This course is taught by Ana González and Marta Guardiola. It deals with the use of computational tools for solving bioelectromagnetism problems. Specific problems tackled by biomedical engineers and researchers in this field will be presented and related practical exercises will be performed using COMSOL Multiphysics. COMSOL is a cross-platform finite element analysis, solver and multiphysics simulation software.
The first part of the course is focused on biomedical applications within the low frequency electromagnetic (EM) spectrum (300 kHz to 1 MHz). In this band, propagation effects can be neglected, and circuit theory can be used. In particular, we are going to study radiofrequency ablation techniques which are used to produce safe and localized heating of target biological tissue. Radiofrequency energy is applied to biological tissue through electrodes and it raises the local temperature to a point at which a thermal lesion is caused, but without implying the mechanical excision of a section of tissue. The clinical applications of radiofrequency heating of biological tissue include different medical fields, such as the elimination of cardiac arrhythmias or the destruction of tumors in different locations. In order to investigate and develop new techniques, and also to improve those currently employed, computational models and simulations are a powerful tool since they provide vital information on the electrical and thermal behaviors rapidly and at low cost. They can even help to plan individual treatment for each patient.
The second part of the course is devoted to the middle-frequency range or microwave spectrum (300 MHz to 300 GHz). This band is used extensively for communications (mobile phones, TV, radio, spatial communications…). So, safety assessment is very important to control the amount of radiation absorbed by the body. This waves can be also focused with a fair tradeoff between resolution and tissue penetration, thus being attractive for imaging and hyperthermia applications. The mid-frequency range is probably the most complex region for calculation of the expected fields because of their wave-like behavior. Waves reflect, transmit, refract, add constructively and destructively, and attenuate as they propagate through and around the body. Analytical solutions only exist for very canonical cases. For the rest, computational simulations are required.
The theory of the course is designed such that it can be followed by students with any engineering bachelor degree. This includes, but is not limited to, biomedical engineers. Students from physics and mathematics will also be able to follow the course. All these bachelor degrees equip the students with the necessary technical and mathematical skills to take this course.
The students should be familiar with fundamental concepts of physics (basic knowledge of EM theory), mathematics (concepts of derivatives, integrals, gradient and divergence) and linear signal analysis (such as the Fourier Transform).
We will use MATLAB for the data analysis done in the lab sessions. The students need therefore to be able to write and understand simple source code in this programming language.
The theoretical contents are organized in seven lectures:
- Part 0: Overview
- Lecture 1: (1 hour) We will start with an overview and motivation of the course contents. We will introduce the concept of “Bioelectromagnetism” and how electric and magnetic fields interact with the body. We will finalize overviewing some biomedical applications in the EM spectrum.
- Part 1: Low frequency electromagnetic spectrum
- Lecture 1: Electrotherapy-Radiofrequency heating (2 hours) We will introduce the fundaments of radiofrequency (RF) heating of biological tissues. We will also detail the equations which describe the physical phenomena of RF heating on which the numerical models are based. We will finally mention the benefits of using computational modelling over experimental approach.
- Lecture 2: Computational modelling of radiofrequency ablation (I) (2 hours) We will see different clinical applications of RF heating with a specific therapeutic purpose. In particular, we are going to focus on the elimination of tumors and subcutaneous fat by means of RF heating. For each application, we will describe the specific procedure, the available clinical devices and some examples of computational models.
- Lecture 3: Computational modelling of radiofrequency ablation (II) (2 hours) We are going to focus on the elimination of cardiac arrhythmias by RF heating. We will start with an overview of the fundamentals of cardiac conduction system to understand how a cardiac arrhythmia occurs. We will continue explaining the surgical methods to perform a RF cardiac ablation to eliminate an arrhythmia and the specific available clinical devices. Finally, we will see some examples of computational models.
- Part 2: Mid-frequency electromagnetic spectrum
- Lecture 1: Microwave theory fundamentals (2 hours) We will introduce the fundamentals of EM waves. We will explain the qualitative meaning of Maxwell’s equations - the fundamental set of equations that form the framework of all of classical EM theory. Once the theoretical basis is established, we will focus on the practical aspects: design of the sources (antennas), transmission lines and link budget.
- Lecture 2: Waves in matter (2 hours) In the previous lecture, we described how waves propagate in free space. However biological bodies are inhomogeneous and lossy, and this changes the propagation behavior of waves. In this lecture we will explain how to model the interaction with biological tissues and the need of using computational models will arise. We will finally explain the effects of EM radiation into the human body, how it is measured and regulated.
- Lecture 3: Microwave imaging (2 hours) In the last lecture we will introduce a medical application of the mid-range EM spectrum - microwave imaging (MI). MI has a great potential in medicine thanks to the ability of microwaves to be impacted by their remote environment, and particularly to the tissue water content. This is a new contrast mechanism, thus MI may be able to see what cannot be possibly seen by means of other medical imaging modalities. MI is harmless for the human body, and offers a fair tradeoff between penetration and focusing capacity (resolution) at an acceptable technological cost.
The students will receive supervision, advice and assistance by the professor during the six lab sessions. We will use the numerical platform COMSOL Multiphysics and MATLAB in the practices. Each lab session is of 2 hours, but the students are expected to carry out most of the work outside classroom.
The three lab sessions of part 1 are based on the implementation of computational models of radiofrequency cardiac ablation by means of catheters to eliminate cardiac arrhythmias situated in different zones in the heart (atrium or ventricular wall). We will assess the effect of using different electrode-tip designs, protocols and modes for applying the radiofrequency energy to determine which one is safer (reduce excessive heating and clinical complications) and more effective (achieve transmural lesions) to eliminate a cardiac arrhythmia in a specific zone in the myocardium.
The three lab sessions of part 2 are devoted to the implementation of a simple microwave imaging system. It will comprise the design of the applicator (antenna) with an analytical model. Then, the antenna will be modeled and simulated to assess its performance in presence of the human body and determine the possible health effects. Finally, a simple imaging algorithm will be implemented and used to obtain images of simple phantoms.
The students have to
- Perform individually the exercises indicated in each lab session.
- Write a short validation report (2-3 pages) for each lab session based on these exercises.
- Each report will have to be electronically delivered within one week after the lab session devoted to the corresponding exercise.
The grades will be derived from the quality of the experimental work and the capacity to analyze the results reflected in the written reports. The attitude and proactivity of the students during lab sessions will be also taken into account in the final grade (10 %).
Bibliography and information resources
- Part 1
- Jaakko Malmivuo & Robert Plonsey, “Bioelectromagnetism - Principles and Applications of Bioelectric and Biomagnetic Fields”, Oxford University Press, New York, 1995. Available online at http://www.bem.fi/book/
- Sverre J. Grimnes & Orjan G. Martinsen, “Bioimpedance and Bioelectricity Basics”, Second edition, Academic Press, San Diego, 2000. Electronic and paper versions available at the UPF library.
- David J. Griffiths, “Introduction to Electrodynamics”, 4th edition, Pearson, 2012
- Part 2
- Cynthia Furse, Douglas A. Christensen, Carl H. Durney, Basic Introduction to Bioelectromagnetics, Second Edition, CRC Press, 2009.
- Constantine A. Balanis, Antenna Theory: Analysis and Design, 3rd Edition, Wiley-Interscience, 2005.
- Natalia K. Nikolova, Introduction to Microwave Imaging, Cambridge University Press, 2017.