How to simulate this endotherm

8/7/2019 How to simulate this endotherm

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How to simulate this endotherm

Consider a 250 g generalised mammal where operative environmental temperatures varyfrom 10 to 40 oC. As an endotherm, assume that it generates heat endogenously whenever

its body temperature falls below 37.5 oC. Assume that its thermal conductance is typicalfor mammals of this size and that it can vary this thermal conductance six fold as manymammals can.

1. Open Calculators.xls and click on Allometric M calculator. Enter mass (250)

into one of the appropriate calculators presented. Using SMR according to White

et al. (2006), SMR is 1.168 W when Tb is 38oC, but you could use other

calculators.

2. Click on Ko calculator and enter 250 to get a minimal thermal conductance of


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0.1355 W/oC for mammals according to Withers (1992).

3. Click on Respiratory variables and enter 250 to get a minute volume of 98.71

ml/min for mammals according to Withers (1992).

4. Open Optemp.xls and enter data into St St Start. While these data will definethe reference equilibrium (see User Guide and paper for explanations) and shouldtherefore eventually be in the Eq End column, we need to use Tlc to balance

and this requires data to be in St St Start. Assume metabolic rate is basal (1.17

W) and thermal conductance is minimal (0.1355 W/oC), minute volume is as

calculated (99 ml/min) when metabolic rate is basal and increases in directproportion with increases in metabolic rate. So the proportionality factor is 1.

Lets have a cooling effect of the nasal turbinates, present in mammals, of say 5oC. Assume an arbitrary humidity of 30 % when air temperature is 20

oC.

Obviously, use respiratory minute volume (as opposed to total evaporative water

loss) and link minute volume to metabolic rate. We havent decided on an

operative temperature yet, but we dont have to. The program can do that for us.Any endotherm thermoregulating according to the Scholander-Irving model

should decrease its thermal conductance with decreasing environmental

temperature until this reaches its limit (maximum insulation). Then, the

endotherm will increase its metabolic rate with further decreasing temperatures tomaintain its body temperature (unless it goes torpid). The environmental

temperature at which body temperature can be maintained with minimum thermal

conductance and basal metabolic rate is known as the lower critical temperatureand Optemp.xls can calculate this using the button Tlc to balance. Enter the

mean body temperature (38) and press the button to obtain T lc of 30.26oC.


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5. Make operative temperature = the above result and press start to solve this

stage (i) simulation and define what will become the endpoint equilibrium and

therefore the reference equilibrium (see User Guide and paper for more

explanation).

6. Before using swap to move these inputs, use the Eq End column to define a

starting point because, after all, were starting our mammal in an environment at

10oC. To maintain its body temperature in environments colder than T lc it needs

to increase its metabolic rate while keeping its thermal conductance at a

minimum (assuming it does follow the Scholander-Irving model). By how much

is the question. While there is a calculator, M to balance that could help, to

work it needs the data in the St St Start column and it needs minute volume.Unfortunately, minute volume varies with metabolic rate, so we dont know what

this will be either. Not to worry, minute volume is calculated automatically for all

simulations subsequent to the first when the Link minute volume to metabolicrate option is ticked. So the easiest option is to try a range of metabolic rates (in

Eq End) together with minimum thermal conductance, the same humidity

parameters and operative temperature of 10oC and find a solution that balances

for a body temperature of 38 oC.


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7. A metabolic rate of 3 to 4 times basal would be a good bet, so enter basal (1.17)for the nominal metabolic rate and the factors 3 and 4 to define the range. Enter

other inputs as before except for operative temperature that should be 10 oC.

Dont bother with minute volume because whatever you enter will be overwrittenby the value calculated by Optemp.xls. In this case, it will be 99, the same as in

St St Start, because the nominal metabolic rate is the same. The actual value used

will be adjusted for each of the nine solutions ranging from 3 99 to 4 99ml/min.

8. A solution for body temperature of 38oC lies somewhere between 3.50 and

3.63 nominal metabolic rate, so adjust the factors accordingly and re-run (press

end) to get a solution of 37.99 oC (which is close enough) for line 8. This

shows that the actual metabolic rate to maintain this body temperature is 4.228W. If you want, you can place 4.228 into the nominal rate in Eq End, make the

range from 1 to 1 (or anything else you fancy) and press End again to see

minute volume calculated out as 357.8 ml/min. Youll get a very slightlydifferent body temperature, but this difference is immeasurable in any practical

sense. The actual evaporative heat lost (0.438 W) was already calculated.


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9. Assuming you didnt play around and still have the inputs and outputs as

depicted above, press swap to get all the inputs into the right places and re-runthe simulations. When you press start, youll probably get an error message.

This is transitional. For the moment, while the start and the end are exactly the

same, Excel is trying to plot the difference between them on a log scale in stage

(ii). You may notice the little stage (ii) results graph in the top right of screen hasdisappeared. We dont care at the moment, because we are about to change the

end anyway, so just ignore the message, press OK on it and then press end.

