A Comprehensive Approach to Modeling Dynamic Biological Systems: Enhancing Critical Thinking and Mathematical Problem-Solving in Biomedical Engineering Education

Caleb Wilson Hendrick; Karissa B Tilbury

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Conference: 2024 ASEE Annual Conference & Exposition
Location: Portland, Oregon
Publication Date: June 23, 2024
Start Date: June 23, 2024
End Date: June 26, 2024
Conference Session: Mathematics Division (MATH) Technical Session 2
Tagged Division: Mathematics Division (MATH)
Page Count: 17
DOI: 10.18260/1-2--46430
Permanent URL: https://peer.asee.org/46430
Download Count: 116

Paper Authors

biography

Caleb Wilson Hendrick University of Maine

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Caleb Hendrick, an undergraduate at the University of Maine, majors in biomedical engineering with minors in electrical engineering and mathematics. He serves as a teaching assistant, committed to creating an inclusive learning environment, particularly in the "Modeling Dynamic Biomedical Systems" (BEN 401) class, and is actively involved in developing course materials. His research focuses on mathematical modeling of complex physiological systems, bridging mathematics and human biology. He is passionate about finding ways to bring mathematical modeling into more fields of research and educational settings.

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Karissa B Tilbury orcid.org/0000-0003-0841-1077

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Abstract

This work-in-progress project is grounded in a biomedical engineering junior-level course dedicated to modeling biomedical systems. The course and project’s primary goal is to integrate fundamental concepts from physics, chemistry, engineering, and mathematics to provide students with a comprehensive foundation for addressing real-world biomedical engineering challenges. Establishing connections and parallels between mathematical methodologies, specifically differential equations, and the constitutive relationships in physics and chemistry are critical in the development of biomedical engineers. A key objective is developing critical thinking skills in students to tackle real-world biomedical problems. BME problems in this course span multiple domains including: 1) bioinstrumentation, 2) drug kinetics, 3) mechanical systems, and 4) organ models. Undergraduate biomedical engineering students frequently struggle with the intersection of mathematics in these domains as the problems require students to freely recall various techniques to solve systems of differential equations in story-problems. This is in contrast with many differential equations textbooks that emphasize rote memorization methods or provide subtle hints of the particular method and or process to be used to solve pre-written mathematical functions. Within engineering disciplines, it is important for students to actively read story problems or interview stakeholders to identify key constraints, and governing physical and biological conditions to derive their own mathematical functions that describe the potential solution space for engineered solutions. The ability to translate physical constraints and apply prerequisite knowledge from physics and biology are often underemphasized in mathematics courses. Furthermore, most mathematics courses focus on analytical solutions and do not employ computational tools for numerical approximations which are critical in engineering. To promote the growth of applied mathematics within BME, we developed a comprehensive text focused on dynamic biomedical systems. The text provides a primer of system characteristics including: 1) linearity, 2) time-invariant, 3) autonomous as well as various different types of input signals (i.e. step, impulse, sinusoidal etc). The text seamlessly interweaves a review of multiple approaches to solving first and second order differential equations including: 1) Variation of Parameters, 2) Underdetermined Coefficients, 3) LaPlace Transforms, and 4) Eigenvectors & Eigenvalues coupled with State Variable format. Alongside these analytical methods, numerical approaches using MATLAB are also outlined. During lectures, students are exposed to complementary instruction leveraging both mini lectures and active learning problem solving using both analytical and numerical approaches that build in complexity from simple word problems to more complex physiological models (i.e. systemic arteries, the body volume compartments, neuron firing). Beyond simply plotting the solution spaces of the mathematical functions, students are asked to write rules to communicate the utility of the models to other stakeholders including healthcare professionals or basic biomedical scientists. In summary, we have created a unique BME focused text for differential equations and linear algebra that encourages students to harness their knowledge of physics, biology, physiology, engineering, and mathematics to formulate dynamic models of physiological systems. Our overall aim is to enhance students’ ability to apply and foster a deep appreciation of the power of mathematics in addressing real-world BME challenges.

Citation
Format

Hendrick, C. W., & Tilbury, K. B. (2024, June), A Comprehensive Approach to Modeling Dynamic Biological Systems: Enhancing Critical Thinking and Mathematical Problem-Solving in Biomedical Engineering Education Paper presented at 2024 ASEE Annual Conference & Exposition, Portland, Oregon. 10.18260/1-2--46430

TY  - CPAPER
AB  -             This work-in-progress project is grounded in a biomedical engineering junior-level course dedicated to modeling biomedical systems. The course and project’s primary goal is to integrate fundamental concepts from physics, chemistry, engineering, and mathematics to provide students with a comprehensive foundation for addressing real-world biomedical engineering challenges. Establishing connections and parallels between mathematical methodologies, specifically differential equations, and the constitutive relationships in physics and chemistry are critical in the development of biomedical engineers. 
             A key objective is developing critical thinking skills in students to tackle real-world biomedical problems. BME problems in this course span multiple domains including: 1) bioinstrumentation, 2) drug kinetics, 3) mechanical systems, and 4) organ models. Undergraduate biomedical engineering students frequently struggle with the intersection of mathematics in these domains as the problems require students to freely recall various techniques to solve systems of differential equations in story-problems. This is in contrast with many differential equations textbooks that emphasize rote memorization methods or provide subtle hints of the particular method and or process to be used to solve pre-written mathematical functions. Within engineering disciplines, it is important for students to actively read story problems or interview stakeholders to identify key constraints, and governing physical and biological conditions to derive their own mathematical functions that describe the potential solution space for engineered solutions. The ability to translate physical constraints and apply prerequisite knowledge from physics and biology are often underemphasized in mathematics courses.  Furthermore, most mathematics courses focus on analytical solutions and do not employ computational tools for numerical approximations which are critical in engineering.  
            To promote the growth of applied mathematics within BME, we developed a comprehensive text focused on dynamic biomedical systems. The text provides a primer of system characteristics including: 1) linearity, 2) time-invariant, 3) autonomous as well as various different types of input signals (i.e. step, impulse, sinusoidal etc).  The text seamlessly interweaves a review of multiple approaches to solving first and second order differential equations including: 1) Variation of Parameters, 2) Underdetermined Coefficients, 3) LaPlace Transforms, and 4) Eigenvectors &amp;amp; Eigenvalues coupled with State Variable format. Alongside these analytical methods, numerical approaches using MATLAB are also outlined. During lectures, students are exposed to complementary instruction leveraging both mini lectures and active learning problem solving using both analytical and numerical approaches that build in complexity from simple word problems to more complex physiological models (i.e. systemic arteries, the body volume compartments, neuron firing). Beyond simply plotting the solution spaces of the mathematical functions, students are asked to write rules to communicate the utility of the models to other stakeholders including healthcare professionals or basic biomedical scientists. 
            In summary, we have created a unique BME focused text for differential equations and linear algebra that encourages students to harness their knowledge of physics, biology, physiology, engineering, and mathematics to formulate dynamic models of physiological systems. Our overall aim is to enhance students’ ability to apply and foster a deep appreciation of the power of mathematics in addressing real-world BME challenges.
AU  - Caleb Wilson Hendrick
AU  - Karissa B Tilbury
CY  - Portland, Oregon
DA  - 2024/06/23
PB  - ASEE Conferences
TI  - A Comprehensive Approach to Modeling Dynamic Biological Systems: Enhancing Critical Thinking and Mathematical Problem-Solving in Biomedical Engineering Education
UR  - https://peer.asee.org/46430
DO  - 10.18260/1-2--46430
ER  -