Incorporating Human Body Variance in an Analytically Focused Undergraduate Biomechanics Course

Human bodies vary widely: height, weight, blood volume, handedness, strength, and variations from disabilities, trauma, genetics, etc. Engineers must be trained to include human variance when designing human-interactive systems. Typically, this is not incorporated into mathematical and modeling focused courses. In the spring of 2019, one of three sections of an introduction to biomechanics course was modified to adopt interactive group problem solving and add human body parameter variation to the problems that students solved. Problems were solved for multiple body sizes. Initial evidence suggests this was successful in increasing students’ consideration of human variation and user needs in mathematical modeling and in increasing their mention of specific body parameters and parameter variation. This can be implemented by a wide variety of instructors without special training in pedagogy or in universal design, especially when a course already features interactive small group problem solving, even during a large lecture by having students’ pair to solve equations briefly. Future steps might consider other parameters of diversity, inclusion, or equity topics. We were pleased to see that small changes in pedagogical approach can pay significant dividends encouraging students to situate analytic work in realistic engineering contexts.

to include) human variance when designing human-interactive systems. When biomedical engineering design products do not account for human variability, the consequences can cause harm (e.g., [1,26]).
Consider the ongoing development of anthropomorphically representative crash test dummies in automobile accident simulation. Despite concerns, they have traditionally been based on a typical adult body's geometry and structure [27]. In the US, this is codified in vehicle crash test safety standards which require only testing an average-sized adult male (50th percentile: 164lb, 5ft 9in) and a small adult female (5th percentile: 108 lbs, 4ft 11in) 7,22]. Numerous demographics are left out of testing (e.g., under-and overweight, tall, short, elderly, those with atypical body mechanics such as spasticity, etc.). The results of real-world crash testing continue to show the implications of these choices: certain demographics experience higher fatality rates per mile driven, and more severe injuries when these crashes do occur [2,13,27].
However, such debates and nuances are often excluded from 'technical' and analytically focused courses. Usually, connecting human variability to engineering design principles [3,5,25] and empathy [10], e.g., understanding 1 3 non-average user perspectives, and the importance of designing systems for them) are integrated into undergraduate engineering design courses instead. In this teaching tips article, we present one intervention to integrate understanding the technical principles of biomechanics with human variance and its interaction with biomechanics. This article will push back against those who think that math and technically focused courses do not need to attend to issues of diversity, access, equity, and inclusion, ostensibly because 'math isn't personal,' and/or, 'math is objective, not squishy' (see [9,18,19]).

Course Context
The course context was a traditional introduction to biomechanics course typically taken by 3rd-year biomedical engineering undergraduates: an introductory course in the principles of mechanics as applied to biological systems. The course is the first in a sequence that is specific to the biomedical engineering department and awards three credit hours. Course prerequisites include a static mechanics course and calculus sequence. The course provides students with basic concepts and approaches for solving linear deformation and rigid body dynamics problems relevant to biomedical applications. The major topics covered in this course are as follows: (1) stress and strain distributions in bone and simple structures under tension, compression, torsion, and bending; (2) mechanical properties of biological tissues, and (3) motions of particle and rigid bodies.
Three sections of the course were taught during this semester. For all sections, the course textbook was An Introduction to Biomechanics: Solids and Fluids, Analysis and Design [14]. The three sections had the same five main topics for their learning objectives: statics (a review topic); deformation in axial loading, torsion, and bending; and rigid body dynamics.

