The human heart is confusing and has befuddled countless musicians and poets. I’m here to throw engineering topics shed clarity on the issue and maybe even help someone like Taylor Swift understand a few things about the heart.
Engineers love it when a system’s inputs and outputs are all measurable, since this lets them model the system and then predict the output. I’ll do this with heart rate as an output and speed and incline as inputs. These are by no means all the inputs and outputs of the human heart, but they should be related.
I used a heart rate monitor and ran on a treadmill at different speeds to plot the relationship between speed and heart rate, shown below.
The correlation coefficient between my speed and heart rate was 0.7483, so there was a significant positive relationship between speed and heart rate. Anyone, such as Taylor Swift, could pick different inputs, like number of times trouble walks in per week and see how the heart rate responds over time.
What is most important to notice is that the 2mph-14mph step input (around the 37 minute mark) causes a very smooth heart rate response, which can be treated as a first order system with the transfer function below.
Treating the data as a first order system results in the following estimate.
However, the heart isn’t simply a first order system with regards to speed as an input. The relationship is complicated. The heart rate oscillates a bit when settling into low running speeds. I did a bit of research into this and found it might be due to the interactions between the sympathetic (speeds up the heart) and parasympathetic (slows down the heart) nervous systems. The figure below shows how the heart rate oscillating when responding to low running speeds and how the oscillations decrease as the running speed increases.
Just for the heck of it, I looked at the oscillations my heart does during the step responses and used an FFT to find that my heart oscillates at about 0.016 Hz (period of 62 seconds). This might suggest you can get the biggest reactions from me if you scare me every 62 seconds. Someone, such as Taylor Swift, could look at the heart rate response to breakups and plan accordingly to reduce system volatility.
Next, I ran the following test so I could add percent grade as an input to the system. I set the treadmill to different speeds and inclines, then recorded the resulting heart rate.
I then used an autoregressive–moving-average (ARMA) model to estimate my heart rate based on input speed and percent grade
Finally, I compared this ARMA model to the first order model by applying them to real world data (instead of the treadmill data I made them from). Below is how the first order model fared with the real world data.
Although the real world data wasn’t that hilly it was hilly enough such that the first order estimate with only speed as an input didn’t do very well.
The ARMA model with both speed and percent grade did much better, shown below:
This ARMA model could become more accurate by including more terms in the model, but then I would be making a simple engineering analysis of the heart complicated. I kept this analysis simple so that any person, like Taylor Swift, could talk to her friends, who would talk to their friends who would talk to others about the benefits of developing models for heart-input relationships.
Learn more about DMC's company culture.