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

Associate Professor

School of Natural 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

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

Fellowships and Memberships

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

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): Biological Mathematics (010202): Dynamical Systems in Applications (010204): Mathematical Sciences (010000): Numerical and Computational Mathematics (010300)

Keywords

Mathematical Biology and Modelling

Applied Mathematics

Industrial Mathematics

Research Projects

Summary of Research Projects

Position	Current	Completed
Project Leader	2	3
Team Member	0	1

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:

Prof Carlo Laing - Project Leader
A/Pro Alona Ben-Tal - Team Member

Project Title: A mechanism for Chayne-Stokes respiration

Date Range: 2006 - 2008

Funding Body: Royal Society of New Zealand

Project Team:

A/Pro Alona Ben-Tal - Project Leader

Research Outputs

Journal

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Ben-Tal, A., Wang, Y., & Leite, MCA. (2019). The logic behind neural control of breathing pattern. Scientific Reports. 9(1)
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A. (2018). Mathematical Modelling Disproves Decades-old Hypothesis, a Potential New Way to Treat Heart Disease.. SIAM news.
[Journal article]Authored by: Ben-Tal, A.

Ben-Tal, A., & Kevrekidis, IG. (2016). Coarse-graining and simplification of the dynamics seen in bursting neurons. SIAM Journal on Applied Dynamical Systems. 15(2), 1193-1226
[Journal article]Authored by: Ben-Tal, A.

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Elstad, M., O Callaghan, EL., Smith, AJ., Ben-Tal, A., & Ramchandra, R. (2018). Cardiorespiratory interactions in humans and animals: Rhythms for life. American Journal of Physiology - Heart and Circulatory Physiology. 315(1), H6-H17
[Journal article]Authored by: Ben-Tal, A.

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Harvey, EP., & Ben-Tal, A. (2016). Robust Unidirectional Airflow through Avian Lungs: New Insights from a Piecewise Linear Mathematical Model. PLoS Computational Biology. 12(2)
[Journal article]Authored by: Ben-Tal, A.

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Molkov, YI., Shevtsova, NA., Park, C., Ben-Tal, A., Smith, JC., Rubin, JE., . . . Rybak, IA. (2014). A closed-loop model of the respiratory system: Focus on hypercapnia and active expiration. PLoS ONE. 9(10)
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A., Shamailov, SS., & Paton, JFR. (2014). Central regulation of heart rate and the appearance of respiratory sinus arrhythmia: New insights from mathematical modeling. Mathematical Biosciences. 255(1), 71-82
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A., & Tawhai, MH. (2013). Integrative approaches for modeling regulation and function of the respiratory system. Wiley Interdisciplinary Reviews: Systems Biology and Medicine. 5(6), 687-699
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A., Shamailov, SS., & Paton, JFR. (2012). Evaluating the physiological significance of respiratory sinus arrhythmia: Looking beyond ventilation-perfusion efficiency. Journal of Physiology. 590(8), 1989-2008
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A. (2012). Computational models for the study of heart-lung interactions in mammals. Wiley Interdisciplinary Reviews: Systems Biology and Medicine. 4(2), 163-170
[Journal article]Authored by: Ben-Tal, A.

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Kiataramkul, C., Wake, GC., Ben-Tal, A., & Lenbury, Y. (2011). Optimal nutritional intake for fetal growth. Mathematical Biosciences and Engineering. 8(3), 723-732
[Journal article]Authored by: Ben-Tal, A., Wake, G.

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Ben-Tal, A., & Smith, JC. (2010). Control of breathing: Two types of delays studied in an integrated model of the respiratory system. Respiratory Physiology and Neurobiology. 170(1), 103-112
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A., & Smith, JC. (2008). A model for control of breathing in mammals: Coupling neural dynamics to peripheral gas exchange and transport. Journal of Theoretical Biology. 251(3), 480-497
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A. (2006). Simplified models for gas exchange in the human lungs. Journal of Theoretical Biology. 238(2), 474-495
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A. (2002). Symmetry restoration in a class of forced oscillators. Physica D: Nonlinear Phenomena. 171(4), 236-248
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A., Kirk, V., & Wake, G. (2001). Banded chaos in power systems. IEEE Transactions on Power Delivery. 16(1), 105-110
[Journal article]Authored by: Ben-Tal, A., Wake, G.

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Ben-Tal, A., Shein, D., & Zissu, S. (1999). Studying ferroresonance in actual power systems by bifurcation diagram. Electric Power Systems Research. 49(3), 175-183
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A., Bar-Yoseph, PZ., & Flashner, H. (1996). Space-time spectral element method for optimal slewing of a flexible beam. International Journal for Numerical Methods in Engineering. 39(18), 3101-3121
[Journal article]Authored by: Ben-Tal, A.

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Ben-Tal, A., Bar-Yoseph, P., & Flashner, H. (1995). Optimal maneuver of a flexible arm by space-time finite element method. Journal of Guidance, Control, and Dynamics. 18(6), 1459-1462
[Journal article]Authored by: Ben-Tal, A.

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Teaching and Supervision

Teaching Statement

Papers taught recently:

160.203 Calculus.

160.319 Mathematical Modelling.

160.715 Advanced Computational Methods.

Courses Coordinated

160.104 Introductory Mathematics for Science
160.319 Mathematical Modelling

Contact Supervisor

Summary of Doctoral Supervision

Position	Current	Completed
Supervisor	2	1
Co-supervisor	1	0

Current Doctoral Supervision

Supervisor of:

Shumaila Noreen - Doctor of Philosophy
The effect of Respiratory Sinus Arrhythmia on coronary blood flow and cardiac output
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

Supervisor of:

2019 - Syed Zaidi - Doctor of Philosophy
IS OUR BREATHING OPTIMAL?

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