Intervention
The intervention incorporated frameworks of problemsolving studio (PSS, [20] and problem-based learning (PBL, see [15-17, 21, 24]). The PSS framework focuses on teaching students to solve difficult analytic problems without resorting to rote memorization. Students work with a partner for a semester, and these teams of two are additionally paired with another team in desk groupings of 4 in the classroom. Instructors and TAs circulate throughout the classroom space working with individual pairs as needed and leveraging the second team of two as needed. In PBL, students work in teams to solve ill-structured, real-world, cross-disciplinary problems that represent challenges faced professionally in the field. This flips traditional learning on its head-it is student-centered rather than instructor-lead (see [12]). Instructors provide information and context as students need it (and generally as students have initiated and identified a need for it), rather than providing it first and guiding students through a body of knowledge.
Two sections of the course were taught traditionally ("Control"). The intervention was implemented in one section of the course ("Intervention") in Spring 2019. Besides the intervention, all three sections remained standardized and consistent and included a set of instructor-defined constraints. Foremost, the course's focus on quantitative analysis could not be compromised, and any material on human variability would need to be integrated without removing existing elements. Also, the intervention could not require instructors to have a background in universal design or concepts related to diversity and inclusion.
To meet these constraints, the intervention included two parts. Both are related to effectively introducing human body variance into the course. The first was structural in nature while the second involved the types of problems given to students. First, we adjusted the use of time in the course. The Control version of the course met three times a week for a total of 4 h (three one-hour lectures and one TA-led recitation session, where a graduate TA solved a series of analytical problems on the board). The Intervention section met for 5 h per week, with 1 h of lecture and two two-hour PSS sessions [20]. In these PSS sessions, students collaboratively solved problems while working with peers.
Second, we modified the problems in the Intervention section to include human body parameter variability. That is, problems did not have singular solutions based on instructor-defined body sizes 1 , but were solved for multiple different body sizes including those of students. In the Control recitation sessions, TAs solved problems with specific defined body sizes. In the Intervention PSS sessions, body size parameters were not given but rather size percentiles were given and had to be looked up or interpolated from a reference [23].
In sum, the problems used in the TA-led recitation sessions and the PSS sessions were similar in technical demands and context. They differed in terms of whether body parameters were identified specifically rather than variably (recitation sessions in Control sections) or specified in terms of multiple size percentiles (PSS sessions in Intervention section). Importantly, based on constraints from the instructors, there was no explicit instruction on how to consider human variability. The topic was not introduced in lectures, placed as a learning objective on the syllabus, or otherwise taught to students.
Each section had different instructors. The Control section instructors were not involved in designing the intervention problems. A total of 27 students enrolled in the Intervention section, while 93 students total enrolled in the two Control sections. Grades and withdrawal rates were comparable between sections. During the course registration period, students were informed that they could enroll in a regular section of the course, or a "prototype" sessionwhere a new intervention was being implemented to address some concerns expressed by prior students. While we cannot be sure, any selection bias was likely due students' scheduling constraints (i.e., timing of course sessions during the week). Student demographics (gender, race, ethnicity, year level) were similar across the three sections.

Exemplar Problem: Forces Acting on Rock Climbers Hanging from a Wall
To explain what 'human body parameter variation' looks like in classroom practice, we present the first such problem used during a PSS session in the Intervention version of the course. The instructor showed a video and images of professional rock climbers, coupled with scaffolded instruction to help students relate their knowledge acquired in prior statics courses to the human body. The goal was to link the biomechanics course to prior instruction: non-biomedical engineering statics. Students were presented with the image shown in Fig. 1 (a screenshot from a video used in the session).
The instructor explained that their challenge was to make a force model of the rock climber for three different body types: 50th percentile male, 50th percentile female, and 5th percentile female [23]. Students had to create a free body diagram and solve it while making appropriate assumptions and interpolations for each of the three cases. The problem was designed to highlight how differences in human geometry could impact both the assumptions and values necessary to solve biomechanics problems as well as to highlight the difficulty in dealing with human geometry in even simple situations.
These specific body type points were chosen to build in human body differentiation based on one facet of UD (male, female averages) and a valid but extreme measure that would "break" the math they were doing. As a person gets shorter the support angles increase. At an extreme, the load is too large to allow for a person to hang. While working on the problem, students were encouraged to make simplifications, to be explicit about the types of joints they specified for hands and feet, and to apply the concepts they had already learned in prior classes-in keeping with other research on engineering model making processes [8]. Similar problems, built on specific course concepts in deformation mechanics and rigid body dynamics, were used throughout the course.

Reflection
The course remained clearly focused on mathematical analysis and retained the same content areas-meeting the instructor constraints. Students solved problems analytically, although in a PSS format rather than individually, but did so with varying parameters not previously required. The intervention was not difficult to implement as the major change was in adjusting or exchanging previously created recitation problems.

