Day 2 (Wednesday 12 April) @ 11:15–12:45

Luc Florack (TU Eindhoven)

A Geometric Framework for the Human Structural Connectome

The human brain is an intriguing piece of evolutionary engineering and probably the most complex system mankind has ever endeavored to investigate. The 21st grand challenge to unravel its structure and function is known in the trade as ‘connectomics’. It is a complex enterprise that requires a transdisciplinary and multiscale approach. In this talk I focus on the structural connectome, i.e. the collection of maps of nerve bundles (‘tracts’) interconnecting functional regions in the brain. At the level of resolution accessible by state-of-the-art magnetic resonance imaging (MRI) such maps can be reconstructed from a protocol known as diffusion weighted (magnetic resonance) imaging via an ill-posed inverse problem known as ‘tractography’. A geometric framework based on a data induced Riemannian or Finslerian metric appears quite promising.

Martin van Gijzen (TU Delft)

Imaging algorithms for low-field MRI

Hydrocephalus is a potentially fatal condition that affects thousands of children each year in Uganda alone. For surgical intervention and follow-up treatment imaging of the brain is needed. The preferred technique for this is MRI. MRI systems, however, are expensive and out of reach for the vast majority of the population in Uganda. In order to provide a sustainable diagnostic tool an interdisciplinary team of researchers from the Netherlands, the USA, and Uganda is developing an inexpensive and easy-to-use MRI system of sufficient quality to diagnose hydrocephalus.  Since the signals obtained with the scanner are of low quality, advanced mathematical techniques are needed to compute images of sufficient quality. The presentation will first give an overview of the project and will then discuss some of the mathematical techniques that can be used to improve the image quality.

George van Voorn (Wageningen University & Research)

Health economic mathematical models and their validation

Mathematics play an important role in health economics. The costs of Dutch basic health care were 48,6 Billion in 2021, while costs for long-term care increased to 25,7 Billion (ZorgInstituut Nederland, 2022). Policy makers face decisions about which medical drugs and interventions they reimburse and which ones not. In the Netherlands and elsewhere, pharmaceutical companies can apply for reimbursement of their developmental costs for new drugs and interventions based on cost effectiveness reports they file. These reports are commonly accompanied by mathematical models to calculate cost effectiveness. Model validation is needed to evaluate whether a model and its output is credible and relevant. But while model validation is desirable, studies towards the quality of health economic models reported that many models used in reimbursement reports contained important flaws. In this presentation I will talk about developments of the last decade regarding the models used in health economic decision making and their validation, aimed at improving the credibility and applicability of these models.

Richard Boucherie (Twente University)

Dynamic assignment of capacity and fair balancing of COVID-19 patients over hospitals

We introduce models that support dynamic fair balancing of COVID-19 patients over hospitals in a region and across regions. Patient flow is captured in an infinite server queueing network. Input for the model is an accurate real-time forecast of the number of COVID-19 patients hospitalised in the ward and the Intensive Care Unit of the hospitals based on the predicted inflow of patients, their Length of Stay and patient transfer probabilities among ward and ICU.  

For given number of available beds, we introduce a dynamic load balancing model for assignment of patients to hospitals within a region, and a stochastic program for allocation of patients across regions. Subsequently, we consider optimal up- and downscaling of capacity for COVID-19 patients leaving maximum capacity for regular (non-COVID) patients. 

We illustrate our models using data from the second COVID-19 peak from hospitals’ data warehouses and regional infection data as recorded in the Netherlands.

Sjaak van der Pouw (Van Vliet Diagnostics and MedTech at Work)

Can Mathematics help to improve quality and lower the cost of Healthcare ?

In many hospitals, the use of innovative medical technologies is more a replacement decision than a conscious investment choice to make the healthcare system run smarter and more effectively. In many cases, based on an established pattern of thinking, a medical technological system is replaced.

While a lot of profit can be achieved if, in addition to the replacement, the impact that a medical technological development can have on the entire work process within a care department, or even within the entire health care system, is also considered.

Insightful mathematical models are often lacking to show users the impact that a medical technological innovation can bring to the healthcare process and what benefits can be achieved with scarce goods such as labour, energy and raw materials.

In my overview I show a number of recent cases in which there are opportunities for mathematicians to make his or her contributions to the design of a sustainable care system.