Introduction to Biophysics PDF

Introduction to Biophysics st For 1 grad Faculty of physical therapy Prepared by Dr. Alaa Hassan Said Associated professor of Biophysics Physics department – Faculty of Science South Valley University...

Introduction to Biophysics st For 1 grad Faculty of physical therapy Prepared by Dr. Alaa Hassan Said Associated professor of Biophysics Physics department – Faculty of Science South Valley University 2024/2025  Introduction to biophysics Dr. Alaa Hassan Said Table of content Chapter 1 Physical Quantities 4 Quantitative and qualitative quantities 5 Scalars and Vectors quantities 6 The Role of Units 6 Divisions of units 7 Fundamental Units (Basic Units) 7 Derived Units 7 The international systems of units 7 Metric Prefixes 8 Dimensional Analysis 9 Accuracy and Precision: 12 Chapter 2 Physical properties of materials 15 Elasticity vs plasticity 16 Elasticity - Stress and Strain ( Hooke’s law) 19 Stress vs. Strain Curves 20 Elastic Modulus 21 Sideways Stress: Shear Modulus 24 Changes in Volume: Bulk Modulus 26 Elasticity of the human bone and tendon 29 Brittle Bones 31 Tendon 32 Strength of Human Bones 35 The Femur 35 Compression 36 Tension 36 Stress 37 Ultimate Strength of the Femur 38 Transverse Ultimate Strength 38 Body Levers 39 Lever Classes 40 Levers in the body 44 Pressure 45 Units, Equations and Representations 46 Pressure in Liquids and Gases: Fluids 46 Variation of Pressure with Depth 47 Gauge Pressure and Atmospheric Pressure 47 Atmospheric Pressure 47 Gauge Pressure 48 1  Introduction to biophysics Dr. Alaa Hassan Said Hydrostatic Based Barometers 48 Aneroid Barometer 49 Pressure and Cardiovascular System 50 Circulation 51 The Role of Pressure in the Respiratory System 54 Pressure in the Eye 55 Surface tension 56 Cause of Surface tension 56 Effects of surface tension 57 Methods of measurement 58 Cohesion and Adhesion in Liquids 59 Adhesion and Capillary Action 59 Contact angle 60 Capillary action 61 Measuring Surface Tension 62 Chapter 3 Heat and temperature in the human body 69 Basic concepts of temperature and heat 70 Temperature scales: 70 Thermometers 72 Heat transfer modes 73 Conduction 73 Convection 73 Radiation 74 Specific Heat 74 Heat capacity 75 Latent heat 75 Temperature measurements in healthcare 76 Thermography 76 IRT in medical science 77 Infrared tympanic Ear Thermometer 79 Work, Energy, and Power in Humans 80 Energy Conversion in Humans 80 Power Consumed at Rest 80 How is energy stored in the body? 81 What are the human energy systems? 82 Human Energy Metabolism 85 Body energy consumption 86 How much energy do I need to consume daily? 88 Chapter 4 Sound waves in medicine 90 2  Introduction to biophysics Dr. Alaa Hassan Said What is Sound? 91 Characteristics of Sound 91 Sound units 93 Speed of Sound 94 Human Hearing 94 How We Hear? 95 Range of Hearing 96 The Doppler effect 97 Ultrasound imaging 98 Ultrasound waves 98 From sound to image 98 Ultrasound Transducer 101 Types of Echo Display 103 Components of an Ultrasound Machine 105 Resolution 106 Doppler Ultrasound 107 Risks and side-effects 109 References 111 3 Introduction to biophysics Dr. Alaa Hassan Said Chapter 1 Physical Quantities 4  Introduction to biophysics Dr. Alaa Hassan Said Physical quantities Physical Quantity refers to a characteristic of a matter or phenomenon that can be quantified. To quantify means to measure and give it a numerical value and a unit of measurement and it classified into two types: Base Quantities: are those quantities which are distinct in nature and cannot be defined by other quantities. Base quantities are those quantities based on which other quantities can be expressed. Like the brick – the basic building block of a house. Derived quantities: are those whose definitions are based on other physical quantities (base quantities). Like the house that was built from a collection of bricks (basic quantity). Quantitative and qualitative quantities Most observation in physics are quantitative for example What can be measured with the instruments on an airplane? Descriptive observations (or qualitative) are usually imprecise, for example How do you measure artistic beauty? 5  Introduction to biophysics Dr. Alaa Hassan Said Scalars and Vectors quantities Scalar quantities are quantities that have magnitude only, for example measuring mass and temperature. Vector quantities are quantities that have both magnitude and direction, for example measuring force. Scalars Vectors Distance Displacement Speed Velocity Mass Weight Time Acceleration Pressure Force Energy Momentum The Role of Units Physicists, like other scientists, make observations and ask basic questions. For example, how big is an object? How much mass does it have? How far did it travel? To answer these questions, they make measurements with various instruments (e.g., meter stick, balance, stopwatch, etc.). The measurements of physical quantities are expressed in terms of units, which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in meters (for sprinters) or kilometers (for long distance runners). 