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Unformatted text preview: MIDTERM EXAM
BioE153 2:00 pm, October 21, 2004 NAME: o /u 'm ID NUMBER: DISCUSSION SECTION Remember to work the problems out clearly and completely — so that I can understand what you are doing.
Here are some equations that may be helpful but may not be required. Uniaxial Loading: 0— : E
A
Mr
Pure Bending 0' = T
M = Moment t = distance from the neutral axis
I = Moment of Inertia
A = Cross Sectional Area BioE 153 Midterm Name l. (30 pts) Myelodyplastic syndrome is a bone marrow disorder characterized by abnormal bone marrow
activity. The disorder is treated by bone marrow transplantation whereby defective bone marrow cells
are replaced by progenitor cells, which are cells that have not yet become adult bone marrow cells. Within a cellular population, a progenitor cell may decide to 1) differentiate e thereby becoming an
adult cell, 2) enter what is called apoptosis — cell death, or 3) divide into more progenitor cells through
a process called mitosis. Let Cr be a given number of cell type X introduced into the patient per unit time.
k] be the rate constant for differentiation, k; be the rate constant for apoptosis, and k3 be the rate constant for mitosis. a) Draw a compartment model describing the possible fate of progenitor cells.
b) Derive the differential equation that can mathematically model this process. c) For the transplantation to be successful, we wish the number of transplanted progenitor cells
remain constant in the patient. For this to be possible, what must Cr equal? d) Does the solution to your equation in part B resemble drug concentration changes within the
body for a rapid bolus or slow infusion drug delivery system? Use a mathematical argument
for your answer. Cr BioE 153 Midterm Name 9%ch 9'» Mt I‘m.4 «.5 ﬂ.» 3/09 incur?" mob; 153 Midterm Name 2. (20 pts) In the ﬁgure below left (a), an athlete is doing shoulder exercises by lowering and raising a
barbell with her arms straight. The position of her arms, when they make an angle 6 with the vertical is
simpliﬁed in the ﬁgure on the right (b). Determine the net moment, Mo, generated about the shoulder as a function of B. BioE 153 Midterm Name 3. (30 pts) A weightlifter is bent forward and lifting a weight, W0, as shown in the leﬁ ﬁgure. At the
position shown, the athlete’s trunk is ﬂexed at an angle 6 as measured from the upright (vertical)
position. You are given the forces acting on the lower portion of the athletes body in middle ﬁgure and
a simpliﬁed model in the right ﬁgure. W is the total weight of the athlete,
M is the weight or the legs including the pelvis,
W + W0 is the total ground reaction force applied to the athlete through the feet (at C). F M. is the magnitude of the resultant force exerted by erector spinae muscle supporting the trunk, F}. is the magnitude of the compressive force generated at the union of the sacrum and ﬁfth lumbar
vertebra. The center of gravity of the legs including the pelvis is located at B. Relative to O, the lengths of the
lever arms of the muscle force lower body weight and ground reaction force are measured as a, b, and
c, respectively. The line of pull of the resultant muscle force exerted by the creator spinae muscles is
parallel to the trunk (i.e. makingan angle 6 with the vertical). Determine FM and F). in terms of a, b, c, 6, W0, W1, and W. 131013 153 Midterm Shag!” Zﬁ “‘0
2:?” =0
Z¢H=0 =1) aﬁer,PC(W*W°)=
I
I
I5” Fm; *wlWO’W’ Name BioE 153 Midterm . Name 4. (20 pts) In skiing the lower bone in the leg undergoes signiﬁcant loading between the bottom of the
. knee and the top of a ski boot. Based on the ﬁgure below, determine the maximum stress and its
location on the bone given that the knee successfully stays together and ﬁxed as Dorian lands on the
ground so that there is a downward force equal to my body weight.
Assume that the bone is homogeneous and has a Moment of Inertia, I, and Diameter, D. A. Where does the maximum stress occur on the bone: a, b, or 6? Why?
B. Develop an expression for the maximum stress. l ‘—" Bottom of Knee from back Sldc .— U Top of boot H. a} 2) MW W luw be I" _
CO lit/fl.” fiV‘ km AMI— a ﬂunk'01 ﬁrst4.
a! Ma 4.. /4.. ’L luau/in} many; 13 fire—ea gw’” “mu— m i=1, ...
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 Spring '10
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