Exam 7: Physics

Passage Sound waves propagate through many conducting structures in the ear before they are transduced into neuronal signals.  When sound waves reach the fluid-filled cochlea, they are detected by hair cells lining the basilar membrane.  The cochlear spiral can be modeled as a resonator system because each section of the basilar membrane is sensitive to a specific frequency (Figure 1). Figure 1  Amplitude pattern of the basilar membrane for different frequenciesPresbycusis (age-related hearing loss) results from a combination of factors that lessens an individual's mechanical and/or neurological sensitivity to sound.  Pure tone audiometry (PTA) is used to determine an individual's ability to detect different sound frequencies and can be used to evaluate presbycusis.  A "pure" tone is characterized by a single sinusoidal waveform.  An audiogram plots the relative intensity required of a given frequency to be detected by the individual (Figure 2). Figure 2  Audiogram of an elderly patient exhibiting presbycusis -In Figure 2, how does the hearing threshold intensity at 1,500 Hz compare to the threshold intensity at 2,000 Hz?

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. -Assume that the average radial artery has a cross-sectional area A of 0.2 cm² and a length L of 30 cm.  What is the total resistance R of the radial artery?  (Note: The resistivity of blood is 200 Ω-cm.)

Passage The flow of blood through the human body is typically laminar, but in certain conditions, as when blood flows through the aorta during a period of heightened physical activity, the flow can become turbulent.  Blood flow can also become turbulent in abnormal cases in which the passage of blood is obstructed by constrictions within the blood vessel.  The energy generated by blood turbulence creates sound vibrations that can be heard with a stethoscope.Using the technique of laser Doppler velocimetry, researchers recorded the blood velocity v at a point in the aorta of an experimental subject at different times during aerobic exercise.  Table 1 shows the blood velocities observed over a 400 ms time interval.Table 1  Blood Velocity within the Aorta of an Experimental Subject (mean velocity v̅ = 101 cm/s) Turbulent kinetic energy (TKE) is the kinetic energy per unit mass associated with turbulence within flowing fluids and is defined as: Equation 1where σ_v is the standard deviation of the fluctuating fluid velocities at a point within the turbulent flow.Reynolds number Re is the quantity that ultimately measures whether a flow is turbulent or laminar.  Re is defined in terms of the fluid density ρ, mean velocity of the flow v̅, conduit diameter d, and dynamic viscosity η of the fluid, as given by: Equation 2In the context of blood flow, d is the diameter of the blood vessel, and blood has a fluid density of about 1,060 kg∙m⁻³ with a dynamic viscosity of about 0.003 kg∙m⁻¹∙s⁻¹. -Blood flow in the aorta becomes turbulent at a Reynolds number of approximately 6,000.  If the diameter of the aorta is approximately 2 cm, what is the average velocity of blood at this Reynolds number?

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. -Fatty tissue has a lower electrical conductivity than lean (non-fat) tissue.  This property allows body fat content to be estimated by modeling the tissue between two points as a single resistor.  For the same amount of current entering the body, relatively high body fat content would be indicated by:

In which of the following processes does energy convert from chemical energy to thermal and kinetic energy?

A monoatomic ideal gas is sealed within a container featuring a piston fixed in place at one end. How will the heat capacity C of the gas change if the piston is allowed to move freely?

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. -An object with the same density as water is stationary and suspended in a container filled with water.  Ignoring the effects of fluid friction, what will happen to the object after a downward force is momentarily applied?

Passage A traumatic brain injury (TBI) is a form of brain injury caused by an external physical force.  In addition to direct injury at the site of an impact, the rapid acceleration-deceleration of the head may cause the brain to move within the skull and result in injury to the part of the brain opposite the impact site.  This is known as a contrecoup injury.If an impact to the head also results in a skull fracture, the injury is classified as an open TBI.  If there is no skull fracture, the injury is classified as a closed TBI.  The type of TBI can be predicted from the collision duration and the average acceleration of the head.  The thresholds for open and closed TBI are shown in Figure 1. Figure 1  Thresholds for open and closed TBIIn an experiment to study head collisions with projectiles, researchers equipped the head of a crash test dummy with sensors that measured acceleration on multiple axes.  The crash test dummy was stationary before its head was subjected to controlled collisions with incoming projectiles of varying mass and impact velocity.  The linear acceleration of the crash test dummy's head was recorded during and after the impact.  The results for a trial in which the impact lasted for 10 ms are shown in Figure 2. Figure 2  The acceleration of the head during and after a 10-ms collision -In one experimental trial, the projectile was uniformly accelerated from rest to a distance of 2 m in 0.1 s.  What was the acceleration of the projectile?

A marble rolls down a slope at a velocity of 10 m/s.  If the kinetic energy of the marble is 2 J, what is the mass of the marble?