6  Introduction to biophysics Dr. Alaa Hassan Said Without standardized units, it would be extremely difficult for scientists to express and compare measured values in a meaningful way. Divisions of units Fundamental Units (Basic Units) Fundamental units are those units that can express themselves without the assistance of any other units. For example: Kilogram (kg) is a fundamental unit because it is independently expressed and cannot be broken down to multiple units. Derived Units Derived units are those units which cannot be expressed in the absence of fundamental units. For example: Newton (N) is a derived unit because it cannot be expressed in the absence of fundamental unit (meter) and can be broken down to multiple units (Newton equals to kg.m /s2). The international systems of units In earlier time scientists of different countries were using different systems of units for measurement. Three such systems, the CGS, the FPS (or British) system and the MKS system were in use extensively till recently. The base units for length, mass and time in these systems were as follows: In CGS system they were centimetre, gram and second respectively. In FPS system they were foot, pound and second respectively. In MKS system they were metre, kilogram and second respectively. Quantity Name Symbol Length Meter m Mass Kilogram kg Time Second s Electric current Ampere A 7  Introduction to biophysics Dr. Alaa Hassan Said Temperature Kelvin k Amount of substance Mole mol Luminous intensity Candela cd Metric Prefixes Physical objects or phenomena may vary widely. For example, the size of objects varies from something very small (like an atom) to something very large (like a star). Yet the standard metric unit of length is the meter. So, the metric system includes many prefixes that can be attached to a unit. Each prefix is based on factors of 10 (10, 100, 1,000, etc., as well as 0.1, 0.01, 0.001, etc.). Example Example Example Example Prefix Symbol Value Name Symbol Value Description Distance light exa E 1018 Exameter Em 1018 m travels in a century peta P 1015 Petasecond Ps 1015 s 30 million years Powerful laser 12 12 tera T 10 Terawatt TW 10 W output A microwave giga G 109 Gigahertz GHz 109 Hz frequency mega M 106 Megacurie MCi 106 Ci High radioactivity kilo k 103 Kilometer Km 103 m About 6/10 mile hector h 102 Hectoliter hL 102 L 26 gallons deka da 101 Dekagram Dag 101 g Teaspoon of butter Less than half a deci d 10–1 Deciliter dL 10–1 L soda centi c 10–2 Centimeter Cm 10–2 m Fingertip thickness mili m 10–3 Millimeter Mm 10–3 m Flea at its shoulder Detail in micro µ 10–6 Micrometer µm 10–6 m microscope nano n 10–9 Nanogram Ng 10–9 g Small speck of dust 8  Introduction to biophysics Dr. Alaa Hassan Said Small capacitor in pico p 10–12 Picofarad pF 10–12 F radio femto f 10–15 Femtometer Fm 10–15 m Size of a proton Time light takes to atto a 10–18 Attosecond As 10–18 s cross an atom Dimensional Analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The importance of dimensional analysis 1. To check the correctness of the form of the equation 2. To derive a relation between the physical quantities but it can't have the values of the constants. 3. To determine the proper units for some particular terms in an equation. Dimension of basic and derived units The Dimension of Length [𝐿] Basic The Dimension of time [𝑇] Units The Dimension of mass [𝑀] The Dimension of Temperature [°𝐾] The Dimension of angle dimensionless The Dimension of velocity [𝐿][𝑇−1] Derived The Dimension of acceleration [𝐿][𝑇−2] Units The Dimension of force 𝑀][𝐿][𝑇−2] The Dimension of frequency [𝑇−1] The Dimension of density [𝑀][𝐿−3] The Dimension of volume [𝐿3] The Dimension of pressure [𝑀][𝐿−1][𝑇−2] The Dimension of work [𝑀][𝐿2][𝑇−2] 9  Introduction to biophysics Dr. Alaa Hassan Said Example (1): Show that the following equation is dimensionally correct: Example (2): Show that the following equation is dimensionally correct: 𝑉 = 𝑉𝑜 + 𝑎𝑡 where (𝑉𝑜) is velocity and (𝑎) is acceleration Example (3): The period (𝑝)of a simple pendulum is the time for one complete swing. How does (𝑝)depends on mass (𝑚)of the bob, the length (𝐿)of the string, and the acceleration due to gravity(𝑔)? 10  Introduction to biophysics Dr. Alaa Hassan Said Example (4): The wave length 𝜆 of a wave depends on the speed (𝑣) of the wave and its frequency (𝑓). Decide which of the following equations is correct: 𝜆 = 𝑣𝑓 or 𝜆 = 𝑣⁄𝑓. Example (5): 11  Introduction to biophysics Dr. Alaa Hassan Said Newton's second law states that acceleration is proportional to the force acting on an object and is inversely proportional to the object mass. What are the dimensions of force? Example (6): Suppose a sphere of Radius (𝑅) is pulled at constant speed (𝑣) through a fluid viscosity 𝜂. The force (𝐹) that is required to pull the sphere through the fluid depends on 𝑣, 𝑅 and 𝜂, (𝐹 = (𝑐𝑜𝑛𝑠𝑡)𝑣𝑅𝜂). Find the dimensions of 𝜂. Accuracy and Precision: Accuracy refers to the closeness of a measured value to a standard or known value. For example, if in lab you obtain a weight measurement of 3.2 kg for a given substance, but the actual or known weight is 10 kg, then your measurement is not accurate. In this case, your measurement is not close to the known value. Precision refers to the closeness of two or more measurements to each other. Using the example above, if you weigh a given substance five times, and get 3.2 kg each time, then your measurement is very precise. Precision is independent of accuracy. You can 12  Introduction to biophysics Dr. Alaa Hassan Said be very precise but inaccurate, as described above. You can also be accurate but imprecise. For example, if on average, your measurements for a given substance are close to the known value, but the measurements are far from each other, then you have accuracy without precision. 