Medical treatments are very different. So are people. PhD student Andris Piebalgs describes how finding the right treatment seems to lie in the ‘hands’ of computers.
Medical diagnostics and treatment have undergone many tremendous changes over the last few decades. For some illnesses, a patient suffering from a chronic disease can now be presented with a myriad of treatment options. For instance, cancerous tumours found in the body can either be removed surgically, burnt to death using ultrasound, or destroyed by cancer-killing drugs. However, how is it possible to know which treatment method will work best? Should the patient undergo surgery and risk complications? Or do doctors expect that the drugs will work with minimal side-effects instead?
Even if a particular treatment is chosen over another, there may be multiple ways to perform it. Additionally, there are many different drugs that can be taken in conjunction with others to create a powerful cocktail. Everyone’s body is different, and sometimes the best option cannot be known before it is actually tried.
Promise of mathematical modelling
Mathematical modelling is helping medicine to peer further into the future. Imagine, just based on a few easily performed scans, detailed segments of a person’s body can be reproduced on a computer screen and a treatment method or therapy can be simulated virtually. The results can be analysed and used to find out how a patient will react to a given therapy.
Additionally, the explosion of personal computing has allowed researchers to simulate a higher degree of accuracy than ever before. Complex mathematics can help describe how the human body works and then computationally solve and analyse it in just a matter of weeks. Modern medicine is observing a growing use of mathematical modelling to help provide patients with better treatments.
Going with the flow
Our research group is one of many at Imperial College who create computational models with good predictive capabilities. The group’s research predominately focuses on modelling the movement of blood within a given artery, and how this affects treatment for individuals suffering from vascular diseases.
Some of the diseases under investigation involve the aorta, the largest artery in the human body. All of the blood that passes through this vessel will reach important organs such as the brain, liver and kidneys. A series of afflictions that compromise the integrity of the aorta are known as aortic aneurysms which claim the lives of more than 15,000 people every year in the US alone.
An aortic aneurysm occurs when the arterial wall of the aorta weakens with age and begins to balloon due the blood pressure exerted on it by the pulsatile motion of the heart. If left untreated, the aneurysm will rupture and cause internal bleeding, leading to death in over 80% of the cases. Many notable figures, like Albert Einstein, have fallen victims to aortic aneurysms. A recent procedure has been developed that performs a non-surgical intervention. A device known as a stent-graft is introduced into the aorta and creates an artificial wall allowing blood to flow through it. This aims to help prevent the weak arterial wall from further expanding and breaking.
However, as with any treatment procedure, complications can arise. There may be difficulties inserting the stent-graft due to abnormalities in the shape of the patient’s aorta. Furthermore, there have also been reports of stent-grafts allowing blood to flow into the weak arterial wall due to incomplete sealing. In an alternative scenario, the stent-graft can be pushed down the aorta thereby failing to protect the weak arterial wall.
The variety of complications that can arise from the implementation of a stent-graft leaves doctors with many questions to answer. Will the implanted stent-graft eventually succumb to any of these complications? Can the patient go about their daily lives or undergo any vigorous exercise without affecting their recovery? Modelling the process beforehand can provide further insights into the design and implementation of the stent-grafts as well as predicting the risk of any future complications.
Computational modelling with CFD
To make a mathematical model of a patient’s aorta, scans of the patient are needed to accurately depict the human body. MRI (magnetic resonance imaging) and CT (computed tomography) scans are typically used to form a comprehensive 3D image of the human arterial system. The geometry of the artery of interest is then analysed in detail and is reproduced in a virtual environment.
Mathematical tools such as the Navier-Stokes equations are used to describe the movement of blood in an artery. These are very complicated differential equations based on the fundamental principles of the continuity of mass and momentum which can be solved numerically by computers.
The process is known as CFD, or computational fluid dynamics, and is a very effective approach for solving the motion of a fluid in any environment. Due to its usefulness it has become ubiquitous in academic and industrial research.
Benefits of modelling
Computational CFD solvers are used in combination with the arterial geometries extracted from medical scans to find out about the actual motion of blood. The efficacy of using stent-grafts to treat an aortic aneurysm and the risk of complications can be ascertained by studying the blood flow patterns predicted by the simulation. For instance, the risk of the stent-graft dislodging can be determined by analysing the net downward force that it suffers from the continuous movement of blood.
This form of modelling has assisted doctors and medical device manufacturers in determining the efficacy of various treatment procedures. Mathematical modelling is increasingly being used together with clinicians and medical companies to optimise existing treatments and also to test novel approaches for solving difficult medical problems.
It is expected that in the future this application will continue to grow. And it will doubtlessly help the health industry to provide patients with more personalised, efficient and informed treatment plans.
Andris Piebalgs is a PhD student in Chemical Engineering
Banner Image: Computer Modelled DNA, Kotkoa