Passage In hemodynamics, blood flow through the cardiovascular system can be modeled as an electric circuit in which the blood serves as electricity, the blood vessels as resistive wires, and the heart as a battery (see Figure 1). Figure 1  Cardiovascular circuit modelOhm's law states that the voltage drop ΔV across each element, the current I flowing through it, and its electrical resistance R are related by ΔV = IR.  In a blood vessel, pressure difference between one vessel and the next ΔP replaces ΔV, volumetric blood flow Q replaces I, and vascular resistance R replaces electrical resistance.  Therefore, Ohm's law for blood flow in a vessel isΔP = QREquation 1Vascular resistance is due to the blood's viscosity η and the dimensions of the vessel through which it flows.  Assuming blood vessels are cylinders, R can be approximated as Equation 2where L is the length of the vessel, and r is its inner radius.  If Equation 2 is combined with Equation 1, the resulting equation is Poiseuille law.In a study of the circulatory system in rats, researchers measured the intravascular blood pressure of the mesenteric blood vessels.  The mesentery is the set of tissues that holds the intestines in place.  Blood flows in the following order:  aorta, superior mesenteric artery (SMA), arterial arcade, venous arcade, superior mesenteric vein (SMV).For the procedure, catheters with pressure transducers were inserted into each vessel via laparotomy.  Laparotomy is an invasive procedure that involves a surgical incision into the abdominal cavity.  Blood pressure measurements were taken simultaneously at the proximal end (beginning) of each blood vessel. Figure 2  Mesenteric blood pressure profile of rats (Note: SMA = superior mesenteric artery; SMV = superior mesenteric vein.) -The blood pressures of an artery in the neck and in the leg of a person lying down are measured, and their difference calculated.  When the blood pressures are taken after the person stands up, their difference:

Passage For a person with perfect vision, light from an object is properly refracted by the eye lens to converge on a single point at the retina, forming a clear image of the object.  Vision defects result from eye shape abnormalities or errors in the refractive power of the eye lens.  Myopia (nearsightedness) occurs when light from a distant object is incorrectly focused in front of the retina.  Hyperopia (farsightedness) occurs when light rays from a nearby object are focused beyond the retina.Many optical techniques are available to measure the refractive error of an individual to determine the necessary correction.  Photorefraction is a photographic technique often used with young children because it does not require the individual to be still for a lengthy duration.  When the patient is looking at the camera, a flash photograph is taken of the eye to determine the amount of light that is reflected off the retina and captured by the camera lens.In healthy eyes, all the light from the flash that enters the eye is reflected off the retina and returns back to the camera's light source.  Because the camera lens does not receive this light, the pupil is completely dark in the resulting image.  A myopic eye cannot properly focus the light at the retina.  Due to the geometry of the eye and its lens, some of the light is reflected to the top portion of the camera lens.  The camera captures an image of a pupil with a crescent of light at the top.  In a hyperopic eye, the crescent appears at the bottom of the pupil.  Ray diagrams for photorefraction are shown in Figure 1. Figure 1  Paths of light in photorefraction for different eyes:  (A) Healthy, (B) Myopic, and (C) Hyperopic. HC. Howland, "Optics of photorefraction: orthogonal and isotropic methods." ©1983 Optical Society of America. -Photorefraction with a camera at a distance of 50 cm away from a child produces a completely dark image of the pupil.  If the child's retina is 2.5 cm from the eye lens, what is the lens strength of the eye?  (Note:  Use the thin lens formula, S = 1/o + 1/i.)

Passage Ultrasound is a technique that uses the propagation properties of high-frequency sound waves to construct images of internal organs or to measure blood flow velocity.  The shape and position of internal organs are resolved by measuring the return time of reflected ultrasound waves.  Similarly, blood flow velocity is resolved by measuring the Doppler shift of reflected ultrasound waves.  An ultrasound device consists of an array of piezoelectric crystals and an acoustic lens.  The piezoelectric crystals generate sound when an alternating voltage is applied, and the acoustic lens increases the transmission efficiency from the device to the body by reducing sound reflection at the skin.Ultrasound is performed using frequencies in the range of 2-15 MHz.  The lower ultrasound frequencies are used for deep abdomen and obstetric/gynecological imaging due to their greater penetrating ability.  The higher ultrasound frequencies have less penetrating ability but provide higher resolution, and therefore are used for blood flow measurements and the imaging of more superficial structures.  Detailed ultrasound penetration data is shown in Figure 1. Figure 1  Penetration in soft tissue for three different ultrasound frequenciesSound waves propagate through soft tissue at an average speed of 1,500 m/s and through blood at 1,570 m/s. -Piezoelectric crystals likely create sound by:

Passage In mass spectrometry, a sample's molecules are ionized in a vacuum and then exposed to a uniform electric field created by a high-voltage plate in the acceleration chamber.  The electric field accelerates the ions until they arrive at the next section of the device, designated as the separation chamber.  In this section, the drifting ions are sorted by their mass-to-charge ratio (m/q).The separation chamber in a time-of-flight mass spectrometer (TOF-MS) is linear and has no electric or magnetic fields.  The ions travel at a constant velocity through the chamber until they reach the detector.  The time it takes for an ion to reach the detector depends on its m/q ratio. Figure 1  Time-of-flight mass spectrometerA magnetic sector mass spectrometer (MS-MS) has a curved separation chamber where a magnetic field is generated.  The magnetic field exerts a centripetal force on drifting ions, bending their trajectories into curved paths.  The radius of the curvature depends on the ion's m/q. Figure 2  Magnetic sector mass spectrometerThe centripetal force (F) acting on a particle can be determined from its mass (m) and velocity (v) and the radius (r) of the curved path:F = mv²/rEquation 1 -In the MS-MS separation chamber, the direction of the magnetic force on a moving ion is:

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. -When the angle of inclination of the ramp increases, kinetic friction:

Passage A traumatic brain injury (TBI) is a form of brain injury caused by an external physical force.  In addition to direct injury at the site of an impact, the rapid acceleration-deceleration of the head may cause the brain to move within the skull and result in injury to the part of the brain opposite the impact site.  This is known as a contrecoup injury.If an impact to the head also results in a skull fracture, the injury is classified as an open TBI.  If there is no skull fracture, the injury is classified as a closed TBI.  The type of TBI can be predicted from the collision duration and the average acceleration of the head.  The thresholds for open and closed TBI are shown in Figure 1. Figure 1  Thresholds for open and closed TBIIn an experiment to study head collisions with projectiles, researchers equipped the head of a crash test dummy with sensors that measured acceleration on multiple axes.  The crash test dummy was stationary before its head was subjected to controlled collisions with incoming projectiles of varying mass and impact velocity.  The linear acceleration of the crash test dummy's head was recorded during and after the impact.  The results for a trial in which the impact lasted for 10 ms are shown in Figure 2. Figure 2  The acceleration of the head during and after a 10-ms collision -What additional information do the researchers need from the crash test dummy to estimate the power of the collision in the experiment shown in Figure 2?

Passage In hemodynamics, blood flow through the cardiovascular system can be modeled as an electric circuit in which the blood serves as electricity, the blood vessels as resistive wires, and the heart as a battery (see Figure 1). Figure 1  Cardiovascular circuit modelOhm's law states that the voltage drop ΔV across each element, the current I flowing through it, and its electrical resistance R are related by ΔV = IR.  In a blood vessel, pressure difference between one vessel and the next ΔP replaces ΔV, volumetric blood flow Q replaces I, and vascular resistance R replaces electrical resistance.  Therefore, Ohm's law for blood flow in a vessel isΔP = QREquation 1Vascular resistance is due to the blood's viscosity η and the dimensions of the vessel through which it flows.  Assuming blood vessels are cylinders, R can be approximated as Equation 2where L is the length of the vessel, and r is its inner radius.  If Equation 2 is combined with Equation 1, the resulting equation is Poiseuille law.In a study of the circulatory system in rats, researchers measured the intravascular blood pressure of the mesenteric blood vessels.  The mesentery is the set of tissues that holds the intestines in place.  Blood flows in the following order:  aorta, superior mesenteric artery (SMA), arterial arcade, venous arcade, superior mesenteric vein (SMV).For the procedure, catheters with pressure transducers were inserted into each vessel via laparotomy.  Laparotomy is an invasive procedure that involves a surgical incision into the abdominal cavity.  Blood pressure measurements were taken simultaneously at the proximal end (beginning) of each blood vessel. Figure 2  Mesenteric blood pressure profile of rats (Note: SMA = superior mesenteric artery; SMV = superior mesenteric vein.) -Which of the following experimental groups would aid in determining if the procedure described in the passage has a confounding variable?

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 the angle between a Compton-scattered photon and an electron is 60°, what is the energy of the scattered photon in terms of the original energy E?

An ideal fluid flows through a tube at an initial speed of 4.0 m/s.  What will be the speed of the fluid if the cross-sectional area of the tube decreases from 6.0 m² to 2.0 m²?

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 -A tissue sample at 275 K is submerged in 2 kg of liquid nitrogen at 70 K for cryopreservation.  The final temperature of the nitrogen is 75 K.  What is the heat capacity of the sample in J/K?  (Note: Assume no heat is lost to the surrounding air.)

Two convex lenses are placed in series such that the image produced by first lens becomes the object of the second lens.  If each lens is capable of producing a three-fold magnified image, what is the maximum magnification that this two-lens system can provide?