Integration of Febio as an Instructional Tool in the Undergraduate Biomechanics Curriculum

Abstract

Computer simulations play an important role in a range of biomedical engineering applications. Thus, it is important that biomedical engineering students engage with modeling in their undergraduate education and establish an understanding of its practice. In addition, computational tools enhance active learning and complement standard pedagogical approaches to promote student understanding of course content. Herein, we describe the development and implementation of learning modules for computational modeling and simulation (CM&S) within an undergraduate biomechanics course. We developed four CM&S learning modules that targeted predefined course goals and learning outcomes within the febio studio software. For each module, students were guided through CM&S tutorials and tasked to construct and analyze more advanced models to assess learning and competency and evaluate module effectiveness. Results showed that students demonstrated an increased interest in CM&S through module progression and that modules promoted the understanding of course content. In addition, students exhibited increased understanding and competency in finite element model development and simulation software use. Lastly, it was evident that students recognized the importance of coupling theory, experiments, and modeling and understood the importance of CM&S in biomedical engineering and its broad application. Our findings suggest that integrating well-designed CM&S modules into undergraduate biomedical engineering education holds much promise in supporting student learning experiences and introducing students to modern engineering tools relevant to professional development.

JBME Figure 3

1 Introduction

Biomechanics-based computational modeling and simulation (CM&S) tools are routinely employed to advance nearly all areas of physiology and medicine [1–7]. Modeling techniques provide numerical approaches to predict diverse mechanical responses across length and time scales, augmenting traditional experimental approaches exhibiting known limitations across a continuum. In the clinical setting, computational modeling is an established tool for interventional/surgical planning and assessment [8,9]. Moreover, the U.S. Food and Drug Administration (FDA) recognizes CM&S as central to evaluating the effectiveness and safety of medical devices [10]. Given increased attention to physics-based simulations in medicine, it is important that biomedical engineering education introduces modeling approaches to understand applications and appreciate their utility. Indeed, stakeholders suggest that engineering educators consider methods to engage students in practices and application of CM&S to advance biomedical research [11–13].

Evidence suggests that exposing students to computational tools improves learning, comprehension, and enhances their ability to apply learned skills to solve problems [11,14,15]. Consistently, CM&S has been integrated into the curriculum in the undergraduate classroom in multiple forms. Students can learn computer modeling tools as an engineering skill, directly learning modeling principles and software [16,17]. Educators can introduce CM&S when presenting a new subject or topic [18]. For example, the open-source, image-based computational fluid dynamics (CFD) software SimVascular™ has been successfully used as an instructional tool to teach the fundamental principles of blood flow at the undergraduate and graduate levels [19,20]. Most commonly, CM&S is introduced within the context of dynamic systems and provides active learning tools, allowing students to manipulate system variables and observe the consequences (i.e., cause and effect relationships) [14]. Collectively, CM&S tools have many attractive features that complement standard pedagogical approaches (e.g., problem-based learning, PBL [21]) and enhance students' abilities to investigate complex systems in biomechanics and biomedical engineering.

Nonetheless, certain challenges practically limit the broad use of CM&S in undergraduate biomedical engineering curricula. For example, finite element analysis (FEA), the most widely used numerical approach for solving problems in computational biomechanics, is traditionally taught in graduate-level courses due to the advanced nature of the topics. Although FEA theory incorporates mathematical principles beyond some undergraduate engineering programs, data suggest that the early introduction of CM&S promotes downstream student learning benefits [22]. In addition, biomechanical engineering instructional materials are not widely disseminated [23,24]. Developing new, impactful CM&S teaching material is time-consuming, particularly for the nonexpert, and thus, established didactic lesson plans with proven efficacy are warranted [25].

To better promote integration of CM&S practices into undergraduate biomedical engineering education and overcome existing barriers, our aim was three-fold: (1) to develop and implement active learning modules created in the open-source FEA software febio (“Finite Elements for Biomechanics,”2) and febio studio [26,27] within an undergraduate biomechanics course; (2) to evaluate the effectiveness of CM&S integration as a foundation for learning biomechanics concepts and for augmenting didactic lecture material; and (3) to document and disseminate new, innovative biomechanics educational and instructional materials to the community for ready implementation by nonexperts.

