PS1F99

42-101 Intro to BME (Przybycien)

Spring 2005

PROBLEM SET No. 1

Posted:

1/10/05

Due:

1/14/05 Jung type test results

1/21/05 remainder of set due in class

1/24/05 bring blank copy of Interim Team Evaluation to complete in class

Organizational Tasks

1.	Establish your first problem set group with three or four members. We will form teams in class on Wed, 12 Jan.
2.	Familiarize self with spreadsheet software (MS Excel or Lotus 1-2-3)
3.	Print out Interim Team Evaluation Form.
4.	Take the Jung Typology Test at http://www.humanmetrics.com/cgi-win/JTypes1.htm When completing this personality type indicator, answer questions from the standpoint of “how you are” rather “how you’d like to be”. Email your “four-letter” type and weights to Todd by Friday, 14 January. I will keep the results confidential, but will discuss the entire distribution of personality types in the class and implications for forming homework teams….

Problems for grading:

1.	Units conversions. Convert the following using dimensional equations: a. 18.1 mmol glucose/L whole blood to mg glucose/dL plasma. Note that this person’s blood contained 63 vol% plasma. b. 1.256 mol electrons/second to Amps c. 15 grams glycerol/(ft³·hr) to moles glycerol/(L·min) d. 373 K to °R. e. a difference between two temperatures of 15°F to a difference in temperatures in °C
2.	Units in equations. A correlation was developed to estimate the volume of a person’s blood, V_blood in liters, from a person’s height, H in centimeters, and mass, M in kilograms. For males, this correlation takes the form: V_blood = aH³ + bM + c, where for males, a = 4.17E-7, b = 0.045 and c = -0.03. In order for this equation to be dimensionally consistent, what must the units associated with the constants a, b and c be?
3.	Dimensionless numbers. The Nusselt number, Nu is a dimensionless group (i.e. the dimensions cancel out) that is important in fluid heat transfer calculations. Nu is defined as Nu º hL/k where h is the heat transfer coefficient, L is the length or significant dimension of the vessel that the heat transfer in occuring in and k is the thermal conductivity of the heat transfer fluid. In practical terms, Nu is the ratio of the rate of heat transfer by convection (fluid flow) to that by conduction in the fluid: if Nu >> 1, convection is more rapid than conduction and so the rate at which heat may be transferred in the system is limited by the thermal conductivity of the fluid; if Nu << 1, conduction is more rapid than convection and the rate at which heat is transferred is limited by the fluid flow rate. Compute the Nusselt number for heat transfer from a blood arteriole to the surrounding tissue if the heat transfer coefficient is 18.7 Btu/(ft²·hr·°F), the thermal conductivity of blood is 584x10^-7 cal/(cm·sec·K) and the diameter of the arteriole is 0.10 in. Is heat transfer in arterioles limited by the flow rate of the blood or the thermal conductivity of the blood?
4.	Propagation of Confidence Limits. Ten healthy male participants in a phase I drug trial had their heights and weights measured into order to estimate their blood volumes via the equation described in problem 2 above. The corresponding data is recorded below. Participant# H M 1 6’3” 217 lbs 2 5’9.5” 184 lbs 3 5’11” 210 lbs 4 5’9” 167 lbs 5 5’7” 174 lbs 6 6’0” 224 lbs 7 5’10.5” 190 lbs 8 5’11” 175 lbs 9 5’9.5” 179 lbs 10 6’1” 238 lbs For this sample of the participant population, determine the average blood volume in liters. Report the average with 95% confidence limits.
5.	Identifying Outliers in Data. Use both the Q-test and the z-test to assess whether or not one of the data points below is an outlier. [Hint: hit reading links for more info or Google “Q-test” or “z-test” and “outliers”] Data point glucose concentration (mmol/L whole blood) 1 23.1 2 22.7 3 22.9 4 22.9 5 21.3 6 22.5 7 22.6

Updated on 1/10/05 by TMP; due dates corrected 1/12/05