In this blog, I often stress the value of toy models. I’m not the only one who feels this way. Anne-Marie Hoskinson and her colleagues suggest that modeling is an important tool for teaching at the interface of physics and biology (“Bridging Physics and Biology Teaching Through Modeling,” American Journal of Physics, Volume 82, Pages 434–441, 2014). They write
While biology and physics might appear quite distinct to students, as scientific disciplines they both rely on observations and measurements to explain or to make predictions about the natural world. As a shared scientific practice, modeling is fundamental to both biology and physics. Models in these two disciplines serve to explain phenomena of the natural world; they make predictions that drive hypothesis generation and data collection, or they explain the function of an entity. While each discipline may prioritize different types of representations (e.g., diagrams vs mathematical equations) for building and depicting their underlying models, these differences reflect merely alternative uses of a common modeling process. Building on this foundational link between the disciplines, we propose that teaching science courses with an overarching emphasis on scientific practices, particularly modeling, will help students achieve an integrated and coherent understanding that will allow them to drive discovery in the interdisciplinary sciences.
One of their examples is the cardiac cycle, which they compare and contrast with the thermodynamic Carnot cycle. The cardiac cycle is best described graphically, using a pressure-volume diagram. Russ Hobbie and I present a PV plot of the left ventricle in Figure 1.34 of Intermediate Physics for Medicine and Biology. Below, I modify this plot, trying to capture its essence while simplifying it for easier analysis. As is my wont, I present this toy model as a new homework problem.
Problem 38 ½. Consider a toy model for the behavior of the heart’s left ventricle, as expressed in the pressure-volume diagram
(a) Which sections of the cycle (AB, BC, CD, DA) correspond to relaxation, contraction, ejection, and filling?
(c) Plot the pressure versus time and the volume versus time (use a common horizontal time axis, but individual vertical pressure and volume axes).
(g) Calculate the work done per beat (in joules).
(h) If the heart rate is 70 beats per minute, calculate the average power output (in watts).
(i) Describe in words the four phases of the cardiac cycle.
(j) What are some limitations of this toy model?
The last two parts of the problem are crucial. Many students can analyze equations or plots, but have difficulty relating them to physical events and processes. Translation between words, pictures, and equations is an essential skill.
All toy models are simplifications; one of their primary uses is to point the way toward more realistic—albeit more complex—descriptions. Many scientific papers contain a paragraph in the discussion section describing the approximations and assumptions underlying the research.
|A Wiggers diagram summarizing cardiac physiology.
Source: adh30 revised work by DanielChangMD who revised original work of DestinyQx;
Redrawn as SVG by xavax, CC BY-SA 4.0, via Wikimedia Commons
I’ll give Hoskinson and her coworkers the last word.
“We have provided a complementary view to transforming undergraduate science courses by illustrating how physics and biology are united in their underlying use of scientific models and by describing how this practice can be leveraged to bridge the teaching of physics and biology.”
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