2 Methods

2.1 Course Description and Student Participants.

We developed and implemented new CM&S learning modules into the Biomechanics I course in the undergraduate curriculum in the Department of Biomedical Engineering at the University of Utah (USA). This course introduces fundamental principles in continuum mechanics and linear elasticity, focusing on finite deformation theory applied to biological materials. The course covers rigid body and finite deformation kinematics, stress and strain, linearized elasticity, mechanical behavior of biological materials, and viscoelasticity. Since the course does not require a textbook, course content is primarily derived from textbooks by Spencer [28] and Humphrey and O'Rourke [29]. Across the 15-week semester, a primary course instructor delivered 80-min didactic lectures twice weekly. Additionally, this course includes a laboratory component where students perform team-based, hands-on experiments to reinforce lecture topics. In the Fall 2022 semester, 83 undergraduate students enrolled in this course at the junior/senior level. The Biomechanics I course has been refined for 20 years.

We developed four CM&S learning modules to supplement the course lectures, in-class discussions, assignments, and laboratory exercises. These modules supported 4 of the 8 learning outcomes in the course (Table 1), and each module consisted of a self-contained (i.e., independent) lesson designed for students to complete in 90–120 min. Students completed the modules in 2-3 person groups, and each group had access to a desktop PC with an Intel^® Core™ i7-6700 (3.40 GHz) processor and 16 GB of memory. Module instruction was led by 1 to 2 teaching assistants (TAs), Ph.D. students with at least 1 year of febio studio experience. The TAs guided the students through the course modules in the teaching lab using presentations on an overhead projector and screen.

Table 1.

Biomechanics I course learning outcomes (i.e., key topics) as presented on the course syllabus

Course learning outcome	Module #
(1) Use both index and direct notation
(2) Understand finite deformation kinematics to analyze deformation and strain	M1
(3) Understand the transformation of coordinate systems and rigid body kinematics
(4) Understand the concept of stress.	M2
(5) Derive and interpret the equations of motion for deformable bodies
(6) Apply linear elasticity to analyze stresses and strains in materials	M3
(7) Interpret differences in the material behavior of biological materials	M4
(8) Perform analysis of viscoelastic systems based on discrete element models

M1–M4 denotes the new CM&S modules developed to support the learning outcomes.

2.2 Computational Modeling and Simulation Content Integration and Pedagogy.

To promote successful CM&S module incorporation within the course, we utilized the backward design approach proposed by Wiggins and McTighe [30]. In brief, the backward design concept advocates the design of course material and learning experiences to meet predefined goals and outcomes (i.e., identify what students are expected to learn and establish course material and activities to meet desired learning results). The approach also facilitates the course designer's evaluation of content effectiveness. Figure 1 illustrates the application of the backward design approach for this Biomechanics I course.

Fig. 1.

Stages of backward course design [30] applied to developing Biomechanics I course CM&S modules. The practical approach includes (a) defining the learning goal(s) and outcome(s) for the course, (b) planning assessments to determine if students have achieved the outcomes, and (c) establishing learning experiences and instruction. These components encompass the new pedagogical content for students to engage in the teaching laboratory.

While the learning outcomes specified knowledge expected for students to obtain in the overall course, each CM&S module had individual learning objectives (i.e., specific knowledge expected for students to obtain in a single lesson) that helped direct each activity—beyond essential knowledge acquisition. As such, learning objectives targeted increasingly higher orders of Bloom's Taxonomy throughout the semester to encourage students to develop critical thinking skills, problem-solving abilities, creativity, and adaptability (Fig. 2 [31]). These skills are beneficial in the academic setting and crucial for achieving success in one's professional, personal, and civic activities. Moreover, the learning activities allowed students to learn factual and conceptual knowledge, whereby students learned by and from modeling, respectively [32]. Students achieved factual knowledge or learning by modeling (i.e., building simulations) through engagement in FEA model construction (i.e., step-by-step model creation). In this component, the modules tasked students with creating geometries, discretizing the model, defining and assigning materials, creating and assigning boundary conditions, setting solver parameters, submitting jobs, postprocessing data, and interpreting results. Students learned conceptual knowledge or learning from modeling (i.e., using simulations) by analyzing and interpreting simulation results from prebuilt models. Importantly, these prebuilt models reflected key concepts from the didactic lecture component of the course.

