Strategies to Make Models Useful

Using computational models to address clinical questions has become common in biomedical engineering field. For example, one may find in the literature a large library of ODE systems describing everything from sub-cellular to whole-body cardiovascular function. However, constructing such models is only half the story. For them to be truly useful in clinical settings, we must be able to tailor them to a specific patient or a condition easily. As the model complexity and the number of equations grew, paradoxically we have moved further away from achieving this goal.

This leaves us in a position where personalised models are difficult to apply to large patient population and the ability to do so would open up new horizons for mathematical modelling. In order to begin working toward larger patient populations, two important objectives must be met: rapid personalisation (fitting), and robustness of the fitted solution in the presence of noise. Novel methodologies developed in different fields have the potential to reduce manual work, improve fitting quality and harness sensitivity to measurement noise. However, these techniques have not yet become the standard in cardiac applications.

" What exactly is the goal ? "

 The aim of this project is to develop a reliable automatic personalisation strategy for a lumped parameter cardiovascular model, which has been developed for patient-specific applications. The performance of the method will be tested based on its ability to reproduce pre- and post- data from patients undergoing surgical procedures.

"How exactly will we achieve this goal ? "

We will begin by extracting a suitable sub-component of the full model and assessing fitting methods for problems in which the ground truth is known. Various methods ranging from gradient-based techniques to sequential filtering and Monte-Carlo methods will be investigated. The algorithm's performance will be judged according to their automatic capabilities, ability to recreate the clinical data and handle noisy data. The complexity of the model will then be increased, and the results of the initial algorithm ranking adjusted if necessary.

"What experience will I gain in this project ? "

By working on this project, you will gain experience in algorithms, algorithm comparison, handling and integrating clinical data and general computational implementation. This experience will be valuable in any further academic or industry work. You'll mainly be working in a Matlab environment so experience with this will be useful.

" Is this an isolated project or am I part of something bigger? "

Something bigger ! This project is useful to an ongoing research project at King's investigating a large patient population (200+ patients)  and response to Cardiac Resynchronisation Therapy. This therapy, think pacemakers, has a response rate of 2 in 3 and its currently unknown why some patients don't get better. At King's, clinicians and basic scientists are trying to investigate this question through mathematical modelling and clinical imaging.

Identification of Culprit Diseased Vessel from Myocardial Perfusion MR Images

Myocardial perfusion imaging is great for assessing the consequence of disrupted blood supply, since it shows how much blood is actually being delievered to different parts of the heart muscle rather than simply looking at the large vessel lesions. Magnetic resonance perfusion imaging (MRPI) is particularly promising due to its superior resolution and a lack of radiation exposure, compared to nuclear imaging.

On the other hand, because MRPI doesn't show individual blood vessels, clinicians face a practical problem when reduced blood flow is detected -- which vessel should be treated?

Previous work on matching the vessels to perfusion territory has shown that the standard 17-segment cannot always be reliably identified with the culprit artery. Below diagram (from Ortiz-Perez et al. 2008) shows the specificity of MR-derived segmental association with the infarct-related artery. Most of the segments could be uniquely attributed.

Other investigators attempted to estimate the perfused mycardial territories directly from detailed vascular images. The example below (Le et al. 2008) used an ex vivo imaging data to divide the myocardium into territories based on their nearness to the neighbouring vessel.

In order to extend these efforts to clinical practice, more work is necessary. In addition, the coronary network used in the second study is more detailed than the typical resolution achievable in patients (note the picture above does not show the full detail of the vasculature), introducing further challenges to clinical translation.

"What is the project plan?"

With the type of data used in the second study, one could design and test an algorithm to define 3D perfusion territories with high accuracy. A key question currently is whether the clinical angiographic images offer enough details to determine the territories reliably -- these objectives will be tackled in the current project, using a high-resolution reconstruction of pig hearts. The project will aim to
i) develop a 'forward' algorithm for assigning each point in myocardium with the feeding vessel. Unlike previous work, this method will use more information than the mere distance, possibly incorporating hemodynamic principles, and
ii) an 'inverse' method will be investigated that, given a perfusion image, will identify the supplying vessel

More questions?

Please feel free to visit/contact me (Jack) or leave a question in the comments below.

3D Model Generation from Cine MR Images

Cine MRI is commonly used in cardiac MR imaging and captures the motion of the myocardium throughout the cardiac cycle. Making a 3D model representation from cine MR helps to quantify clinically-relevant functional indices as well as allowing finite element models to be built from it. An example of a long axis view cardiac cine MR is shown on the right.