Evaluation
Initial evidence suggests the innovation was successful in increasing students' consideration of human variation and user needs in mathematical modeling and in increasing their mention of specific body parameters and parameter variation. A rigorous experimental design and analytic strategy was not the intent. The faculty developers working with the instructors collected impact data from the students enrolled in the course in order to evaluate whether this minimalist intervention made students more aware of human body parameter variations, especially when not specifically prompted to do so. One question specific to the intervention was added to a multi-part survey administered to all three sections near the end of the semester. Based on designing an exercise bike, the question sought to elicit the factors Fig. 1 Exemplar problem: forces acting on climber hanging from wall. Alt Text Adult is hanging from a "climbing wall," a wall that has surfaces in various directions with variously sized grips to hold. The adult is hanging horizontally with torso oriented upwards in a semi-V shape, with legs on left, right arm on right, and left arm moving to a new grip somewhere near the lower legs. On the right hand side, an arrow is drawn on the figure pointing left to the mid torso area labeled "Center of Gravity Moves." Another arrow is drawn on the left side of the figure pointing left from the core/buttocks area, labeled "pointing toward toe." students might consider when beginning to analyze a biomechanics problem. The question provided space for openended text responses to the following prompt: You have been asked to use your biomechanics knowledge to design a stationary bike for use in physical therapy. The bike should be designed with the user in mind. The customer has given you constraints related to cost, materials, weight, strength, and reliability. Please list other characteristics you would consider and explain how you would use those characteristics in the analysis process.
Participation was voluntary, and the survey was administered during class time by researchers not involved in course instruction. The overall response rate to this survey was 80%, with a rate of 76% in the Control sections and 93% in the Intervention section. While the Intervention group had a higher response rate than the control sections (odds ratio of Int respond:not respond vs. Cntl respond:not respond = 3.9), the response rate between the control and intervention groups was not statistically significant at the .05 level (χ 2 = 2.51, df = 1, p < 0.12; assumptions of 2*2 Chi Square test for independence were met; Yates correction used).
These responses (n = 71 from control group, n = 25 from intervention group) were coded in four ways: Whether or not they 1. Mentioned using biomechanics (UBM) in the solution (e.g., "…durability, stress, strain, deformation factors to withstand the weight"), 2. Considered user needs (CUN; e.g., "Details about patient's daily life… how will they transport bike?" "Potential weakness from injury needing physical therapy"), 3. Referenced human body parameters (RHBP; "Weight of the customer/height," "Body dimensions," "Leg length of patient"), and if so, 4. Whether they mentioned body parameter variation (BPV; e.g., "...consider the typical range of heights and weights of people…," "Ability to adjust to patients of different heights, abilities, ages…". The BPV code is a subset of the RHBP code. Table 1 summarizes frequency counts for those who responded to the assessment question, as well as independent sample Chi Square tests (Control group vs. Intervention group). Descriptively, the control sections made somewhat higher use of mentioning body mechanics (UBM) than did the intervention group (56% vs. 42%). For the other three categories, the intervention group was notably higher: 44% vs. 76% for considering user needs, 35% to 72% for referencing human body parameters, and 28% to 50% for referencing body parameter variation specifically. Two of these were statistically significant at the 0.05 level: CUN and RHBP. Students in the Intervention section were more likely to consider user needs in their answers compared to the Control section students, and they were more likely to reference human body parameter variation. Table 1 also summarizes the odds ratios of the Intervention group using the four measures versus the Control group using them. An odds ratio is a measure of relative risk of an outcome in one population compared to another population-here, students in the intervention section versus in the control sections. If an odds ratio equals 1 the outcome is equally likely in both groups (i.e., a ratio of 1:1). If an odds ratio is greater than 1, it indicates that the outcome is more likely for Intervention section. Conversely, if an odds ratio is less than 1, it indicates that the outcome is less likely for the Intervention section. Specifically, the intervention group considered user needs (vs. not considering them) in their answer over four times as often as those control group (CUN; ratio 4.09:1) and referenced human body parameters about 4.75 times as often (RHBP; ratio 4.73:1). For the two measures that were not statistically significant, the Intervention group was still more likely to mention body parameter variation and use biomechanics principles than their peers in the control sections: the odds ratio was 2.6 for referencing body parameter variation (RPV; ratio 2.57:1) and 1.74 for using biomechanics principles (UBM; ratio 1.74:1).  Figure 2 plots these odds ratios and their 95% confidence intervals. A bolded reference line indicates where it is equally likely for the Intervention and Control groups to use the coded measures. In two cases, the lower end of the two confidence intervals overlaps the "equally likely" reference. This is not a surprise because the chi square tests for these two measures are not statistically significant at the 0.05 level. Here, odds ratios are close to 1, and thus, likelihood is about equal for the code of mentioning body mechanics and considering user need. For both referencing body parameters in general and mentioning body parameter variation in particular, the odds ratios are above 4, with 95% confidence intervals ranging between about 1.5/1.75 to about 12 times as likely as the control groups.
Overall, results suggest that students from the intervention section were more likely to have answers coded with the considering user needs code and the referencing human body variation code. While not statistically significant at the 0.05 level, the direction of their answers being coded for mentioning biomechanics principles and specific body parameter variation was also higher than that in the control group. This is despite the instructors not lecturing or explaining the role of such parameters or their variance as a consideration in biomechanics solutions. Student inclusion of those parameters also seems to occur even when not specifically prompted to activate that knowledge. Of course, the intervention was two-pronged: Body parameter variability was added to the problems, and sessions were changed from recitations to PSS sessions. We cannot uncouple these two parts of the intervention and thus cannot assert definitively whether the change from recitation to PSS sessions and the inclusion of body parameter variation increased students' likelihood of considering user needs or referencing body parameter variation, or whether it was one of these changes or an interaction between both.
The multi-part survey administered at the end of the course also asked a variety of questions about student perceptions of things like motivation, self-concept, and classroom climate, most of which were not the focus of this study in body parameter variation. Students were asked an open-ended question about their engagement, "I felt most engaged in this course when….". In the Intervention section, 23 of the 25 students responded meaningfully to this prompt. Of those, 14 (60%) mentioned the studio sessions or working with their team on the problems (one student mentioned solving problems alone, one mentioned attending office hours, and a couple of other students mentioned the lectures). In the Control sections, 66 students responded to this prompt, and 35 (53%) of them mentioned doing the "recitation" problems in class or with class peers. Of these 35 students, 15 specifically mentioned working with peers, a few mentioned "solving problems myself," and most were non-specific about whether the recitation problems were interactive with their peers or not. (Others mentioned things like clear lectures, office hours, and doing homework and assessments). We did not analyze these data with statistical tests due to the self-report nature of the question and the limited idea of whether this measure impacted their understanding of UD and body parameter variation. In general, all three sections had positive reviews from students in response to this question.