Fig. 2.

CM&S learning modules (M1–M4) and associated learning objectives are organized within Bloom's taxonomy [31]. Early modules targeted lower-order thinking skills (e.g., remembering, understanding, and applying knowledge), while the latter modules targeted high-order thinking skills (e.g., evaluating and analyzing). The modules did not focus on creating new information, which was reserved for advanced graduate-level courses.

The modules implemented a learner-centered approach to leverage PBL strategies [21]. Students completed the module lessons independently to promote active learning and student autonomy. Central to lesson planning, the TA prioritized a respectful, inclusive, and supportive educational environment that encouraged discussion. The TA provided supplementary instruction and assistance (e.g., assist with febio) and engaged with students by asking topical questions that feature contextualized learning (e.g., Can you describe real-world applications of this model?), critical thinking skills (e.g., Can you predict the modeling results before examining the FEA results file?), and reflection elements (e.g., How do the FEA results differ to the analytical solution you learned from lecture?) The TA posed the questions throughout the module to promote peer-to-peer discussion and teamwork within student groups (i.e., collaborative learning).

2.3 febio Learning Modules.

We developed four learning modules with learning objectives that directly supported course outcomes (Table 2; Fig. 3). Modules began with a traditional instructor-centered teaching approach in the form of a 10-min lecture to provide the rationale for the exercise and relevant background information. Next, students completed a series of guided tutorials with step-by-step procedures and prebuilt models to achieve learning objectives and reinforce learning outcomes. Finally, students were tasked with completing CM&S exercises to assess learning and competency and answered survey questions to evaluate module effectiveness.

Table 2.

CM&S module learning objectives, learning activities, and student assessment

Module	Learning objectives	Learning activities	Student assessment
M1	• Remember the basic principles of FEM and applications of FEA. • Understand simple deformations of basic shapes.	• Learn basic principles of the FE method and applications of FEA in biomedical engineering. • Construct FEA models of translation, tension, compression, and shearing. • Visualize differences between homogeneous vs. Nonhomogeneous deformation and incompressible vs. Compressible materials.	• Can students remember the basic principles of the finite element method? • Can students remember the basic steps to create an FEA model? • (E1) Do students understand the correct boundary conditions for biaxial stretch? • (E2) Do students understand the correct boundary conditions for confined compression?
M2	• Understand how to calculate strain and stress. • Apply FEA to simulate a tensile testing experiment.	• Develop FEA model of uni-axial loading. • Extract and analyze metrics of stress and strain. • Identify differences in Cauchy and 1st Piola-Kirchhoff stress. • Interpret the impact of modeling assumptions. • Quantify material properties from tensile test data.	• (E1) Can students understand how to postprocess FEA results and create stress-strain curves? • (E2) Can students apply the correct boundary conditions to mimic a tensile testing experiment? • (E3) Can the students explain the differences in stress between the rectangular strip and dogbone-shaped geometries?
M3	• Apply FEA to visualize traction and displacement. • Analyze material symmetry and elasticity constants.	• Visualize the physical meaning of engineering elastic constants through FEA models. • Differentiate between elasticity constants. • Implement isotropic and anisotropic material models in FEBio.	• (E1) Can students apply tractions and displacements in FEA models to identify whether an isotopic or anisotropic material describes a body? • (E2) Can students analyze an FEA model to determine the preferred direction of a transversely isotropic material? • (E3) Can students determine the engineering elasticity constants from FEA stress-strain data?
M4	• Analyze material failure due to applied loads. • Evaluate a beam-bending FEA model with V&V.	• Critique material models for elasticity and plasticity. • Differentiate between ductile failure stress criteria (e.g., Von Mises, stress-strain, necking) • Perform verification testing to evaluate errors between FEA results and analytical solution. • Perform validation testing to evaluate errors between FEA results and experimental data.	• Can students apply the correct boundary conditions for 3-point bending? • Can students build an FEA model of the lab experiment for 1-point bending? • Can students analyze and discuss the V&V data for 1-point bending?

