# Heart rate and Metabolic rate relationship

Metabolic rate in humans can be approximated using the Penn State equation.

It can also be estimated using direct and indirect calorimetry.

According to Kleiber's law, metabolism scales across species proportionally to the mass by a power of 3/4 (also by 2/3 or the [2/3, 3/4] range for other models).

Now, despite the known relationship between temperature, mass and metabolism, the relationship between heart rate and metabolism is less clear. Heart rate also scales with body mass approximately by a power of -1/4.

Usually, as a human ages, both its metabolic rate and heart rate decrease. Also, there are many examples of animals with a very high metabolism that have a very fast heart rate, like the hummingbird or the etruscan shrew.

I want to know if metabolism, after controlling for mass, is related to heart rate. I find it suprising that nobody has studied this relationship. I guess more data is needed to generate a model (I found this site, which could be useful, beats-per-life).

Heart rate is related to the distribution of nutrients and oxygen to all organs in the body. I think a faster metabolism would require/imply a faster distribution. We know this is true at least within the same individual organism, for example, during the elevated metabolic demands of exercise. Despite all of this, I haven´t found examples of it being used in relation to metabolism.

Any ideas about why this might be the case? What's the relationship between metabolic rate after controlling for mass, and heart rate, if there is any?

What about cardiac output? Cardiac output is stroke volume times heart rate. A bigger body tends to have a bigger heart, a bigger heart likely implies a greater stroke volume. Maybe if you adjust stroke volume by weight, and combine it with heart rate, you get an even better indicator of metabolism.

I think this is correct, the relationship between heart rate and metabolism exists, and can be explained by oxygen consumption. This is given by the Fick principle. That is:

$$VO_2 = CO (C_a-C_v)$$

Where $$(C_a-C_v)$$ is the arteriovenous oxygen difference. So:

$$VO_2 = (HR·SV)(C_a-C_v)$$

$$MR ∝ VO_2$$

$$MR ∝ (HR·SV)$$

Given that:

$$SV ∝ Weight$$

You could estimate Metabolic rate using a combination of Weight and Heart rate. Let's assume the stroke volume follows an allometric power law given by the exponent $$e_{SV}$$. Then:

$$SV≈ a_1+b_1M^{e_{SV}}$$

(I guess lean body mass is more related to organ size than just Mass, so you probably could use it instead of Weight to estimate the Stroke volume)

$$MR ∝ a_1+b_1M^{e_{SV}}·HR$$

Alternatively: $$MR ∝ LBM·HR$$

So, to summarize, I think Heart rate, through its effect on cardiac output and oxygen consumption, gives information about the metabolic rate that goes beyond mass, and can be used in combination to estimate it. The specific model type (logarithmic, linear, exponential...) that uses $$a_1+b_1M^{e_{SV}}$$ and $$HR$$ is unclear but It might still work.

• Please make sure to readers where Fick's principle ends and your personal assumptions start. While your assumed correlations individually seem plausible, they are presented without any source whatsoever. Especially, the step from 𝑀𝑅∝𝑉𝑂2 to 𝑀𝑅∝(𝐻𝑅·𝑆𝑉) seems dubious. Sure, there is a correlation between cardiac output and metabolic rate, but what is the margin of error? The OP, based on their research, asked the question WHY the heart rate is NOT used in the literature to determine MR. Jun 8, 2022 at 17:22