Exam 7: Physics

Blood flows through a vessel in the leg at an average velocity of 10 cm/s.  How much glucose passes by a segment of the blood vessel each second if the radius of the blood vessel is 0.20 cm and each 1.0 cm³ of blood contains 1.0 mg of dissolved glucose?

A charged particle is accelerated in a uniform electric field.  When its velocity is 2 m/s, its electric potential energy is 100 J and its kinetic energy is 10 J.  What is the particle's potential energy when its velocity reaches 4 m/s?

Passage Hydrostatic weighing is a technique used to determine an individual's overall body density.  The weight of the individual is measured when their body is completely submerged in water.  Because the volume of air in the respiratory system affects the measured underwater weight, the individual must exhale completely before entering the water.  However, residual volume, the volume of air that always remains in the respiratory system, must also be accounted for.By comparing an individual's in-air weight to their underwater weight, their total body volume can be determined.  The density of the body D_b excluding any air in the respiratory system is calculated with the in-air mass of the individual m_air, the individual's total body volume V_total, and an estimate of residual volume V_res by: Db=mairVtotal-VresEquation 1Body density can be used to calculate an individual's body fat composition, the percentage of total body mass that is made up of fatty tissue.  Human fatty tissue has an average density of 0.9 kg/L, and the density of water is 1 kg/L.  The acceleration due to gravity is 10 m/s². Adapted from Siri, WE, Body composition from fluids spaces and density. Nutrition 1956 Springer Nature. - The hydrostatic weighing container above is filled with water.  If point A is 0.7 m above the bottom of the container, what is the fluid pressure at point A?  (Note:  The density of water is 1,000 kg/m³.)

Passage Osteoporosis is a degenerative bone condition in which healthy bone degenerates into porous bone.  Because bone provides the structural integrity that allows the musculoskeletal system to bear weight, osteoporosis is associated with a higher risk of bone fracture.Researchers conducted an experiment designed to assess the strength and elasticity of osteoporotic bone relative to normal bone.  Osteoporotic and normal bone samples with identical physical dimensions were collected and placed within an pneumatic compression device, as shown in Figure 1. Figure 1  Bone compression device loaded with a bone sampleThe force required to compress the bone samples longitudinally (lengthwise) by a given distance was measured, with the results shown in Figure 2. Figure 2  Relationship between force and compression for normal and osteoporotic bonesResearchers observed that bone samples returned to their original dimensions for deformations not exceeding 1% of the original length L₀.  For each deformation, the associated strain ε is defined as the change in length of an object ΔL divided by the object's original length (Equation 1). Equation 1Based on these observations, researchers concluded that both osteoporotic bone and normal bone behaved as an elastic material under a wide range of applied forces. -According to the data in Figure 2, what is the spring constant k for normal bone?

Passage Nitrogen is extremely cold in its liquid phase.  It is used in the cryopreservation of small tissue samples and in cryosurgery to freeze and destroy diseased tissues.  Liquid nitrogen can be produced from nitrogen gas using the Hampson-Linde cycle (Figure 1). Figure 1  Hampson-Linde cycle apparatus used to liquefy nitrogenThe cycle begins by compressing nitrogen gas and forcing it through a coil in an external cooler that contains dry ice.  The gas proceeds to a heat exchanger, where it cools further due to the countercurrent heat exchange with colder nitrogen gas returning from a later stage of the cycle; this process is known as regenerative cooling.  The gas is subsequently forced through a narrow valve, where it expands and cools significantly upon exiting.  As a result, a portion of the gas becomes liquefied.The temperature change of the gas exiting the valve is described by the Joule-Thomson effect, which occurs without heat transfer with the surroundings.  Finally, the liquefied nitrogen is collected, and the remaining gas is sent through the regenerative cooler back to the compressor to reenter the cycle.  The physical properties of nitrogen are given in Table 1.Table 1  Thermal Properties of Nitrogen -Which thermodynamic quantity involved in the Hampson-Linde cycle is a state function?