Fig. 3.

Summary of the four FEBio learning modules used in Biomechanics I laboratory exercises. (M1) Introduced students to basic FEA terminology (e.g., analytical versus discrete model) and its applications in biomechanics. Students constructed FEA models of simple deformations on a unit cube. (M2) Students focused on concepts of stress and strain, creation of a tensile test FEA model, interpretation of modeling idealizations/assumptions, and recognition of different stress measurements (Cauchy versus first Piola Kirchhoff). (M3) Students applied tractions and displacements and visualized the physical differences of elastic coefficients (e.g., Young's modulus, Poisson's ratio) and their effects on stress and strain. (M4) Students focused on concepts of material failure with various loads applied to geometries ranging from a simple rectangular beam to a prosthetic hip implant. Students performed a minor V&V study to evaluate a 1-point beam bending model.

Module 1 focused on introducing students to FEA, including basic terminology (e.g., discretization, elements, nodes) and its application in biomechanics. Module learning objectives directed students to comprehend the basic principles of FEA, learn its application within febio studio (i.e., software introduction), and recognize differences in model results of finite deformations previously covered in lectures. The activities guided students through constructing FEA models of simple deformations on a unit cube (e.g., tension, compression, translation, rotation, and shear).

Module 2 emphasized the concepts of stress and strain. Objectives focused on students' understanding of stress–strain curves, interpreting the effects of modeling idealizations/assumptions, and recognizing differences in measures of stress (Cauchy versus first Piola Kirchhoff). The activities directed students through creating an FEA model of a tensile test on a rectangular strip.

Module 3 reinforced the principles of linearized elasticity and material symmetry. Learning objectives facilitated students to differentiate between the physical meaning of the coefficients of elasticity and distinguish the differences in deformations across changes in coefficients of elasticity and material symmetry. Students completed exercises to visualize stress and strain differences in FEA models with different material properties (e.g., Young's modulus, Poisson's ratio) by applying applied tractions and displacements.

Module 4 aimed to introduce students to verification and validation (V&V) and emphasize concepts from material failure. Specific objectives were for students to evaluate V&V testing for beam bending and contrast material failure theories. The activities guided students through applying distributed/point loads and the deformations for elastic and elasto-plastic materials, including the loading on a prosthetic hip implant obtained from the GrabCAD online community3 [33].

2.4 Exercises, Assessments, and Surveys.

Following module tutorials, exercises in each module tasked student groups to construct and analyze more advanced FEA model(s) that combined and extended multiple concepts from that CM&S module, classroom lectures, and the experimental labs (Table 2). Module 1 exercises assessed the ability of students to prescribe loading boundary conditions (biaxial stretch, confined compression) from a provided deformation gradient on a noncuboidal geometry and interpret model results from concepts in finite strain theory. Module 2 exercises charged students to create an FEA model of an experiment performed in a prior lab (uni-axial loading of a dogbone-shaped object) and postprocess FEA data to generate stress–strain curves. Module 3 required students to identify whether an unknown material was isotropic or anisotropic solely through FEA. Also, students quantified material properties (e.g., elastic modulus) from FEA-derived stress–strain data. Finally, Module 4 tasked students to collect analytical, experimental, and FEA data and analyze V&V within the context of one-point beam bending (performed in a prior lab).

