Biophysics Long Exam 1 Reviewer PDF

Biophysics Lecture Long Exam 1 Reviewer FORMULA BANK Volume Strain = ΔV/V Kinematic Equations Pascal’s Laws for Pressure vf = vo + at F1/A1 = F2/A2 Δx = vot + 1/2at2 F = ma...

Biophysics Lecture Long Exam 1 Reviewer FORMULA BANK Volume Strain = ΔV/V Kinematic Equations Pascal’s Laws for Pressure vf = vo + at F1/A1 = F2/A2 Δx = vot + 1/2at2 F = ma vf2 = vo2 + 2aΔx Continuity Equation p1A1v1 = p2A2v2 (Note: symbols stand for density, area, velocity) Reynold’s Number: ratio of a characteristic convective inertial momentum to the impulse of the body due to the viscous force R < 1 - streamline flow 1 < R < 100 - vortex flow R > 150 - turbulent flow R = (pvfL)/n; wherein p is density, v is velocity, L is length and n is the friction coefficient Newton’s Laws Bernoulli’s Principle F = ma v = 2𝑔∆ℎ FG = G(m1m2/r2) Blood Flow Torque F = ΔP/R T = r f sin Θ 8𝑛𝐿 Work, Energy and Power R= 4 ; n is viscosity, l is length, r π𝑟 W = F d cos Θ is radius P = W/t ∆𝑃 π 𝑟 4 F= P.E. = mgh 8𝑛𝐿 Uniform Circular Motion Wave Speed vt = 2πrf v = fλ w = 2πf (angular velocity) Loudness Pressure B = 10 log[I/Io]; wherein Io = 1 x 10-12 P = F/A I = Io(10B/10) Strain Inverse Square Law Linear Strain = ΔL/L I = P/(4𝛑r2) Biophysics Lecture Long Exam 1 Reviewer MODULE 1 What is Biophysics? Study of life enlightened by physical principles Can be divided to: molecular biophysics, cellular biophysics and systems biophysics Application of theories and methods of physics to understand biological systems Models are used to study the said principles, and these definitions should be clear and consistent ○ The models used to study biophysical principles synthesizes a set of observations into a mental structure which includes a predictive scheme Models to theories Maxwell’s prediction of radio waves (1984) Einstein’s prediction of the energy equivalence of mass (1905) Darwin’s theory of evolution (1859) Mendel’s rules of inheritance (1865) Understanding conceptual models There has to be limitations within the system ○ a model must be defined into ‘localizable systems’ which are devoid of external influences ○ systems that can be isolated in a vacuum distinction must be made between the number of independent observables within a system and the complexity of its ramifications Sir Henry Poincare ○ Recognized in the 19th centuries that even simple mechanical systems can exhibit chaotic behavior a simple change within the initial conditions can result into exponentially different trajectories in the resultant path of motion Types of Systems Disordered systems ○ large system that needs a large amount of information to specify its dynamics Chaotic systems ○ systems whose long-time behavior became unpredictable or uncontrollable due to inevitable information loss Complex systems ○ System whose behavior depends on substructures with each substructure having a relationship between each other Biophysics Lecture Long Exam 1 Reviewer Biophysical studies historically has been macroscopic, but focus has now shifted to microscopic and molecular level ○ macroscopic -> microscopic -> molecular understanding the physical laws and principles to the understanding of life systems and to instruments aid in the advancement of biology, medicine, and diagnostics Organization of Study Biophysics identify particular phenomena in nature which arise from basic physical interactions. For each natural effect, the following are attempted to be given (when applicable): ○ Defining concepts ○ Nature of the phenomenon ○ Relation to other phenomena ○ Generation, detection and measurement ○ Bioreceptors, biogeneration and functional organs ○ Uses in research, diagnosis and treatment ○ Dosimetry and safety Biophysics Lecture Long Exam 1 Reviewer MODULE 2 Laws of Mechanics Forces, accelerations, stress, strain and viscous flow Follows rules of Isaac Newton (1665) Biostatistics and Biodynamics Each level of life systems are intrinsically governed by forces Macroscopic: electrical and gravitational (classical mechanics) Microscopic: nuclear and weak Atomic and molecular: quantum mechanics Vectors and Scalars Vectors ○ Has both magnitude and direction ○ Note: don’t forget to put if + or - !!! Scalars ○ Magnitude only Kinematics Equations vf = vo + at Δx = vot + 1/2at2 vf2 = vo2 + 2aΔx TIP: when choosing what equation to use, use the one that when you input the given, only 1, not 2, is unknown Solving Projectile Motion Problems 1. Draw free body diagram 2. Identify given 3. Identify the type of projectile motion problem 4. Think in components. Solve x-axis and y-axis separately Projectile Motion Will have a horizontal and vertical component X-axis ○ range: horizontal distance ○ ax = 0m/s2 Y-axis ○ peak: maximum height; vf = 0 ○ Ay = -9.81 m/s2 Remember SOH CAH TOA (sin Θ = opp/hyp, cos Θ = adj/hyp, tan Θ = opp/adj Biophysics Lecture Long Exam 1 Reviewer Newton’s Laws Law of Inertia ○ Forces are balanced; stay at rest or stay in motion Law of Momentum ○ Change of momentum is equal in both magnitude and direction to the force imposed on it ○ F = ma ○ Mas masakit bullet than ball Law of Action and Reaction ○ For every action, there is an equal and opposite reaction ○ Static equilibrium ○ Drag Force opposite the direction of motion Not equal in magnitude but directly proportional to the velocity of the object Law of Linear Superposition ○ Assumes a linear system ○ Values within the same system may be additive (reinforcement) or subtractive (cancellation) Law of Universal Gravitation ○ FG = G(m1m2/r2) Torque Force that you get from the rotation on an axis T = r f sin Θ In Nm (Newton meter) Work, Energy and Power Power is the rate of doing work, and energy is the capacity to do work W = F d cos Θ Work is in J (joules) P = W/t P.E. = mgh Energy computation ultimately depends on the context Biophysics Lecture Long Exam 1 Reviewer Uniform Circular Motion Acceleration and velocity are perpendicular Acceleration is constant in magnitude but not velocity vt = 2πrf w = 2πf (angular velocity) Velocity and angular velocity are different in uniform circular motion Frictional Force Perpendicular to normal force and opposite to applied force Phenomenological not universal law; applies to surfaces that are not smooth Pressure Force per unit area P = F/A Stress Types: ○ Normal Longitudinal Tensile Compressive Volume/bulk ○ Shearing Strain Linear Deformation ○ Linear Strain = ΔL/L Volume Deformation ○ Volume Strain = ΔV/V Biophysics Lecture Long Exam 1 Reviewer MODULE 3 Fluids ○ Can be liquid or gas ○ Any material that exhibits macroscopic movement under stress or when they reach a limiting boundary ○ Quantities are depicted as density ○ Forces that act on fluids: gravity and thermal pressure E.g. heating up water ○ What differentiates liquids and gases: both gases and liquids flow but liquids have an equilibrium volume influenced by their own molecular interactions from their structure Simplified version from chatgpt: Liquids have a certain amount of space they naturally take up, which is controlled by how their molecules interact with each other. This is different from gases, where the molecules are spread out and can fill any space available. In liquids, the molecules are close enough to stick together, but not so tightly packed that they can’t move, giving them a definite volume. Gases, on the other hand, don’t have a fixed volume because their molecules move freely. Gas molecules are always mobile with each having different kinetic energy; some particles move slower than others; it is hard to identify the individual kinetic energy so you get an average and that is your “equilibrium volume”(?) Any shearing force on liquid causes movement of layers of fluids against adjacent layers; H2O is polar so they will stick together and move together A liquid at rest can exert pressure on its wall however since it’s under stress, it can not exert a shearing force internally on a bounding surface E.g. when you are at reset under still water, it can exert pressure on your skin but it will not push you Laws for Fluids (Newtonian Fluids) ○ Particles within the fluid need to be uniformly distributed throughout the system with each one being able to move relative to each other ○ A particle within the fluid move the same relatively to the whole system; velocities of the component in a small segment has little deviation but the segments should be large enough so that the averages of the