Passage The electric capacitance of biological tissues serves as the basis for numerous medical technologies.  For example, dielectric spectroscopy glucose reading (DSGR) is a noninvasive diagnostic technique that uses the electric capacitance of blood to estimate blood glucose levels.A DSGR device records the electric current that results from applying a voltage source to the skin and underlying blood vessels.  DSGR can be modeled by the circuit shown in Figure 1, in which V represents the applied potential, C_B represents the capacitance of the blood, and R_E, R_D, and R_B represent the electrical resistances of the epidermis, the dermis, and the blood, respectively. Figure 1  DSGR circuit model including skin and superficial blood vesselThe capacitance of charged blood may be explained by red blood cell membranes acting as physical barriers that separate electrons introduced into the blood from positively charged ions in the red blood cell cytoplasm.  The dielectric constant k of red blood cell membranes varies with glucose concentration (Figure 2) because glucose uptake by red blood cells alters the activity of membrane-bound proteins that regulate the flow of ions into and out of the cell. Figure 2  Blood dielectric constant vs blood glucose concentrationDSGR readings vary with blood glucose concentration because the time needed to fully charge the blood is related to total blood capacitance.  However, interpreting DSGR readings may be complicated by changes in biological variables other than blood capacitance.  For example, the resistivity of blood varies in accordance with osmolarity such that changes in diet or hydration status influence the current measured by DSGR devices. Livshits, L. et al.  Dielectric response of biconcave erythrocyte membranes to D- and L-glucose.  J. Phys. D: Appl. Phys. 40 (2007), 15-19. -Assuming that the size and shape of red blood cells are uniform, by what factor would the quantity of red blood cells need to change to raise the capacitance of a blood sample to 250% of its original value?

Passage Positron emission tomography (PET) is a medical imaging technique used for the detection of tumors and the evaluation of neurological functions.  A radiopharmaceutical (radioactive tracer) injected into a patient undergoes positive beta decay and emits a positron.  The positron undergoes an annihilation event with a nearby electron (<1 mm away), which emits a pair of 511 keV gamma ray photons traveling in opposite directions.  The gamma rays are detected by a ring of scintillation detectors surrounding the patient, as shown in Figure 1.  The difference in detection time between the two gamma rays from the same annihilation event is used to determine its location.  An image is constructed from data collected from multiple emission events. Figure 1  Basic setup and process of positron emission tomographyScintillation, the emission of detectable light when excited electrons return to their ground state, occurs in crystals within the detectors due to the transfer of energy from the high energy gamma rays.  The wavelength of the emitted light depends exclusively on the type of scintillation material used (Table 1).Table 1  Common PET Scintillating Crystal Materials The electrons in the scintillating crystals are excited through Compton scattering, a process in which a gamma ray photon acts as a particle, and transfers energy to an electron via collision.  Subsequently, the photon scatters (travels in a new direction) and its wavelength changes.  The percent change in the wavelength of the photon due to the energy loss is Equation 1where θ is the angle between the scattered photon and electron.  Equation 1 is represented in Figure 2. Figure 2  Percent change in photon wavelength due to Compton scattering -If one gamma photon out of a pair is Compton-scattered within the patient (not at the detector) and both gamma photons are still detected, which of the following would be seen?The frequency of the scattered photon would be lower.The point of origin would appear to be at a different location.The velocity of the photon would decrease.

The table above gives the angle of refraction measured when light encounters three unique smooth interfaces.  In each case, the refractive index of the new medium and the angle of refraction are identical.  Some light reflects off the media interface in each condition.  How does the angle of reflection θ_r in the high refractive index condition compare to the angle of reflection in the low refractive index condition?

Passage Positron emission tomography (PET) is a medical imaging technique used for the detection of tumors and the evaluation of neurological functions.  A radiopharmaceutical (radioactive tracer) injected into a patient undergoes positive beta decay and emits a positron.  The positron undergoes an annihilation event with a nearby electron (<1 mm away), which emits a pair of 511 keV gamma ray photons traveling in opposite directions.  The gamma rays are detected by a ring of scintillation detectors surrounding the patient, as shown in Figure 1.  The difference in detection time between the two gamma rays from the same annihilation event is used to determine its location.  An image is constructed from data collected from multiple emission events. Figure 1  Basic setup and process of positron emission tomographyScintillation, the emission of detectable light when excited electrons return to their ground state, occurs in crystals within the detectors due to the transfer of energy from the high energy gamma rays.  The wavelength of the emitted light depends exclusively on the type of scintillation material used (Table 1).Table 1  Common PET Scintillating Crystal Materials The electrons in the scintillating crystals are excited through Compton scattering, a process in which a gamma ray photon acts as a particle, and transfers energy to an electron via collision.  Subsequently, the photon scatters (travels in a new direction) and its wavelength changes.  The percent change in the wavelength of the photon due to the energy loss is Equation 1where θ is the angle between the scattered photon and electron.  Equation 1 is represented in Figure 2. Figure 2  Percent change in photon wavelength due to Compton scattering -In which of the given scintillation materials will light travel the slowest?