The assessment measured student learning and competency with FEA based on the quality of the solutions proposed, the depth of understanding demonstrated, and the effectiveness of the problem-solving process rather than traditional quizzes or exams. For each exercise across modules 1–3, the TA recorded the number of attempts each student group (n = 32) took to execute febio successfully. An attempt was defined as executing the FEBio model with the possibility that it could terminate normally or fail. For module 4, students built and analyzed a 1-point beam bending model and discussed the V&V data in a lab report. A reduction in the number of simulation attempts before achieving successful model termination was directly correlated to student learning and achievement of the module's learning objectives.

Students completed questionnaires to measure module effectiveness. To evaluate student learning and competency, online surveys via Canvas (Instructure Inc., Salt Lake City, UT) were offered at multiple points during the semester (Table 3). Students answered survey Questions 1 and 5 as Yes/No. Questions 2, 3, and 4 utilized a five-point Likert scale to measure interest and agreement (1—not interested, strongly disagree, 5—extremely interested, strongly agree). Questions 6–8 allowed open-ended responses to collect student opinions on module effectiveness in supporting course outcomes, their presumed applications of FEA from the modules (i.e., contextualized learning), and how to improve the teaching and educational material. To qualitatively analyze each open-ended response, we developed an inductive coding scheme to categorize and label responses based on common themes or concepts. Emerging categories that reflected the underlying trends were summarized into illustrative quotes of select student responses. Qualitative responses and data were anonymized.

Table 3.

Student survey prompts at three time points throughout the semester

Time point(s)	Question prompt	Time point(s)
Before M1	(1) Before this course, have you heard of “finite elements” or “finite element analysis”?	Before M1
Before M1, before M3, and after M4	(2) How interested are you in continuing to learn CM&S?	Before M1, before M3, and after M4
Before M3, after M4	(3) Have the FEBio modules integrated important concepts from the lecture to help students achieve the learning outcomes?	Before M3, after M4
Before M3, after M4	(4) Have the FEBio modules educated biomedical engineering students on the value of FEA for future professional activities?	Before M3, after M4
After M4	(5) During this course, have you explored FEBio on your own?	After M4
After M4	(6) What was the most beneficial aspect of these modules for you?	After M4
After M4	(7) What biomedical applications or diseases would you find most interesting to apply FEA to study?	After M4
Before M3, after M4	(8) Please provide feedback on the modules' overall effectiveness, the TA's instruction/teaching, and what can be changed or improved for the future	Before M3, after M4

Quantitative assessment and survey data were analyzed in MATLAB (ver. R2023b, MathWorks, Natick, MA). Descriptive statistics are reported as mean±standard deviation. Survey data were ranked, and inferential statistics were calculated using the nonparametric Wilcoxon signed rank test and Friedman test, with a $p$-value less than 0.05 indicating a significant difference between time points. The University of Utah IRB considered the study procedures to constitute nonhuman subjects research and thus did not require IRB oversight.

3 Results

Prior to introducing the new CM&S instructional modules, only 34% of the students (28 out of 83) recognized the terms finite elements or finite element analysis (Question 1). Students were neutral to learning CM&S, as the average score in response to Question 2 was 3.1 ± 1.1 (Fig. 4(a)). However, it became evident as students progressed through the CM&S modules that their interest in the topics and applications of FEA significantly increased (Fig. 4(b)). Following Modules 2 and 4, the average response scores for Question 2 were 3.6 ± 1.0 and 3.5 ± 1.2, respectively. A significant increase in student interest was observed from before M1 to before M3 ( $p\hspace{0.17em}$< 0.001) and from before M1 to after M4 ( $p$ < 0.01). Likewise, data demonstrated a significant increase in interest across all modules ( $p\hspace{0.17em}$< 0.01). Finally, the number of students who were extremely interested (Likert score of 5) in continuing to learn CM&S increased from 9.6% (eight students) before the start of the modules to 21.8% (17 students) following the completion of Module 4.

Fig. 4.

Student survey responses to Question 2, “How interested are you in continuing to learn CM&S?” at time points before, at the midpoint, and after completing the modules. (a) Histogram distribution of responses ranges on a Likert scale from 1—not interested to 5—extremely interested (b) Box-plot distribution of Question 2 responses with statistical testing results.