velocity is meaningful ○ We have to imagine them as segments that move the same way not as individualistic particles ○ Just treat fluids as one whole system, as having the same quantities as a system ○ Assume that the molecules within the fluid are interacting sufficiently so that the average is true Pascal’s Laws for Pressure ○ Pressure applied to an enclosed fluid will be transmitted without a change in magnitude to every point of the fluid and to the walls of the container Biophysics Lecture Long Exam 1 Reviewer ○ E.g. pistons ○ Important equations: F1/A1 = F2/A2 F = ma Viscosity ○ Friction for liquids ○ Friction grows as the area of contact grows ○ Friction is also directly proportional to the difference in speed between the top and bottom motion ○ Expressed in ‘poise’ or 1 gm/cm sec ○ Measure with a viscometer; fluid fills the gaps between 2 plates ○ Note: no need to memorize equation, just remember the concept n is the friction coefficient; heavily dependent on the material; innate characteristic Viscosity in Blood ○ Viscosity depends on temperature; higher temperature, lower viscosity ○ Hematocrit: total blood volume that influences viscosity ○ Medical conditions Hypothermia: because of low temperature, blood is more viscous, making it harder to flow Leukemia: higher WBC impedes the blood flow Buoyancy and Archimedes’ Principle ○ Buoyancy: net pressure force on fluids needed to maintain mechanical equilibrium Recall: to be in mechanical equilibrium, net force should be 0 ○ Archimedes’ Principle: upward buoyant force exerted on a body immersed in fluid Equal to the weight of the fluid that the body displaces ○ Buoyancy points inward to the mass with magnitude opposite to weight ○ Highly dependent on the density of the object Taken advantage by fishes; they change the parts of their body that are filled with gases (makes use of cavities) to manipulate their buoyancy ○ Center of mass (dependent on mass) is different from center of buoyancy (dependent on density) Biophysics Lecture Long Exam 1 Reviewer Surface Tension ○ Force per unit length needed to hold a surface cut together; occurs because of intermolecular forces ○ Expressed in ‘dynes’ ○ Insects can walk on water due to hydrophobic feet Separation between hydrophobic and hydrophilic molecules essentially creates a film ○ A fluid surface disrupted will tend to have an elastic restoring force Fluid Flow ○ Flow is caused by pressure difference; higher pressure differential, greater flow rate ○ Poiseuille’s Law: fluid flow follows a parabolic trajectory Due to friction/viscosity; outer layer of the fluids are interacting more with the walls compared to the internal layer; outer layer is impeded; inner layer is flowing faster Continuity Equation ○ Law of conservation of mass for fluids ○ p1A1v1 = p2A2v2 ○ Note: symbols stand for density, area, velocity Navier-Stokes’ Law ○ Only takes into account Newtonian fluids ○ Navier incorporated viscosity; Stokes incorporated two-dimensional flow of fluids ○ Equation that combines conservation of mass and momentum for fluids; includes body force, pressure force and viscous force ○ If the stress is proportional to the strain in the fluid, the fluid is newtonian Non-Newtonian fluids: lava, magma, blood in capillaries and suspension of cornstarch in water ○ Model for fluid flow that takes into account different values in the system: net stress, net external force, density and other forces Streamline vs Turbulent Flow ○ Reynold’s Number: ratio of a characteristic convective inertial momentum to the impulse of the body due to the viscous force R < 1 - streamline flow 1 < R < 100 - vortex flow R > 150 - turbulent flow Biophysics Lecture Long Exam 1 Reviewer R = (pvfL)/n; wherein p is density, v is velocity, L is length and n is the friction coefficient dimensionless number Defines the flow velocity pattern Bernoulli’s Principle ○ Law of conservation of energy for fluids ○ Pressure (potential energy) is indirectly proportional to velocity (kinetic energy) [IN THE CONTEXT OF BERNOULLI’S] ○ Energy per unit mass does not change along a streamline flow ○ An increase in a speed of the fluid happen simultaneously with a decrease in the pressure or a fluid’s potential energy ○ Used to explain movement of fluids in a Venturi tube or blowing in a straw Fluid must be: Laminar and steady ○ Velocity doesn’t vary with time Inviscid ○ Shear forces due to viscosity are negligible Incompressible ○ Density can be assumed to be constant ○ Bernoulli's principle talks about ideal, frictionless fluid: smaller pipes = faster flow (speed) and lower pressure. ○ Poiseuille's law deals with real, sticky fluids: smaller pipes = harder to push through, so you need more pressure and flow (speed) actually slows down. ○ P1 + 1/2pv12 +pgh1 = P2 + 1/2pv22 +pgh2 [NO NEED TO MEMORIZE] P is pressure at elevation, p is density, v is velocity, g is acceleration due to gravity and h is height of elevation ○ v = 2𝑔∆ℎ [NEED TO MEMORIZE] Can be used for set-ups wherein a body is pierced, both points are exposed to the same atmosphere, size of thole is so small compared to the body; if you know the height of the hole and bernoulli’s principle is applicable, you can use the equation Blood Flow ○ Blood is Non-Newtonian because of the red blood corpuscles; other laws do not apply [debatable] A Newtonian fluid means that stress is directly proportional to strain but this is not the case for blood Biophysics Lecture Long Exam 1 Reviewer ○ Conservation of mass applies to blood flow ○ Blood flow is not uniform but it is smooth enough for Poiseuille’s law to be applied ○ Capillaries Capillaries are where blood exchanges oxygen and nutrients; it is imperative for blood flow to be slowest there for transfer to be efficient Since blood is non-newtonian: smaller area, lower velocity, lower pressure ○ Blood Flow (F): Total quantity of blood that passes through a given point in circulation in a given period E.x. renal blood flow = 1000 mL/min ○ Blood pressure (P): force exerted by blood against the vessel wall ○ Resistance (R): force opposing blood flow; depends on viscosity, length of blood vessel and radius of vessel ○ Blood Flow (F) = ΔP/R 8𝑛𝐿 R= 4 ; n is viscosity, l is length, r is radius π𝑟 4 ∆𝑃 π 𝑟 F= 8𝑛𝐿 However, in the case of our bodies, viscosity and length are the same, so we can consider radius and change in pressure as factors that affect blood flow Since radius is raised to the fourth (r4) in the formula, it has a huge impact compared to blood flow ○ Doubling the radius would make F 16 times greater ○ Application of Poiseuille's law; when you decrease the radius, you lose the inner layer wherein flow is fast ○ Autoregulation Some organs can regulate their own blood flow by changing the radius of the vessels going towards it (vasodilation or vasoconstriction) Microfluidics Systems ○ Study or manipulation of fluid behavior through microchannels ○ Carefully designed to achieve the specific feature (e.g. lab-on-a-chip, organ-on-a-chip, etc.) ○ Allows analysis and requires small amounts of analyte ○ Compact size allows ease of operation, transport, etc. ○ Designed to be handle by non-experts ○ Scientists want to shrink conventional macroscopic systems to a chip to simulate it E.g. drug discovery Makes it easier instead of testing on humans In vivo are still better than in vitro but it could be good benchmarks E.g. Ted Ed video says na it can cut expenses by 50%, minimize animal testing, etc. Biophysics Lecture Long Exam 1 Reviewer MODULE 4 Nature of Sound Waves Sound waves are longitudinal and mechanical in nature Vibration that propagates as an audible wave of pressure Sound: physiological sensation that accompanies hearing (vibration) Coherent vibration propagating in materials ○ Coherent: group-like behavior of numerous elements and systems ○ Incoherent: occur in all ordinary materials above absolute zero in temperature ○ No vibration at absolute zero or belo Higher sound intensity can lead to increase in temperature Acoustics: study of sound Sound Energy Form of energy that is audible Caused by collision of particles with each other (vibrations) Sound requires medium Potential energy + kinetic energy of sound energy Affected by multiple factors ○ Volume ○ Sound pressure ○ Pressure velocity ○ Density of the medium without sound present ○ Local density of the medium ○ Speed of sound Affected by the energy of the wave and the medium at which it propagates Sound power