heart beats
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From Scaling and Invariants in Cardiovascular Biology John K-J.Li:
"the total number of heart beats in a mammal's lifetime is invariant." Since we had the discussion of beatless heart pumps and because I have nobody local to argue with about these things, I thought I'd ask y'all. A friend of mine reminded me of this (seemingly false to me) invariant the other day while discussing the life expectancy of the new kitten they adopted. My question is whether or not it's believable given the large variance and lack of data in such measures. And although I reluctantly accept the scaling relationship between basal metabolic rate and mass, it seems pretty questionable to claim that BRM is a linear composition. Does anyone have any cites validating or refuting that mammals, across scales, have the same number of heart beats over their lifetime? Am I just being stubborn? -- glen e. p. ropella, 971-222-9095, http://tempusdictum.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
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On the face of it, it's pretty absurd. If a human has an average heart rate of 70 beats per second and an average lifetime that is 10 times that of a dog, the dog's average heart rate would be 700 beats/sec. Don't think so.
Ed __________ Ed Angel Chair, Board of Directors, Santa Fe Complex Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab) Professor Emeritus of Computer Science, University of New Mexico 1017 Sierra Pinon On Oct 23, 2011, at 1:41 PM, glen e. p. ropella wrote:
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
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On 10/23/2011 1:48 PM, Edward Angel wrote:
> On the face of it, it's pretty absurd. If a human has an average heart > rate of 70 beats per second and an average lifetime that is 10 times > that of a dog, the dog's average heart rate would be 700 beats/sec. > Don't think so. And it is inverted within the species -- small dogs live longer than large dogs (large dogs having heart rates of 60-100 bps), yet have higher heart rates (100-140 bps). http://biomedgerontology.oxfordjournals.org/content/51A/6/B403.abstract Anyway, how do you pin down this invariant unless you know the cause of death was heart failure? Marcus ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
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It is approximately invariant. See for example Joseph Bronizino's "The Biomedical Engineering Handbook: biomedical engineering fundamentals", section 17.4 "Comparative Analysis of the Mammalian Circulatory System"
—R P.S. So has the Google broken down in your corner of New Mexico? If you Google "the total number of heart beats in a mammal's lifetime is invariant" you get the above as the very first link. How much easier does the interweb need to be for members of FRIAM? ;-)
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In reply to this post by Marcus G. Daniels
Marcus G. Daniels wrote circa 11-10-23 01:16 PM:
> On 10/23/2011 1:48 PM, Edward Angel wrote: >> On the face of it, it's pretty absurd. If a human has an average heart >> rate of 70 beats per second and an average lifetime that is 10 times >> that of a dog, the dog's average heart rate would be 700 beats/sec. >> Don't think so. > And it is inverted within the species -- small dogs live longer than > large dogs (large dogs having heart rates of 60-100 bps), yet have > higher heart rates (100-140 bps). > > http://biomedgerontology.oxfordjournals.org/content/51A/6/B403.abstract > > Anyway, how do you pin down this invariant unless you know the cause of > death was heart failure? Well, this is as far back as I can get until I get my hands on some physical paper: Scaling, why is animal size so important? By Knut Schmidt-Nielsen I'd like to get my hands on this one, though: Life History Invariants Some Explorations of Symmetry in Evolutionary Ecology Eric L. Charnov It's odd that they're _books_ instead of journal articles. I'm hoping that if I do get my hands on them, they'll cite some peer-reviewed articles and show the actual data. The google preview for Knut's book shows straight line models for the heart rate to mass relationship, but no the data. The preview did show one observed/model comparison for the shrew: observed: 600(rest)/1320(max) in min^-1 expected: 1029 observed/expected 0.6 0.6*1029 => 617.4 ..., so I assume he used 600/1029. As far as I can tell, the _derivation_ of the "approximately invariant" heart beats is only implied by West et al: Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals, PNAS 99, 2473–2478. "This value follows from the empirical observation (2) that heart rate scales as MϪ1/4, ..." That seems pretty flimsy to me. So, I'm still looking. -- glen e. p. ropella, 971-222-9095, http://tempusdictum.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
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glen e. p. ropella wrote circa 11-10-24 11:11 AM:
> Scaling, why is animal size so important? > By Knut Schmidt-Nielsen I checked out a copy of this one, and in Chapter 11, we find these gems: "The rate of oxygen consumption in mammals, relative to body size, decreases with increasing body size." "... the decreased relative need for oxygen and blood flow in the large animal is not achieved through a relatively smaller heart or stroke volume, but through a decrease in heart rate." So, as far as I've found West et al merely imply the derivation of hear beats from heart rate. There is data for heart rate. But the explanation of the heart rate data (above) relies on common knowledge I don't have or assumptions that are/were considered reasonable. I'm still looking for an explicit derivation of the heart beat invariant, which I would hope includes an analysis of variance. > Life History Invariants > Some Explorations of Symmetry in Evolutionary Ecology > Eric L. Charnov I also checked out a copy of this. And we see a hint at the confirmation bias in this quote: "Allometries can of course be multiplied or divided by each other to make up new allometries." I ran some _naive_ numbers on heart beats per lifetime (hble) in relation to heart rate (hr) and life expectancy (le) for humans (H), cows (C), and dogs (D). If I ass/u/me hr and le are independent (I know that's a false assumption, but since cov(hr,le) <= sqrt(v_hr*v_le), I think it's close enough) and my arithmetic is somewhere near correct, then it seems to me that the variance (v) in the inputs: v^H_hr: 81, v^H_le: 49 v^C_hr: 56, v^C_le: 6 v^D_hr: 49, v^D_le: 5.6 explodes when you combine them to get the "invariant" (m := mean): m^H_hble: 2.96e9, v^H_hble: 4.5e8, > 3s m^C_hble: 5.8e8, v^C_hble: 1.2e16, > 8s m^D_hble: 1.1e9, v^D_hble: 1.6e17, > 1s s := standard deviation. West et al states hble ~= 1.5e9, which is just over 1 s for dogs, but over 3s for humans and over 8s for cows. With numbers like that, I doubt Charnov's claim to be able to derive one allometry from another. But even if I accept that, my doubt is compounded in the derivation of the invariants, no matter how much magic is installed in the "approximation". I'm coming around to believe (parts of) the argument made here: The Illusion of Invariant Quantities in Life Histories http://www.sciencemag.org/content/309/5738/1236.abstract Anyway, I'm still looking for heart beat data and a published derivation. I welcome hits from the clue stick. -- glen e. p. ropella, 971-222-9095, http://tempusdictum.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
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