The photoelectric effect refers to the ejection of electrons from a material when the material absorbs electromagnetic radiation of sufficient energy.  As the frequency of electromagnetic radiation increases, what happens to the kinetic energy of ejected electrons?

Passage In the event of end-stage heart failure, a left ventricular assist device (LVAD) can be used as a heart transplant bridge to keep a patient alive.  The first iterations of LVADs were pulsatile and mimicked the physiological pumping action of the heart (Figure 1). Figure 1  A pulsatile-flow LVAD schematicA pulsatile-flow LVAD assists ventricular systole by mechanically pumping blood from a weakened left ventricle into the aorta through a pair of one-way valves.  The pressure differential ΔP generated by the pump is related to cardiac output (CO) and vascular resistance (VR):ΔP = CO × VREquation 1The efficiency and performance of the heart (or LVAD) can be determined by the patient's cardiac pressure-volume (PV) loop.  A cardiac PV loop plots the pressure and volume of the blood in the left ventricle throughout a single cardiac cycle (Figure 2). Figure 2  Cardiac PV Loop of a pulsatile-flow LVADBlood pressure is often represented by only two numbers:  arterial systolic and diastolic pressures.  A more detailed representation of blood pressures is shown in a blood pressure profile, which graphs the blood pressure throughout the length of the different vessel groups (Figure 3).  Multiple pressure fluctuations are shown within a vessel because the pressure is traced across multiple cardiac cycles. Figure 3  Blood pressure profile of the different vessels -If the radius of the outflow tube is 1 cm and the LVAD pump generates a pressure of 45 mm Hg, what is the velocity of blood through the outflow tube if peripheral resistance is 1 mm Hg⋅s⋅mL⁻¹?

Passage In the event of end-stage heart failure, a left ventricular assist device (LVAD) can be used as a heart transplant bridge to keep a patient alive.  The first iterations of LVADs were pulsatile and mimicked the physiological pumping action of the heart (Figure 1). Figure 1  A pulsatile-flow LVAD schematicA pulsatile-flow LVAD assists ventricular systole by mechanically pumping blood from a weakened left ventricle into the aorta through a pair of one-way valves.  The pressure differential ΔP generated by the pump is related to cardiac output (CO) and vascular resistance (VR):ΔP = CO × VREquation 1The efficiency and performance of the heart (or LVAD) can be determined by the patient's cardiac pressure-volume (PV) loop.  A cardiac PV loop plots the pressure and volume of the blood in the left ventricle throughout a single cardiac cycle (Figure 2). Figure 2  Cardiac PV Loop of a pulsatile-flow LVADBlood pressure is often represented by only two numbers:  arterial systolic and diastolic pressures.  A more detailed representation of blood pressures is shown in a blood pressure profile, which graphs the blood pressure throughout the length of the different vessel groups (Figure 3).  Multiple pressure fluctuations are shown within a vessel because the pressure is traced across multiple cardiac cycles. Figure 3  Blood pressure profile of the different vessels -Which group of blood vessels is the main source of peripheral resistance?

Circularly polarized light results from the vector sum of the electric field oscillations of two linearly polarized transverse waves traveling along the same axis.  To achieve circular polarization, the two transverse waves must be out of phase to one another.  The necessary phase difference is:

Uniform magnetic fields created by advanced medical imaging devices most likely come from the:

Two transverse waveforms (A and B) travel through the same medium with a phase difference of 180°.  If the amplitude of the waveforms is ±100 m, what is the combined displacement of both waveforms as waveform A reaches maximum displacement?

