A groundbreaking mathematical equation has been discovered, which could transform medical procedures, natural gas extraction, and plastic packaging products in the future.

The new equation, developed by scientists at the University of Bristol, indicates that diffusive movement through permeable material can be modeled exactly for the very first time. It comes a century after world-leading physicists Albert Einstein and Marian von Smoluchowski derived the first diffusion equation and marks important progress in representing motion for a wide range of entities from microscopic particles and natural organisms to man-made devices. 

Until now, scientists looking at particle motion through porous materials such as biological tissues, polymers, various rocks, and sponges, have had to rely on approximations or incomplete perspectives.

The findings provide a novel technique presenting exciting opportunities in a diverse range of settings including health, energy, and the food industry.

Lead author Toby Kay, who is completing a Ph.D. in Engineering Mathematics, said: “This marks a fundamental step forward since Einstein and Smoluchowski’s studies on diffusion. It revolutionizes the modeling of diffusing entities through complex media of all scales, from cellular components and geological compounds to environmental habitats.

“Previously, mathematical attempts to represent movement through environments scattered with objects that hinder motion, known as permeable barriers, have been limited. By solving this problem, we are paving the way for exciting advances in many different sectors because permeable barriers are routinely encountered by animals, cellular organisms, and humans.”

Creativity in mathematics takes different forms and one of these is the connection between different levels of description of a phenomenon. In this instance, by representing random motion in a microscopic fashion and then subsequently zooming out to describe the process macroscopically, it was possible to find the new equation.

Further research is needed to apply this mathematical tool to experimental applications, which could improve products and services. For example, being able to model accurately the diffusion of water molecules through biological tissue will advance the interpretation of diffusion-weighted MRI (Magnetic Resonance Imaging) readings. It could also offer a more accurate representation of air spreading through food packaging materials, helping to determine shelf life and contamination risk. In addition, quantifying the behavior of foraging animals interacting with macroscopic barriers, such as fences and roads, could provide better predictions on the consequence of climate change for conservation purposes.

The use of geolocators, mobile phones, and other sensors has seen the tracking revolution generate movement data of ever-increasing quantity and quality over the past 20 years. This has highlighted the need for more sophisticated modeling tools to represent the movement of wide-ranging entities in their environment, from natural organisms to man-made devices.

Senior author Dr. Luca Giuggioli, Associate Professor in Complexity Sciences at the University of Bristol, said: “This new fundamental equation is another example of the importance of constructing tools and techniques to represent diffusion when space is heterogeneous, that is when the underlying environment changes from location to location.

“It builds on another long-awaited resolution in 2020 of a mathematical conundrum to describe random movement in confined space. This latest discovery is a further significant step forward in improving our understanding of motion in all its shapes and forms – collectively termed the mathematics of movement – which has many exciting potential applications.”

Artificial intelligence could help clinicians assess which patients are likely to encounter the harmful side effects of some commonly used antidepressants, antihistamines, and bladder medicines.

Research led by the University of Exeter and Kent and Medway NHS and Social Care Partnership Trust, published in Age and Ageing, assessed a new tool designed to calculate which medicines are more likely to experience adverse anticholinergic effects on the body and brain. These complications can occur from many -prescription and over-the-counter drugs which affect the brain by blocking a key neurotransmitter called acetylcholine. Many medicines, including some bladder medications, anti-depressants, and medications for stomach and Parkinson’s disease have some degree of anticholinergic effect. They are commonly taken by older people.

Anticholinergic side effects include confusion, blurred vision, dizziness, falls and a decline in brain function. Anticholinergic effects may also increase the risks of falls and may be associated with an increase in mortality. They have also been linked to a higher risk of dementia when used long-term.

Now, researchers have developed a tool to calculate the harmful effects of medicines using artificial intelligence. The team created a new online tool, International Anticholinergic Cognitive Burden Tool (IACT), it uses natural language processing which is an artificial intelligence methodology, and chemical structure analysis to identify medications that have an anticholinergic effect.

The tool is the first to incorporate a machine learning technique, to develop an automatically updated tool available on a website portal. The anticholinergic burden is assessed by assigning a score based on reported adverse events and aligning closely with the chemical structure of the drug being considered for prescription, resulting in a more accurate and up-to-date scoring system than any previous system. Ultimately, after further research and modeling with real-world patient data the tool developed could help to support prescribing and reducing risks from common medicines.

Professor Chris Fox, at the University of Exeter, is one of the study authors. He said:: “Use of medicines with anticholinergic effects can have significant harmful effects for example falls and confusion which is avoidable,  we urgently need to reduce the harmful side effects as this can leads to hospitalization and death. This new tool provides a promising avenue towards a more tailored personalized medicine approach, of ensuring the right person gets a safe and effective treatment whilst avoiding unwanted  anticholinergic effects.”

The team surveyed 110 health professionals, including pharmacists and prescribing nurses.  Of this group, 85 percent said they would use a tool to assess the risk of anticholinergic side effects, if available. The team also gathered usability feedback to help improve the tool further.

Dr. Saber Sami,  at the University of East Anglia, said: “Our tool is the first to use innovative artificial intelligence technology in measures of anticholinergic burden – ultimately, once further research has been conducted the tool should support pharmacists and prescribing health professionals in finding the best treatment for patients.”

Professor Ian Maidment, from Aston University, said: “I have been working in this area for over 20 years. Anticholinergic side effects can be very debilitating for patients. We need better ways to assess these side-effects.”

The research team includes collaboration with AKFA University Medical School, Uzbekistan, and the Universities of East Anglia, Aston, Kent, and Aberdeen. They aim to continue the development of the tool with the aim that it can be deployed in day-to-day practice which this study supports.