Students agreed that the modules effectively aided their understanding of theoretical concepts introduced during lectures (Question 3 score: 4.4 ± 0.6 before module 3, and 4.6 ± 0.5 after module 4; Fig. 5(a)) and provided a strong CM&S foundation (Question 4 score: 4.7 ± 0.5 before module 3, and 4.8 ± 0.5 after module 4; Fig. 5(b)). Notably, >60% of students (50 out of 83) explored febio outside the teaching lab, including exploring user projects in the febio studio model repository (Question 5).

Fig. 5.

Student survey responses to (a) Question 3, “Have the FEBio modules integrate important concepts from the lecture to help students achieve the learning outcomes?” and (b) Question 4, “Have the FEBio modules educated biomedical engineering students on the value of FEA for future professional activities?” The histogram distribution of responses ranges on a Likert scale from 1—strongly disagree to 5—strongly agree. Time points were taken at the midpoint and after completing the modules.

In addition to increased interest in CM&S as modules progressed, students demonstrated increased understanding and comprehension of FEA model development and using febio studio to achieve the learning objectives. Within Modules 1, 2, and 3, students required fewer attempts (i.e., successful execution of the FEBio models) to complete the exercises at the end of the module (Fig. 6). In Module 1, for example, the number of attempts to complete exercise 1 (biaxial stretch) and 2 (confined compression) reduced from 4.6 ± 2.2 to 2.9 ± 1.6, respectively ( $p\hspace{0.17em}$< 0.001). In module 2, the number of attempts across the three exercises decreased from initially 3.0 ± 1.1, to 2.2 ± 1.2, and finally to 1.8 ± 1.4 ( $p$<0.001). In module 3, the number of attempts across three exercises were 1.6 ± 1.3, 1.8 ± 1.0, and 1.8 ± 0.9. No significant reduction in the number of attempts were observed across the three exercises ( $p\hspace{0.17em}$> 0.1). Moreover, the total number of attempts decreased across modules. For modules 1, 2, and 3, students required 3.8 ± 2.1, 2.3 ± 1.3, and 1.7 ± 1.1 attempts, respectively, to successfully complete the FEA model exercises.

Fig. 6.

Number of attempts to successfully execute FEBio models within and across exercises in Modules 1–3

Responses to the open-ended Questions 6, 7, and 8 were overwhelmingly positive. Students acknowledged the value of visualizing deformations and modeling examples of theoretical concepts introduced in the classroom. Also, students recognized the importance of coupling theory, experiments, and modeling, and, importantly, how modeling can guide experiments. Select student responses to Question 6 included:

“[The modules] were a good visualization of what we were learning in class. Sometimes it is hard to know exactly what is happening unless I can see how the object is being deformed.”

“Just observing what difference deformations looked like helped give context to everything learning in class.”

“The most beneficial aspect of these modules was the step-by-step directions and getting to simulate experiments from actual lab computationally. It really helped reinforce lecture material and bettered my understanding of the labs.”

“The most helpful component of these modules was the opportunity to use the software for a lab that was performed in another week. It was very helpful to see the experiment in real life then to use finite element to model that experiment. This made the software not so abstract and allowed for me to more clearly understand the software's purpose in engineering.”

In response to Question 7, students proposed numerous areas in medicine and biomedical engineering where they thought FEA might be best applied. The design of orthopedic devices and treatment of cardiovascular disease were the most common responses, but students identified that FEA had applications in, for example, ophthalmology, cancer, and tissue engineering. It was apparent that students grasped the importance of CM&S in biomedical engineering and its broad application. Select student responses to Question 7 included:

“I think the most interesting application is testing designs, instead of having to go through the process of a bunch of prototypes, testing them via FEA to find faults, then reiterating before a prototype is made seems more effective and efficient.”

"I'd like to look at different soft tissue implants or soft biological tissue application. Simulating a concussion would be really cool (using different helmet models to see which dissipates force better!!), or perhaps analyzing a cartilage implant using different materials to make informed decisions on the best materials to use.”

