local metabolism releases vasodilating chemicals into the blood stream to replenish resources and discard of waste. It is not fully understood how sensitive the cerebral flow is to these changes. A one-dimensional computer simulation, Nektar, is used to study the effects of decreasing terminal resistance on blood flow through the circle. This shows the workings of the collateral capability of the CW whilst not under stress, such as stenosis or occlusion. Circles containing 'normal' and variation configurations are being utilized. This is essential background work as it is important to understand the flow through this simple model before coupling with an H-Tree model that mimics the bifurcations of the arteries to the cortical tissue. At the end of the arterioles in the tree will be an NVU (neurovascular unit) that simulates the chemical reactions from the lumen to the neuron. The NVUs will be stimulated causing the attached vessel to contract or dilate. This will create a new resistance value for the Nektar model that will in turn calculate a new flow. These two parameters will be passed between the two models creating a dynamic representation of blood flow through a stimulated brain.

##### Publications

French, C.L. ,T. David, R.G. Brown, and J. Alastruey. (2014) Affects of Changing Terminal Resistance on Blood Flow Through the Circle of Willis. Presented at AWCBR 2014, conference proceedings.

#### Jaijus Pallippadan Johny, PhD candidate

**A numerical study into propagation of calcium waves in a population of smooth muscle cells**

Intercellular communication plays an important role in many pathophysiological conditions such as atherosclerosis, hypoperfusion, hyperaemia following with ischeamia, hypertension, diabetes etc. Study of calcium dynamics in a population of blood vessel cells is important to understand the mechanism underlying the development of above mentioned pathophysiological situations. Propagation of calcium waves from the point of stimulation to far distance is controlled by intercellular transport. Gap junction is the key pathway that allow the exchange of information in the form of chemical and electrical signals between cells. Intercellular transport through the gap junction is mediated either by ions or by secondary messengers like IP3 , ATP etc. In this research work, a mathematical model will be developed with appropriate intercellular transport to study the propagation of calcium waves in smooth muscle cells.

##### Publications

**Jaijus, P. J.** and Singh, A. (**2010**), Flow visualization and solute transport in
evaporating droplets, AIChE J., 56:1674-1683.

Gustavo Zarruk, **Jaijus, P. J.** and Atle Jensen (**2011**), Accuracy of PIV/PTV
measurements in bubbly flows, ISMTMF conference, Tianjin, China, September 17-
19.

Ashish, K. Thokchom, Abhishek, K. Gupta, **Jaijus, P. J.** and Singh, A. (**2013**),
Analysis of Fluid Flow and Particle Transport in Evaporating Droplets Exposed to
Infrared Heating, International Journal of Heat and Mass Transfer, 68: 67-77.

**Jaijus, P. J.** and Tim David (**2013**), A Numerical Study into Minimal Conditions of Arterial Vasomotion, proceedings of WCRI2K13 conference, Thrissur, India, December 17-20, 234-242.

#### Elshin Mathias, PhD candidate (2013-2016)

Supervisors: Prof. Tim David and Dr. Michael Plank

##### Computational modelling of neurovascular coupling pathways with the effects of oxygen dependency of the sodium-potassium exchange pumps (Na+/K+ -ATPase) in the neuronal membrane

Neurovascular coupling is the mechanism by which neural stimulation affects the vascular constriction or dilation and hence blood flow in the brain. This mechanism facilitates the almost instantaneous supply of nutrients (oxygen and glucose) to the region of the brain in need. A disrupted neurovascular coupling is noticed in pathological conditions such as hypertension, Alzheimer disease and ischemic stroke. My project aim is to computationally model the neurovascular coupling mechanism pathways from a neuronal input to the mechanical vessel response with the effects of oxygen dependency of the neuronal membrane for energy (ATP) production. The model framework may help to understand the complex interactions between various structures involved to suggest the exact set of neurovascular coupling pathways and thereby an understanding of the various associated pathological conditions.

This work is funded by College of Engineering and UC High Performance Computing Unit.

##### Publications

Joel, M.E., David, T. and Plank M.J. (2014) Computational modelling of neurovascular coupling pathways with the effects of oxygen dependency of the neuron. Poster presented at AWCBR 2014, conference proceedings.