Implications for Teaching
The largest effort in implementing the intervention was to replace some problems that either did not involve humans or excluded human body variation (e.g., the deformation of the leg of a hospital bed for an average male) with those that centered variability in human bodies (e.g., deformation of a crutch with different user sizes). We believe that these small changes in student-worked problems are able to activate existing commonplace knowledge (i.e., humans have bodies, not all bodies are the same) rather than to teach it. These problems and concepts can also be revisited later in other contexts. If instructors confer and connect across the curriculum, later instructors focused on designing for diverse user populations can refer back to examples from the analytical courses. In effect, this is the "spiral curriculum" approach [4], already used in both medical and some engineering fields [6,11], where the same problems end up doing double duty at different times to address both analytical skill-building and contextual awareness necessary to effective and inclusive engineering practice.
In current iterations of the course, sessions still rely largely on incorporating PSS problems and principles (although the specifics of the problems vary depending on who is teaching the course). While we don't have department-level implementation data, as a whole the department is involved in discussions of lateral fidelity of implementation (across multiple sections and iterations of a course) and spiraling-specific concepts vertically through multiple courses (including human body variation, and active problem-solving-based pedagogy). This intervention of adding human body variation can be implemented by a wide variety of instructors, especially if their course designs already feature interactive small group problem solving, which could also be done by having students' pair to solve equations briefly during a lecture. While this exercise focused on varying parameters of body mass and length, it is not hard to imagine varying other parameters of human diversity. Changing the numbers on problems involving human bodies and stating explicitly that a parameter value is for different bodies-of a child, or a person with a particular medical condition, or differences between genders-requires no specialized pedagogical training. This kind of intervention fit seamlessly into the context of an analytical class that did not specifically discuss or teach universal design, suggesting that there may be more opportunities for increasing inclusive engineering skills than has been previously realized. Future steps might consider variations of diversity, inclusion, or equity topics. We were pleased to see that small changes in pedagogical approach can pay significant dividends encouraging students to situate analytic work in realistic engineering contexts.