10. Once the inputs are in the right places and the final stage (i) outputs have been

generated (as depicted below), click on stage (ii).


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11. Note the reproduced output from stage (i) with line 8 steady state start bodytemperature of 37.99. Enter mass (250) and line (8) and press Use steady state

start for stage (iii). Then go to the stage (iii) sheet.

12. Enter the lower set point (37.5), an upper set point (38.5) and Q 10 (2.81 from

Calculators.xls). Allow the animal some aerobic scope by entering a maximumM (12 ~ 10 BMR). Enter thermal conductance values, minimum (0.1355) and


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maximum (= 6*e7 or .183) and effects of turbinal scrolls (std effect = 5). Enterthe range of operative temperature (maximum 1 = 40, minimum 1 = 10) and

length of sim (2880). Press Define the dynamics for a stage (iii) simulation.

13. Work through the tabs in the Set Parameter Functions form.


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14. In the M tab choose Varies according to a Q10 and defend Tb fromdropping.

15. In the Ko tab choose Maximise approach of Tb to Tpref and Adjust Ko to

maintain midpoint of Tpref.


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16. The next two are really simple. In the Vi/E tab choose Maintain and in the Tuetab choose constant Tue at all Te.

he next two are really simple. In the Vi/E tab choose Maintain and in the Tuetab choose constant Tue at all Te.

17. In the Te tab choose Sinusoidal Function starting at minimum.17. In the Te tab choose Sinusoidal Function starting at minimum.

18. Press Run the stage (iii) simulation and wait for the simulation to complete.


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Various indicators show the simulation is running including one showing how farthe simulation has

progressed (in sim time

and as a percentage).When complete, a form,

Summary Statistics andAnalysis? appears givingyou several options to

calculate statistics for part

or all of the output. You

may choose to ignore it bclicking No or Ex

you do select Yes fill

out start and finish timeand select the stats you

want. (For explanatio

leeway, see the UserGuide.pdf.).

yit. If

n of

And here are the results displayed in the Lg Graphs worksheet: they are also

displayed in (stage (iii) at a smaller scale. For most of the two days of the


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simulation, the endotherm maintained its body temperature between 37.3 and 38.1oC

through a combination of variations in thermal conductance (when operative

temperatures were thermo-neutral) and increases in endogenous metabolic heat

(when operative temperatures were lower). Only at high operative temperatures didthe body temperature deviate from homeothermy. The combination of high

environmental heat load and (increased) metabolic heat was too great for the animalto maintain Tb despite dumping heat at the maximum rate allowed by its thermalconductance. (Increasing maximum thermal conductance from 6 to 8 minimum

reduces the maximum Tb during the simulation by about oC). Metabolic heat

increases when Tb increases because of the effect of body temperature on metabolic

rate, generally a 2 to 3 fold increase for every 10oC increase in temperature. Thus

while metabolic rate influences body temperature by providing some of the heat in

the system, body temperature influences metabolic rate through the Q10 effect: there

is a feedback loop between the two. This feedback loop is incorporated at the heart ofOptemp.xls and is one of the reasons Optemp.xls can be used for both

ectotherms and endotherms in a variety of circumstances. While still there, the

feedback loop is masked in endotherms by their ability to generate extra heat overand above the Q10 effect, either to keep warm in cold places or, perhaps, to run

cooling mechanisms in hot places.

Clearly, our hypothetical animal in this environment needs cooling mechanisms toavoid Tb > 38.5

oC in the circumstances modelled. While Optemp.xls does not yet

include sweating, it does include panting at least in a rudimentary way. Panting is

merely a dramatic increase in minute volume initiated, perhaps, at a metabolic cost.


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Enter a value for high Vi and metabolic cost in the inputs part of the spreadsheet.I chose about 20 Vi when M is basal (20 ~ 99 = 2000) because experience has

shown me this is the smallest factor sufficient to bring Tb within about o of the

upper set point, and 0.1 W (a substantial increase over BMR) as a pure guess. In theVi/E tab of the Set Parameter Functions form, select Increase at high Tb and

then run.

The output shows a substantial increase in evaporative heat loss leading to more

pronounced homeothermy with Tb being reduced below Te during the hottest part ofthe day. Interestingly, the lower Q10 effect of this reduced Tb on M more than

compensates for the increase in metabolic rate expected from a substantial cost of

panting.

Congratulations! You have simulated a homeothermic endotherm in a fluctuating

environment. And, with a bit of luck, you have thought of a few questions about

endothermic thermoregulation along the way! Now play with the programming toeither break it, or to generate more questions. If you do break it, or you have any

questions or suggestions, let me know. Remember though, there is a more

comprehensive user guide that contains many of the details omitted here.

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How to simulate this endotherm