is measured in Watts Sound intensity ○ sound power per unit area ○ Indicates the flow of sound through a specific area Properties of Sound Waves Biophysics Lecture Long Exam 1 Reviewer Amplitude ○ Height of the wave ○ In cm Wavelength (λ) ○ Period where the wave repeats along the x-axis ○ Distance between adjacent identical parts of a sound wave ○ In meters ○ Varies as sound travels through different mediums Time period ○ Time it takes for one oscillation Frequency (f) ○ 1/period ○ Sound frequency does not change from one medium to another Wave speed ○ v = fλ ○ f is frequency ○ λ is wavelength ○ In meters/second Pitcht Determined by frequency Low pitch (flat), lower frequency; high pitch (harsh), higher frequency All tones which are perceived to have a single pitch are given one value for the pitch in a unit called a Mel Perception in change of frequency is really dependent on intensity (how we hear the sound) Speed of Sound Dependent on the density and temperature of the medium at which it propagates Biophysics Lecture Long Exam 1 Reviewer Higher density, sound will travel faster; higher density, molecules are closer and sound is transferred more readily Sound travels faster in solid than air Higher temperature, sound will travel faster; higher temperature provides more kinetic energy Sound follows the principle of linear superposition Nodes: places where waves completely cancel during the whole time of observation Antinodes: places where waves maximally add during the whole time of observation Intensity Determined by sound amplitude amount of energy transferred to a unit area over time that is perpendicular to the direction in which the sound waves are traveling Can be measured through energy or work Measured in Watts/m2 (power/unit area) Loudness In decibels ○ Man made scale ○ B = 10 log[I/Io]; wherein Io = 1 x 10-12 ○ I = Io(10B/10) Directly proportional to intensity, pressure and amplitude Sample Problem Solving Determine the decibel rating of the following sound sources and their estimated sound intensities. Remember: Io = 1 x 10-12 Arise at 5 PM on a weeknight: I = 1 x 10-9 W/m2 B = 10 log[1x10-9/1x10-12] B = 30 Rizal library after school: I = 1 x 10-6 W/m2 B = 10 log[1x10-6/1x10-12] B = 60 BIO 30.01 at the beginning of class: I = 1 x 10-4 W/m2 B = 10 log[1x10-4/1x10-12] B = 80 Araneta on a Friday night during basketball season: I = 8.1 x 10-3 W/m2 B = 10 log[8.1x10-3/1x10-12] B = 99.08 Maki concert = front row: I = 7.4 x 10-2 W/m2 B = 10 log[7.4x10-2/1x10-12] B = 108.69 Additional: Arise at 5 PM on a weeknight: 30 dB Biophysics Lecture Long Exam 1 Reviewer I = Io(10B/10) I = 1x10-12(1030/10) I = 1 x 10-9 W/m2 Rizal library after school: 60 dB I = Io(10B/10) I = 1x10-12(1060/10) I = 1x10-6 W/m2 Sound Propagates as a Sphere Inverse square law I = P/(4𝛑r2) ○ 4𝛑r2 - surface area of sphere The relationship between intensity (I) and (d) is an inverse square relationship which follows the equation: I = P/(4𝛑r2) where P is the power of the sound source, usually expressed in Watts. As the distance from the point source increases, the sound decreases in a hyperbolic manner Sample Problem Solving Roody recently purchased a stereo system for his basement recreation room. Determine the maximum intensity of the sound waves at the following distances from his 120-Watt main speaker. a. 1.0 meters b. 2.0 meters c. 3.0 meters Given: P = 120 Watts Required: maximum intensity of sound waves at a) 1.0 m, b) 2.0 m and c) 3.0 m Equation: I = P/(4𝛑r2) Solution: a) I = 120/(4𝛑(1.0)2) I = 9.5492 W/m2 Biophysics Lecture Long Exam 1 Reviewer b) I = 120/(4𝛑(2.0)2) I = 2.3873 W/m2 c) I = 120/(4𝛑(3.0)2) I = 1.0610 W/m2 Answer (significant figures): a) 9.5 W/m2, b) 2.4 W/m2 and c) 1.1 W/m2 Acoustic Impedance Kind of similar to refraction Degree at which a material resists transfer in sound energy Measured by the ratio of pressure needed to cause motion to the current that pressure causes Affected by three factors: ○ Degree of coupling between the adjacent layers of the materials (determines speed of sound in material) ○ Dissipative processes within the materials (affects conversion of sound energy to heat or other forms) ○ Density Can be seen in musical instruments especially