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8.2 Surge Functions
Theory & Practice in Science (SCIE1000)
University of Queensland
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8 – Surge Functions – Average and instant change
Learning - Understand the meaning and applications of average rates of change - Understand the meaning and use of derivatives Science - Cyanide from smoking - Metabolism of alcohol Maths - Calculate average rates of change - Understand the meaning of derivatives
Derivatives – used to measure values over time Tmax = p/b – the concentration of Cmax in the bloodstream - Pharmacokinetics is concerned with the rate at which the drug concentration changes - The concept of one quantity changing as another quantity changes and the rate atwhich the change occurs is crucial to understanding science
Looking at 2 methods for analysing rates of change – average rates of change and instantaneous rates of change
The average rate of change - Measures the average change between two observed values of some phenomenon - Average rates of change are usually measured by e., 60 m s^- Example The concentration of atmospheric CO2 has risen by about 90 ppm over the last 60 yearstherefore the average rate of change is
90/60 = 1 ppm year ^-
Instantaneous rate of change - Rather than measuring the average rate of change with 2 points, the instantaneous rate of change only uses 1 - Math term for instantaneous rate of change is a derivation Nicotine is an addictive and poisonous alkaloid is found in tobacco Nic enters your bloodstream within 5 secs and reaches your brain after about 10 Also contains heavy metals, poisons and radioactive materials – some are toxic or carcinogens
What types of parameters could be measured to investigate the physiological effects of smoking? - Blood pressure - Hormone levels - Oral health - Lung capacity - Cardiovascular ability
While smoking, the body absorbs many chemical compounds in addition to nic including cyanide This table shows blood cyanide concentrations after smoking a cig starting at t = 0 minutes
b) The derivative of f(t) = atpebt is f0(t) = atp1ebt(p bt) Therefore C0(t) = 0.3t0.4e0(0 0) What is the physical meaning of C? Instantaneous rate of change of concentration of cyanide in blood
For what value (s0 of t is C1(t) = 0? Reading from the graph tmax = 4 minutes, therefore
C1(t) = 0 becomes
0.3t0.4e0(0 0) = 0 T = 0.6/0 approximately 3 minutes
On the graph, identify all regions where C1 is positive/negative? Is positive –
Cyanide concentration is increasing absorption/distribution dominates
Zero –
Cyanide concentration is constant – absorption/distribution balanced by metabolism/excretion
Negative –
Cyanide concentration is decreasing metabolism/excretion dominates
Case study – Whisky BAC
A standard drink contains 10g of alcohol
In aus, the legal blood alcohol content for driving is 0% or 0 g/L
The rate of alcohol metabolism is roughly constant – unlike most other drugs – this is called a zero-order reaction
The rate of metabolism is usually independent of BAC because typical levels of alcohol consumption saturate the metabolising capacity of enzymes within the liver Example of the difference between cyanide and alcohol of absorption of chemical
The exact rate of metabolism varies between people, influenced by factors such as age, mass and sex
Graph of BAC from the time drinking commenced with show rapid initial rise during the absorption, prior to a decline in concentration during the elimination phase
Because the rate of alcohol metabolism tends to be constant a graph of BAC from the time of peak concentration shows a linear decline until metabolism is almost complete
This graph shows a BAC measurement B(t) represents a straight like model of this graph, t = 1 hour to 6 hours
Fitting a linear model to match the line drawn about is B(t) = -0 + 0. Where b^l (t) = -0 %/hour
8.2 Surge Functions
Course: Theory & Practice in Science (SCIE1000)
University: University of Queensland