“Before this class, I mostly thought of medical device compatibility in the setting of device rejection by the body. However, I should also think about it in the sense of biomechanics. Making sure a medical device does not physically break has to be one of the most important considerations in this field.”

Several students commented on the course teaching environment and how FEA was introduced in an interactive lab environment, not the didactic classroom. Students appreciated the thoughtful design of the new CM&S teaching modules and the ability to explore modeling scenarios through guided tutorials and independent group tasks. Select student comments include:

“[I]t was nice to experience engineering in a low pressure environment where my curiosity could run a little.”

“The modules were laid back enough to provide a low stress introduction to the terrifying and intimidating world of FEA. It allowed students to casually become more comfortable with the software while also teaching us how to use it to apply and expand on class concepts. Due to this class and the experimentation with FEA it encouraged, I feel far more confident in my ability to not only perform a finite analysis, but to create and use models to solve problems on my own.”

Lastly, students provided valuable feedback to aid the improvement of the module content and pedagogical strategies. These comments ranged considerably, for example, to create prerecorded lecture videos to allow for more active learning time, to remove instances of intricate wording in the guides, and to add another TA to support student groups. Select student responses to Question 8 include:

“I believe that giving some preparation work before the FEBio modules would allow for them to get started much quicker. Maybe pre-recording instructions that people must watch would allow for more work to get done at the same time.”

“the wording is sometimes confusing on some things when it comes to which element or node to select.”

“I wish there was an additional TA that would also rotate around. Sometimes I felt like the only TA there would only attend some groups more than others.”

4 Discussion

This study describes the development, integration, and assessment of new CM&S learning modules within an undergraduate biomechanics course. Utilizing febio and febio studio software [26,27], this study demonstrated the successful incorporation of learning modules that directly supported the course goals, serving as an effective instructional tool to augment existing lecture and experimental lab content. Moreover, the innovations introduced students to modern FEA software and provided students with a foundation for CM&S. Student survey responses and assessments revealed an increasing interest and competency in CM&S, indicating that these modules promoted the learning of biomechanics course content and application of CM&S for biomedical problems. Moreover, students' desire for additional FEA exposure and continued use in their coursework was notably enhanced.

An essential component deliberately designed into the newly developed CM&S modules was course integration and pedagogical utility (see Table 2 and Fig. 2). Given the application of the backward course design approach (see Fig. 1) [30], course goals and learning outcomes were considered prior to module content creation, guiding module development from the beginning [32]. Leveraging previous reports of integrating CM&S into undergraduate engineering education [34], learning activities developed in the CM&S module targeted factual and conceptual knowledge. Student survey results showed that the modules promoted classroom learning, and students indicated the modules contributed to their success in meeting the overall course goals/outcomes and learning practical engineering skills (see Fig. 5). Critical to the interpretation of the survey data, development of the questionnaire prompts did not involve engagement with cognitive scientists. This limitation could imply student responses were prone to bias and subjective interpretation. It is recommended that the future prospective of this study consult with teaching centers. These efforts will improve the design of the survey questions to ensure validity, reliability, and consistency.

Through the completion of assessment exercises that targeted higher orders of Bloom's taxonomy (see Table 2 and Fig. 2), results demonstrated that students were able to successfully execute models in fewer attempts over the semester's course (see Fig. 6). Although direct assessment on module material, such as homework or exams, was not conducted, these data suggest the achievement of learning objectives. Such knowledge gain improvements and cognitive growth have the potential to promote learned problem-solving skills and design-oriented activities. Achieving higher orders of Bloom's Taxonomy is essential for undergraduate engineering education to enable students to address and solve diverse and complex problems effectively. Thus, integral to CM&S module design and development was ensuring that the relevant assessment exercises targeted higher orders of Bloom's taxonomy (see Table 2). While the CM&S assessment exercises initially targeted the ability of students to remember, understand, and apply knowledge (e.g., application of boundary conditions for simple deformations; Module 1), the latter assessment exercises required students to evaluate and analyze FEA results (e.g., V&V exercise; Module 4). Indeed, the students demonstrated increased competency in FEA and using febio (see Fig. 6), highlighting module effectiveness in promoting students learning. Furthermore, students demonstrated an increased ability to become self-directed learners (see Table 3; Question 5). The collective experience and results from this CM&S innovation support the continued integration of well-designed, properly implemented CM&S practices into biomedical engineering education. In addition, the new teaching emphasis facilitates student training in modern engineering techniques and tools broadly used in the professional setting (see Fig. 5(b)). Importantly, this can guide curricular development that aligns with accreditation requirements [35] and with the academic-industry Delphi process ranking the importance of engineering concepts in the biomedical engineering curriculum (e.g., see Table 4 in Ref. [23]).