in musical wind instruments Particular configurations produce certain frequencies due to acoustic impedance ○ Different fingering in guitars determines the acoustic response of the instrument Sound Resonance Transfer of energy from one oscillatory system to another near a natural frequency of the receiving system. At this frequency (natural frequency), energy transfer is greatest. When pushing a swing rhythmically, if your intent is to make the swing gain amplitude, your rhythm should match the swing’s natural frequency. Over many cycles, it takes only a little effort on each cycle to cause a build up in the energy stored in the swinging motion ○ If you want to push for a natural frequency, it will take only little effort on each cycle if you produce the same swing every time Ear Three Parts ○ Outer ear Pinna collects as much sound waves as possible and channel it to the auditory canal The sound waves meet the eardrum - a transparent membrane that is super sensitive to vibrations ○ Middle ear Ossicles - three tiniest bones in the body Malleus (hammer) Incus (anvil) Stapes (stirrup) Biophysics Lecture Long Exam 1 Reviewer Main job is to increase or amplify the pressure of the sound waves when it reaches the inner ear Increase the pressure of sound ~20x Stapes is much smaller than eardrum so when the force gets transmitted, it gets concentrated in a very tiny area ○ Inner ear Consists of a liquid Vibrating liquid is harder so to set this liquid in vibration, pressure should be high enough Consists of bony structure Top part consists of three semicircular rings that help us maintain balance (not involved in hearing) Cochlea: snail-like structure; convert vibrations to electricity and sends it to our brain through auditory nerves Physics of Hearing Ear: organ that converts sound energy into pressure to electrical signal to the brain Bioacoustics Field dedicated to identifying animals in the ecosystem based on the sound Audiomoth: algorithm used to record a wide range of frequencies Sonar and Echolocation A certain source transmits sound waves which an object receives and the object sends a reflected wave and based on the time it takes for the reflected sound waves to be collected, you can use the distance What whales use to scan the area and to find food Sonography Utilizes ultrasound waves Procedure in medicine used in various purposes such as ○ Mapping out children of suspected pregnant women ○ Identification of possible defects in organs and tissues such as muscle pull, muscle tears, nerve problems etc. A gel is applied to the patient and a transducer is used, which gives out sounds. and based on the collected data from the received sounds, you can identify the things above Acoustic Tweezers Tools used to separate/manipulate bioparticles ranging from nm to mm size Three types ○ Standing wave For particle and cell manipulation by forming resonance patterns inside channels then the acoustic waves collected from the reflection layer form standing waves and establish a pressure distribution in the fluid which lets you manipulate bioparticles Biophysics Lecture Long Exam 1 Reviewer ○ Traveling wave Active Passive Form arbitrary pressure nodes in 3D space by controlling the face patterns of the acoustic waves ○ Acoustic streaming The steady flow generated by the absorption of acoustic energy by the liquid can also be used to indirectly manipulate the particles in a solution Commonly generated by oscillating microbubbles or solid structures Sound in Medicine Stethoscopes: used to hear the heartbeat and pulse ○ Air chamber with a thin flexible wall to put into contact with the skin of the patient ○ Chamber is designed to roughly match the sound impedance of the skin with that of the air inside, allowing the skin, which normally reflects or absorbs some sound waves, to transmit vibrations more efficiently. Microphones in medical procedures can be used to augment hearing or monitor heart sounds ○ Phonocardiogram (PCG) Acoustic recording of the amplified sounds of the heart “lub-dub” ○ Electrocardiogram (ECG) Recording of the electrical activity of the heart Histrotrispy ○ Non-invasive, non-thermal and non-ionizing method to treat cancer ○ Destroys tumors with sound