Using the standard open-source tools, segmenting and making a 3D model from a cine MR image is easy. However, this involves significant manual effort, and the results tend to be less than ideal. Some of the issues are:

  • because the z-resolution is poorer than the in-plane resolution, segmentation leads to a jagged appearance
  • short axis images lack the detail at the top and bottom of the heart, effectively truncating it
  • the presence of the papillary muscles can confuse the whole process and introduces variability
  • characterising the full right ventricular wall geometry is almost impossible
3D meshes generated from high resolution morphological scans -- these will serve as the gold standard for this project

3D meshes generated from high resolution morphological scans -- these will serve as the gold standard for this project

Despite these issues, those approaches are commonly used in research work probably because they provide the "path of least resistance". This project aims to provide a better alternative. In particular, we plan to develop an image-to-mesh generation pipeline that does not require specialist knowledge to operate, and does a decent job automatically, with the possibility for manual improvement.

In fact, this work goes far beyond the undergraduate project -- the developed algorithm will be ported into a comprehensive software platform being written currently and King's BME, for use by both clinicians and researchers. This platform is designed to integrate many different facets of research undertaken around the division into a common tool, in order to aid collaborative research. 

"What will the work involve?"

There are a huge range of approaches for segmentation of cine MR (see this for a review), and probably just as many for generating a 3D mesh. We will limit ourselves to manual /semi-manual segmentation and high-order meshes in this project. Using the existing array of tools developed in-house, we will implement different mesh fitting/generation methods (high-order projection, free-form deformation, voxel-mask pre-processing, slice-based vs full 3D) and manual-correction approaches. The best algorithm will be identified by comparing to the gold standard provided by high-resolution morphological MR images.

"Is this project suitable for me?"

As with any project, the content will be tailored to the interest and strength of the student, however, in general this project will require the ability for mathematical thinking and matlab programming. The experience will be relevant for future industry or academic work.

"I'm still unclear / unsure / undecided"

If you would like more information on the project (or anything else) feel free to drop me an email and visit me. I will do my best to clarify any issues. You can also leave your questions below in the comments section.

Search for the Horizon: Where Do Coronary Waves Originate?

This project tries to answer an obvious question that's been largely overlooked by the research community -- when we measure pressure and velocity in a patient's vessel, where are those signals coming from? 

When a person experiences a heart attack, a majority of the time it is due to the blockage of one of the vessels supplying the heart muscle. While the treatments focus on re-establishing the flow (revascularisation), having more information on the hemodynamics helps doctors plot the future course of therapy. After all, the coronary circulation is a complex system that consists of hundreds of millions of both large and small vessels, and a single approach definitely does not fit all patients!

Thanks to previous research, there is a technique called Wave Intensity Analysis, which allows us to figure out what's happening deep down in the small vessels embedded within the myocardial walls, as opposed to events taking place in the upper circulation. However, because pulse waves have a tendency to reflect at vascular junctions, we don't get to see what's going on in most of the deeper circulation. The question is, how deep? The depth at which we can't observe at the top of the tree any originating waves is referred to as the Horizon.

Why do we care about this horizon? Many reasons - a parameter derived from these pulse waves has been shown to correlate with the recovery of the heart muscle following a heart attack, for example (see this article). Doctors are interested in using these indices to infer the health status of the affected myocardial regions and the integrity of the microcirculation. If the waves do not actually originate from the microcirculation (or are entirely trapped so as to be unobservable), this would be quite misleading!

It is difficult to find out directly where this horizon is, in a patient. Fortunately, (with much effort) we have acquired a very high-resolution geometry of the whole coronary network in animal models, which will serve as the starting point of this project. Specific work involved is described below.


"What will I be actually doing in this project?"

The idea is to simulate flows in the extracted networks to emulate the cathlab procedures. We have the freedom to prune away deeper vessel segments (shown below), so it's expected that the higher we prune, greater the change in the observed flow profile will be. Conversely, the lower we prune, at some stage, the changes in flow will become negligible, identifying the horizon. To do this you will learn how to run our in-house 1D flow simulation program, manipulate vascular networks in matlab, and a little bit of the theory behind pulse wave propagation. The rest of the time will be devoted to fun stuff.

"I am not confident at coding... am I going to be able to handle it?"

The work involved is mainly learning to use already-completed programs to answer a question, rather than to implement any new ones. We understand the time allocated in an undergraduate projects doesn't allow lengthy development work, and you will get plenty of help if you require it.

"How much supervision will be offered?"

There are two supervisors for this project, and one of us will always be available if you need help. In the project we did last year, we typically had two full days of work a week plus a web-based progress tracking system (so you can do the work where/when it suits you).

more questions?

By all means come in and talk to myself (Jack) or Simone, we're both on 3rd floor of Lambeth wing. Drop us an email to make sure we're in. Or, you can leave your question in the comments below.