Elec Eng 3BA3: Structure of Biological Materials Page 1 of 12 Day Class Instructor: Dr. I. C. BRUCE Duration of Examination: 3 Hours McMaster University Final Examination December 5, 2008 This examination paper includes twelve (12) pages and fourteen (14) questions. You are responsible for ensuring that your copy of the paper is complete. Bring any discrepancy to the attention of your invigilator. Special Instructions: Use of Casio fx-991 calculator only is allowed. Some equations that may assist you are provided on pages 6 12. Questions 1 8 are multiple-choice questions, each worth 5 pts. Only one answer, a, b, c or d, is correct for each question. Questions 9 14 are short answer and/or mathematical questions, each worth 10 pts. 1. The most abundant structural protein in vertebrates is: a. keratin, b. proteoglycan, c. elastin, or d. collagen. (5 pts) 2. A material s fatigue endurance limit is: a. the number of loading cycles at which it suffers a fatigue fracture, b. the strain at which it undergoes a permanent plastic deformation, c. the stress below which a material will not exhibit fatigue fracture, or d. the bending moment at which it breaks. (5 pts) 3. For a complicated loading of a biomaterial, the von Mises stresses can be calculated to determine where in the material: a. plastic yielding will occur, b. the elastic modulus is the highest, c. fracturing will occur, or d. wear will occur due to abrasion. (5 pts) Continued on page 2
Page 2 of 12 4. Airflow in the respiratory system (considering both quiet and vigorous breathing) is: a. never turbulent, b. less likely to be turbulent than blood flow in the circulatory system, c. more likely to be turbulent than blood flow in the circulatory system, or d. equally likely to be turbulent as blood flow in the circulatory system. (5 pts) 5. Transdermal delivery is suitable for administration of: a. all drugs, b. small-molecule drugs, c. large-molecule drugs, or d. no drugs. (5 pts) 6. Drugs diffuse through tissue: a. from regions of low drug concentration to regions of high drug concentration, b. because of differences in electrical potential within the tissue, c. because of gravity, or d. none of the above. (5 pts) 7. In medical imaging, the abbreviation MRE is typically used to refer to: a. medical radiation emission, b. minimum Rayleigh energy, c. magnetic resonance elastography, or d. maximum resonance estimation. (5 pts) 8. In SPECT imaging, the antiscatter grid is placed: a. between the x-ray source and the body, b. between the body and the scintillation camera, c. before the collimator, or d. none of the above SPECT imaging does not use an antiscatter grid. (5 pts) Continued on page 3
Page 3 of 12 9. Explain why body mass has relatively little effect on the optimal walking speed for a person. (10 pts) 10. At first glance, it might appear from the flow velocity equation for Poiseuille flow, i.e.,: that the flow velocity u in a cylindrical vessel of radius a approaches infinity (i.e., u ) as the viscosity becomes negligible, i.e., μ 0. Explain why this is not the case. (10 pts) 11. Describe how x-rays are generated in a medical x-ray imaging system. (10 pts) 12. The vertical velocity of the center of mass (COM) of a 90 kg person over a 1 second period can be described by: 2 () t vz t = 0.25 e 1, 0 t 1, where the vertical velocity () t Assume that the acceleration due to gravity is vz is in units of meter/second and the time t is in units of second. 9.8 m s 2. a. Calculate the vertical component of the ground reaction force, F ( ) as a result of this movement over the period 0 t 1. b. Calculate the vertical displacement d ( ) 0 t 1. z gz t, that would be measured t of the COM as a function of time over the period (10 pts) Continued on page 4
Page 4 of 12 13. You are given the job of designing the RF generator for an MRI machine. The slice select gradient (SSG) that is applied in the z direction (i.e., in line with the static B 0 field) has a magnetic field 1 gradient of G z = 0.4 T m. The total field in the z direction when the SSG is turned on is referred to as the B field; the magnitude of the SSG field ( B B0 ) as a function of z is given in panel b below. The longitudinal position where the SSG field is zero ( B = B0 ) is referred to as the isocenter. Assume that hydrogen nuclei with a gyromagnetic ratio of and that the static magnetic field B 0 = 3T. γ 2π 1 = 42.58 MHz T are being imaged, a. What bandwidth Δ f should the B 1 RF pulse have in order to select an axial slice of thickness Δ z = 1mm? b. What center frequency f 1 should the B 1 RF pulse have in order to select an axial slice centred at the position z 1 = 10 cm (relative to the isocenter)? c. What center frequency f 2 is required to select a slice centred at z 2 = 40 cm? (10 pts) Continued on page 5
Page 5 of 12 14. A medical ultrasound company is testing out a new gel to help in impedance matching between their ultrasound transducer and the skin. They utilize the experimental setup illustrated below to determine the acoustic impedance of the new gel. The transmitting transducer on the top produces an ultrasound signal with intensity I 0 and the receiving transducer on the bottom consequently measures a signal of intensity I. transmitting transducer I o gel receiving transducer I In the company s experiment, the intensity of the ultrasound pulse produced by the transmitting 2 transducer on the top is I 0 = 150 mw cm. The maximum ultrasound pulse intensity that is 2 measured by the receiving transducer on the bottom is I = 114.7298 mw cm. Assume that: i. the acoustic impedance of both transducers is Z T = 6.5 10 6 rayls; ii. the attenuation of the acoustic signal in the gel is negligible; and iii. the acoustic impedance of the gel Z G is less than that of the transducers. From this measurement, determine the acoustic impedance of the gel Z G. (10 pts) THE END Continued on page 6
Page 6 of 12 Supplied Equations Axial stress equations: Axial strain equations: Linear elasticity equation: Ideal rubbery elasticity: Ground reaction force equations: Kinetic energy: Gravitational potential energy: Continued on page 7
Page 7 of 12 Force versus velocity relationship for contracting muscle: Net joint power: Mapping of Cartesian stress tensor to principal stresses: Von Mises stresses: Specific gravity of a liquid: Shear stress versus shear rate for a Newtonian fluid: Continued on page 8
Page 8 of 12 Bulk modulus (fluid compressibility) equation: Speed of sound in a substance: Fluid acceleration equation: Fluid acceleration along a streamline: Fluid acceleration normal to a curving streamline: Hydrostatic equilibrium equation: Hydrostatic pressure difference equation: Continued on page 9
Page 9 of 12 Conservation of mass for flow within a stream-tube: Conservation of mass for flow within a stream-tube of constant volume: Conservation of momentum for flow along a stream-line: Bernoulli equation (conservation of momentum for steady flow along a streamline): Reynolds number criterion for laminar flow: Poiseuille flow velocity profile (laminar viscous flow in a circular tube): Continued on page 10
Page 10 of 12 Poiseuille flow entry length equation: Mean kinetic energy of a particle: Fick s law of diffusion: Photon attenuation equation: Radionuclide decay equation: Physical half-life: Acoustic intensity, pressure, velocity and impedance relations: Acoustic impedance: Continued on page 11
Page 11 of 12 Pressure reflection coefficient: Intensity reflection coefficient: Intensity transmission coefficient: Ultrasound attenuation equation: Doppler frequency equation: Doppler frequency shift: Continued on page 12
Page 12 of 12 Larmor equation: Spin echo sequence NMR signal strength: END OF SUPPLIED EQUATIONS