Mathematical approaches and tools have long been used in medicine and biology; however, their application on day-to-day clinical practice has yet, to become a reality. Nevertheless, we are witnessing the dawn of a new era in which their application is increasing at dramatic speed thanks to novel modelling developments, better software, significant increase in computer power, a change in culture in which ‘multidisciplinary’ is seen as a must as well as the emergence of the new paradigm of ‘personalised medicine’, tailored to individual patients. Evidence-based medicine will be replaced eventually by explanation-based (or explanatory) medicine and this change must come sooner, rather than later.

Mathematical approaches are poised to become a critical component in the prognosis, diagnosis and treatment of human diseases as well as in the management of long-term chronic conditions in the near future. We are currently facing the age of ‘Big Data’ and the amount of information that is being generated in all aspects of modern life, including healthcare, has increased exponentially, becoming a challenge in itself due to the lack of tools and expertise to analyse heterogeneous datasets. Moreover, in this ‘Big Data’ era, there are specific challenges linked to healthcare data due to data protection, a fragmented data collection system and ethical constraints, which makes ‘Big Data’ in healthcare extremely challenging. Effective approaches to mathematical modelling in healthcare often require the seamless integration of data from a myriad of sources (e.g. patient records, imaging and/or sensor data, genomics/proteomics/metabolomics data, social media information, nutrition etc.). The development of new and improved approaches to modelling systems that span multiple temporal and/or spatial scales (e.g. genes → cells → tissues → organs → whole body or individual → population) in combination with the ever growing clinical data is a crucial step towards overcoming the above mentioned challenges.

Recent advances in mathematical sciences have shown that robust and precise mathematical models of complex processes/networks, which are ubiquitous in healthcare and medicine, are critical to understanding many aspects of human biology and disease, just to name a few, tumour development and treatment response mechanisms, the interplay of haemodynamics and cellular or sub-cellular mechanism in the development of atherosclerosis, the human brain and its interplay with the cardiovascular system or infectious disease propagation. In addition, the understanding of complex processes and networks is important in optimising the provision of healthcare. This area includes the development of mathematical and statistical tools able to facilitate improvements in the design of clinical trials and the use of the resulting data.

Last but not least, the language used by clinicians and healthcare practitioners on one hand and the mathematical modelers on the other is vastly different. Therefore, substantial efforts are needed in order to initiate a dialogue between both. In effect, mathematical approaches are useful tools that still remain incomprehensible for most of the clinicians and medical scientists and hence their potential is poorly exploited in the healthcare domain.

By proposing this topic our aim is three-fold
1) to disseminate how mathematical models can help to interpret clinical data;
2) to show how models can enable better design and evaluation of new diagnostic and therapeutic strategies;
3) to show that mathematical models can be used to explain disease progression or to provide disease management strategies in individual patients.

Manuscripts describing approaches that combine clinical and/or medical experiments/data with innovative analytical tools to help to understand the processes driving disease progression, and to evaluate currently available tools to tackle human diseases are welcome. This research topic will set the scene of the current state-of-the-art mathematical tools for healthcare, raising awareness of their potential usefulness and various applications.

In summary, this research topic aims to explain how advanced mathematical modeling could help in a practical way the clinicians and researchers while representing an update for those already familiar with it, in order to achieve a multidisciplinary approach to healthcare problems.

Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.