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Model 1: Drug Transport into the Heart 40%]

Figure 1. Schematic of blood flow in the heart.

Nutrients and therapeutics are transported throughout our body and into organs via the circulation of blood. Suppose that blood flowing in and out of the heart with rate r [cm3 min- ] carries a drug at a concentraaon c [mg cm-3]. The volume of blood in the heart is also given by Pg [cm3]. The average human heart can pump 4 litres of blood per minute and has an average volume of 280 cm*.

a) [30 marks] Assume that r is constant and obtain an equahon for the quanaty of therapeutics in the heart as a function of time yp(I) [mg]. You will need to write and solve an ordinary differential equation that models the mass rate of {mg min-`] at any time the heart. At I = 0 there is no drug in the heart, but the concentration in the bloodstream is r.

Although r was assumed to be constant in queshon la, the eoncentrahon of drugs injected in the bloodstream is known to decay as an exponential function of time given by:

In this expression, D [mgJ is the dose of drug injected, d = 1.3 R !8"* [ “1 is

constantforthe drugand tisthetñnein {mi"]

TheerxpBieenB1 • `=• ol d()[ â ]* 8 the * ” an•‹ied,o,Nspapw;nE«a(xL)andMATLA8(magfonnatusethammm

urruznu4auoninihehean,oGeoneobtaIneJing«rsHo› JswiGacomtarab1oo•J

Table 1. Experimental measurements for drug concentration in blood plasma.

I [otin]	Meaauzezneat 1	Meaauzezneot 2	hteaauzement 3
0	0.044899	o os5775	o.0445zt
0.2	o.os9223	0.040378	o.04
0.4	0.034452	0.033888	0.034524
0.6	0.029701	0.029814	0.02P149
0.8	0.026727	0.02711	0.026908
1	0.023718	0.02256	0.022417
12	0.019134	0.020123	0.019274
1.4	0.016724	0.018039	o.m6481
1.6	0.015413	0.015993	0.014639
1.8	0.012824	0.013373	0.012533
2	0.012316	0.010604	0.011679
2.2	o.o1084	0.tO8988	0.tD`9tH7
2.4	0.008908	0.008857	0.008179
16	0.00822	o ooz64	0.007076
2.8	0.006342	0.00745	0.007288
	0.005951	0.tXifi177	0.O3SS8
3.2	0.005914	0.005275	0.fDS46
3.4	0.00443	0.tXi4359	0.fD4S17
3.6	0.004612	0.003279	0.004315
3.8	0.003704	o.O341as	o.a2S05
4	0.002814	0.002925	0.003792

Model 2: Conservation of Endangered Species [io• ]

Assume that r is constant and obtain an equahon for the quanaty of therapeutics in the heart as a function of time yp(I) [mg]. You will need to write and solve an ordinary differential equation

Model 1: Drug Transport into the Heart 40%]

Although r was assumed to be constant in queshon la, the eoncentrahon of drugs injected in the bloodstream is known to decay as an exponential function of time given by:

Table 1. Experimental measurements for drug concentration in blood plasma.