Passage During deep underwater dives, scuba divers must overcome the external ambient pressure in order to expand their chests to inhale.  To assist underwater breathing, air from scuba tanks is administered at high pressures to keep divers' lungs inflated.  Scuba tanks are often filled with a mixture of N₂ and O₂ gas.  Due to the increased pressure of the gases in the lungs, a greater amount of the gases are dissolved into the bloodstream during underwater dives.  At a body temperature of 37°C, the solubility of N₂ gas in blood is 6.0 × 10⁻³ mol/L⋅atm and the solubility of O₂ gas is 1.3 × 10⁻² mol/L⋅atm.If a diver ascends too quickly after an extended dive, there is an increased risk of vascular bubble formation.  Due to the decrease in ambient pressure, the excess gas dissolved in the blood may come out of solution as gas bubbles and cause a number of adverse effects.  This condition is known as decompression sickness, or "the bends."  To avoid this problem, scuba divers limit their rate of ascension to allow the excess gas dissolved in their blood to be safely removed through respiration.  Because gas bubbles are good reflectors of sound, these bubbles can be detected using Doppler ultrasonic flowmetry after the diver has surfaced. Adapted from M. Spencer, Journal of Applied Physiology. ©1976 American Physiology Society. -A diver is using a tank filled with 20% O₂ and 80% N₂ (by volume).  If the pressure in the lungs is 5 atm, what is the expected equilibrium concentration of N₂ dissolved in the diver's blood?  (Note:  Assume that the mixtures of the gases in the lungs and tank are equal.)

Passage Laparoscopy is a minimally invasive surgical procedure where small surgical instruments are inserted into the body through cannulas (hollow tubes 0.5 to 1.0 cm in diameter).  A cannula is inserted into the skin while sleeved around a trocar (Figure 1).  The skin incision can be made directly with a sharp-tipped trocar as it is being inserted with the cannula.  If a blunt-tipped trocar is used, the incision is made beforehand with a surgical blade.  After insertion, the trocar is removed, leaving the cannula as an access point for laparoscopic procedures. Figure 1  Cannula, trocar, and two types of tipsLow-friction trocars increase surgical precision and reduce postoperative scarring.  Friction between the skin and trocar tip is tested with synthetic skin and a stationary ramp whose surface is made of the same material as the trocar.  For testing, the synthetic skin is pressed against the ramp's surface by a load, weighted to allow the skin to slide down at a constant speed (Figure 2).  In this setup, the weight of the synthetic skin layer is negligible. Figure 2  Experimental setup to test the friction between trocar and skin Adapted from W. Firme-Gustavo et al., (C)2015 Society of Laparoendoscopic Surgeons. -In the experiment, the magnitude of the kinetic frictional force between the ramp and the synthetic skin depends on:the area of the contact surface.the mass of the load.the speed of the synthetic skin.

Passage Positron emission tomography (PET) is a medical imaging technique used for the detection of tumors and the evaluation of neurological functions.  A radiopharmaceutical (radioactive tracer) injected into a patient undergoes positive beta decay and emits a positron.  The positron undergoes an annihilation event with a nearby electron (<1 mm away), which emits a pair of 511 keV gamma ray photons traveling in opposite directions.  The gamma rays are detected by a ring of scintillation detectors surrounding the patient, as shown in Figure 1.  The difference in detection time between the two gamma rays from the same annihilation event is used to determine its location.  An image is constructed from data collected from multiple emission events. Figure 1  Basic setup and process of positron emission tomographyScintillation, the emission of detectable light when excited electrons return to their ground state, occurs in crystals within the detectors due to the transfer of energy from the high energy gamma rays.  The wavelength of the emitted light depends exclusively on the type of scintillation material used (Table 1).Table 1  Common PET Scintillating Crystal Materials The electrons in the scintillating crystals are excited through Compton scattering, a process in which a gamma ray photon acts as a particle, and transfers energy to an electron via collision.  Subsequently, the photon scatters (travels in a new direction) and its wavelength changes.  The percent change in the wavelength of the photon due to the energy loss is Equation 1where θ is the angle between the scattered photon and electron.  Equation 1 is represented in Figure 2. Figure 2  Percent change in photon wavelength due to Compton scattering -The radiopharmaceutical administered to a patient is carefully chosen to provide a specific number of positron emissions per second.  If the rate of positron emissions is increased, which of the following can be expected?

An 8-F parallel plate capacitor generates a voltage of 5 V when fully charged.  How much charge is stored by the capacitor?

A gram-negative bacterium moves along a flat surface.  What is the maximum displacement of the bacterium during a 1-hour period if the bacterium moves at a constant speed of 25 µm/s?