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Associate Professor Alona Ben-Tal staff profile picture

Contact details +6492136608

Associate Professor Alona Ben-Tal BSc, PhD, MSc, NZMS

Associate Professor in Mathematics

Doctoral Supervisor
School of Mathematical and Computational Sciences

My research is truly interdisciplinary and lies in the fields of applied mathematics, dynamical systems, numerical methods and physiology. My main interest is the integrated behaviour of the cardiorespiratory system and over the years, I have studied different aspects of this system including lung mechanics, gas exchange, neural control of breathing and heart rate control. My research involves mathematical modelling at different levels of complexity and mathematical analysis using a variety of mathematical techniques. 

Professional

Qualifications

  • Bachelor of Science - Israel Institute of Technology (1991)
  • Doctor of Philosophy - University of Auckland (2001)
  • Master of Science - Israel Institute of Technology (1994)

Fellowships and Memberships

  • Member, New Zealand Mathematical Society (Fellow) (2016)

Certifications and Registrations

  • Licence, Supervisor, Massey University

Research Expertise

Research Interests

Dynamical systems.

Mathematical modelling.

Numerical methods.

Regulation and function of the cardio-respiratory system.

Thematics

Health and Well-being

Area of Expertise

Field of research codes
Applied Mathematics (010200):
Curriculum and Pedagogy (130200): Education (130000): Education Systems (130100):
Engineering (090000):
Higher Education (130103):
Interdisciplinary Engineering (091500):
Mathematical Sciences (010000):
Medical And Health Sciences (110000): Medical Physiology (111600):
Numerical and Computational Mathematics (010300):
Science, Technology and Engineering Curriculum and Pedagogy (130212):
Systems Physiology (111603)

Keywords

Mathematical Biology and Modelling

Applied Mathematics

Industrial Mathematics

Research Projects

Completed Projects

Project Title: Complexity reduction in neural models

Mathematical models of biological systems provide understanding and predictive power. However, as more information about a particular system is collected, its model becomes increasingly complicated. This makes the models better, because they are becoming more realistic and therefore potentially more useful, but in turn they are becoming harder to simulate and analyse. The aim of this research is to overcome this problem by using recently-developed, so-called 'equation-free' techniques for the study of complex systems, concentrating on a variety of model neural networks. In particular we will study the respiratory neural system. This complex system regulates breathing by sending electrical signals to the diaphragm and other respiratory muscles, causing them to periodically contract and relax. Equation-free techniques allow one to automatically simplify a complex system such as the respiratory neural network by using judiciously designed computer simulations to capture the 'essence' of the original complex system in terms of the correct variables. This provides insights and understanding that cannot be found in any other way.
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Date Range: 2009 - 2012

Funding Body: Marsden Fund - Full

Project Team:

Research Outputs

Journal

Noreen, S., Ben-Tal, A., Elstad, M., Sweatman, WL., Ramchandra, R., & Paton, J. (2022). Mathematical modelling of atrial and ventricular pressure–volume dynamics and their change with heart rate. Mathematical Biosciences. 344
[Journal article]Authored by: Ben-Tal, A., Sweatman, W.

Teaching and Supervision

Teaching Statement

Papers taught recently:

160.203 Calculus.

160.319 Mathematical Modelling.

160.715 Advanced Computational Methods.

Current Doctoral Supervision

Main Supervisor of:

  • Sidra Zafar - Doctor of Philosophy
    Equation-free investigations of heterogeneous networks.

Co-supervisor of:

  • Neelum Bashir - Doctor of Philosophy
    Computational Studies in the Planar Symmetric Few-Body Problem

Completed Doctoral Supervision

Main Supervisor of:

  • 2021 - Shumaila Noreen - Doctor of Philosophy
    Mathematical modelling of the cardiovascular system to study the effects of respiratory sinus arrhythmia and heart failure.
  • 2019 - Syed Zaidi - Doctor of Philosophy
    IS OUR BREATHING OPTIMAL?