Joel, M.E. and Anburajan, M. 3D Modeling of Stenotic Internal Carotid Artery Treated with Stent – A CFD Analysis of Blood. International Conference on Computer, Networks and Communication Engineering (ICCNCE) held in Beijing, China, May 2013. doi:10.2991/iccnce.2013.36

Sriraam, N., Balaji, T.S.B., Joel, M.E. and Prasanna, S. A ubiquitous healthcare system using a wearable shirt for a smart home-a pilot study .Biomedical Engineering and Sciences (IECBES), 2010 IEEE EMBS conference. doi:10.1109/IECBES.2010.5742229

#### Ealasukanthan Thavanayagam, PhD candidate

__Current project description__

Biological structures are heterogeneous on many scales such as nano scale, micro scale and macro scale. As a result, an attempt to incorporate these structures poses difficulties to the mathematical modeller because of the computational size of the model. Also, there are hundreds of thousands of homogenic (same type) and heterogenic (different type) biological cells, and gap junctions between them. But within each biological cell there are thousands of nonlinear ion pathways that are nano scale structures. Mathematical models of these communities of cells are typically a system of thousands of millions of ordinary differential equations requiring simulation on distributed high performance computer. However, another way to approach this problem is to use homogenisation theory to obtain a small number of partial differential equations which will give mathematical means of obtaining macro scale behaviour. The goal of this project is to further develop the homogenisation partial differential equations so far derived into a more comprehensive and cohesive model so as to be able to predict the communication protocols likely to being play between these homogenic and heterogenic cell types.

__Other projects initiated__

Pharmacokinetic study of time dependent urinary excretion of metabolite in human. Collaborator: Professor Choi-Hong Lai, University of Greenwich, London.

Further existence of approximate first integrals for ordinary differential equations and its approximate group invariant solutions.

Collaborator: Dr Andrew Gratian Johnpillai, Eastern University, Sri Lanka.

__Research Interest__

**Mathematical Medicine**

- Cellular communication in the artery and its pathological initiation and progression.
- Pharmacokinetic modelling of drugs in human organs, and subsequent risk assessment and suggestion for clinical trials.

**Industrial Mathematics**

- Mathematical modelling in material moulding.

**Applied Mathematics **

- Construction of approximate conservation laws/first integrals for nonlinear PDEs/ODEs, and group-invariant solutions.

__Conference Publications__

Ealasukanthan Thavanayagam, David J N Wall, Tim David, A Study of Arterial Cellular Communication and Homoginisation of Homocellular Coupling, ICMCMM, 2013, MACFAST, India. (Abstract)

T. Ealasukanthan, A. G. Johnpillai, Integration of Nonlinear Differential Equations using Lie Point Symmetries, 5th Annual Research Session, 2006, proceedings, 42-50, EUSL, Sri Lanka.

#### Michelle Goodman

My background is Mechanical Engineering with a focus in Bio-engineering. My PhD research title is “Homogenisation Theory Applied to Coupled Mammalian Cells”

Up to 20% of the population suffer from migraines. Approximately three quarters of those affected are female. There is now some indication that the perfusion of blood to the brain tissue is related to migraine. One of the common symptoms prior to a full migraine attack can be disturbed vision known as a visual “Aura”. These auras are thought to be caused by Cortical Spreading Depression (CSD); a slow moving large amplitude wave consisting of potassium K+ ions traversing the occipital lobe in the brain.

//en.wikipedia.org/wiki/Occipital_lobe#Structure

We try to model and thereby understand this phenomenon using a mathematical formal procedure called homogenisation. This is really a way of finding a continuous equation for what is in reality millions of linked neurons and other cells in the brain. This mathematical model then provides spatial and temporal simulations of the potassium waves.

The motivation and purpose of my PhD research is summed up by the following questions.

- Can homogenisation theory accurately capture CSD behaviour?
- To what level of does mathematical homogenisation of the domain change the effects of cellular structure on CSD behaviour?
- What type of model elements would make homogenisation impossible (model non-linearity, discontinuity)?
- What are the physiological mechanical processes that could potentially benefit from this homogenisation process?