One advantage of CM&S is that it provides direct visualization of phenomena traditionally taught didactically through fundamental principles and governing equations. In biomedical engineering, stresses in biological tissues, laminar flow in conduits, and tissue thermal damage are some examples of where students naturally and intuitively leverage CM&S software to visualize examples of theoretical concepts. Student responses to Question 6 (see Table 3) prove that the modules facilitated students' improved understanding of theoretical concepts taught in the classroom (e.g., deformation gradient) through active learning activities. These data suggest that the continued integration of CM&S into additional undergraduate biomechanics and biotransport courses should aid students' understanding of complex relationships between theory and practice through effective PBL strategies [23]. Although no direct assessment of promoting overall course goals was performed in this initial implementation, future offerings will allow for the comparison of student performance on classroom assignments and exams. It should be highlighted that febio is already integrated into the advanced-level Biomechanics II and Biofluid Mechanics courses in the Department of Biomedical Engineering at the University of Utah. Further, the upper graduate-level Computational Biomechanics course in the Department's curriculum focuses on learning both theory and application of febio. Thus, extending important FEA concepts and technical features into Biomechanics I to prepare students for more advanced courses was a logical step based on the success and student interest in those classes.

The febio and febio studio software [26,27] offers many advantages as an instructional tool to enhance undergraduate (and graduate) classroom settings and capabilities. As the software is tailored to address problems in biomechanics and biophysics, it provides the computational resources and numerical approaches to tackle real-world problems in biomedical engineering. In addition, extensive software documentation and curated tutorials, regular webinars and workshops hosted by the developers, excellent user support and forums, and mechanisms for disseminating results, models, and data accompany each suite. Importantly, febio features an extensive online model repository, where the febio development team posts numerous model tutorials and test suites for the community. In addition, febio users can submit projects often linked to peer-reviewed manuscripts to promote further dissemination. Indeed, the teaching materials and FEA models described herein are available on the model repository4. Lastly, febio and febio studio are open-source software providing easy access to state-of-the-art FEA tools without financial burden to the institute or student.

In conclusion, integrating CM&S into undergraduate biomedical engineering education materials holds much promise in promoting improved student learning experiences and outcomes and introducing students to modern engineering tools relevant to professional development. We report the benefits of integrating carefully designed FEA and the febio software into an undergraduate biomechanics course and the effectiveness of these innovative materials in supplementing lecture material and providing students with a broad foundation of computational biomechanics. Importantly, the approach is consistent with accreditation criteria and program outcomes, and engineering students can immediately leverage their learned skills in senior capstone design, graduate courses, and thereafter, in the modern workplace.

Funding Data

• National Institute of Biomedical Imaging and Bioengineering (Award No. U24-EB029007; Funder ID: 10.13039/100000070).

• National Institute of General Medical Sciences (Award No. R01-GM083925; Funder ID: 10.13039/100000057).

• University of Utah (University Teaching Assistantship (UTA); Funder ID: 10.13039/100007747).

Nomenclature

CM&S =

computational modeling and simulation

FDA =

food and drug administration

CFD =

computational fluid dynamics

PBL =

problem-based learning

FEA =

finite element analysis

TA =

teaching assistant

V&V =

verification and validation