13  Introduction to biophysics Dr. Alaa Hassan Said Quiz (1) 1- Write the dimensions of: Velocity – acceleration – force – work – density – pressure 2- Using the dimension analysis check the correction of the following equations: 𝒗𝟐 = 𝒗𝟎 𝟐 + 𝟐𝒂 𝑣2 𝐹=𝑚 𝑟 𝐿 𝑇 = 2𝜋√ 𝑔 3- Using the given data in the table draw the following formula: 𝑽𝟏 𝑳= −𝟎∙𝟔𝒓 𝟒𝝊 ν (Hz) 256 256 320 384 520 L (cm) 35 35 27 22 15 4- Using the dimension analysis, complete the following table: Physical quantity Dimension unit Density …………………….. …………………….. …………………….. [M1 L2 T-3] …………………….. …………………….. …………………….. dyne g−1 5- The density of material depends on mass and volume, using the dimension analysis drive the expression for the density? 6- For the equation F α Aa vb dc, where F is the force, A is the area, v is the velocity and d is the density, find the values of a, b and c? 14 Introduction to biophysics Dr. Alaa Hassan Said Chapter 2 Physical properties of materials 15  Introduction to biophysics Dr. Alaa Hassan Said Elasticity vs plasticity Objects deform when pushed, pulled, and twisted. Elasticity is the measure of the amount that the object can return to its original shape after these external forces and pressures stop. This is what allows springs to store elastic potential energy. Plasticity is the opposite of elasticity; when something is stretched, and it stays stretched, the material is said to be plastic. When energy goes into changing the shape of some material and it stays changed, that is said to be plastic deformation. When the material goes back to its original form, that's elastic deformation. 16 Introduction to biophysics Dr. Alaa Hassan Said 17  Introduction to biophysics Dr. Alaa Hassan Said Most materials have an amount of force or pressure for which they deform elastically. If more force or pressure is applied, then they have plastic deformation. Materials that have a fair amount of plastic deformation before breaking are said to be ductile. Materials that can't stretch or bend much without breaking are said to be brittle. Copper is quite ductile, which is part of why it is used for wires (most metals are ductile (but copper especially so). Glass and ceramics are often brittle; they will break rather than bend! 18  Introduction to biophysics Dr. Alaa Hassan Said Elasticity - Stress and Strain (Hooke’s law) A change in shape due to the application of a force is a deformation. Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed.  First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations.  Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke’s law is obeyed. In equation form, Hooke’s law is given by: F = kΔL, where ΔL is the amount of deformation (the change in length, for example) produced by the force F, and k is a proportionality constant that depends on the shape and 19  Introduction to biophysics Dr. Alaa Hassan Said composition of the object and the direction of the force. Note that this force is a function of the deformation ΔL it is not constant as a kinetic friction force is. Rearranging this to makes it clear that the deformation is proportional to the applied force. 𝑭 ∆𝒍 = 𝑲 Stress vs. Strain Curves If you apply stress to a material and measure the strain, or vice versa, you can create a stress vs. strain curve like the one shown below for a typical metal. Let’s discuss the important parts of the graph: 1. The absolute highest point on the graph is the ultimate strength, indicating the onset of failure toward fracture or rupture. 2. Notice that after reaching the ultimate strength, but before full failure, the stress can actually decrease as strain increases, this is because the material is changing shape by breaking rather than stretching or compressing the distance between molecules in the material. 3. In the first part of the elastic region, the strain is proportional to the stress, this is known as the linear region. 4. After the stress reaches the linearity limit (H) the slope is no longer constant, but the material still behaves elastically. 20  Introduction to biophysics Dr. Alaa Hassan Said 5. The elastic region ends, and the plastic region begins at the yield point (E). In the plastic region, a little more stress causes a lot more strain because the material is changing shape at the molecular level. In some cases, the stress can actually decrease as strain increases, because the material is changing shape by re- configuring molecules rather than just stretching or compressing the distance between molecules. 6. The green line originating at P illustrates the metal’s return to non-zero strain value when the stress is removed after being stressed into the plastic region (permanent deformation). Elastic Modulus We now consider three specific types of deformations: changes in length (tension and compression), sideways shear (stress), and changes in volume. All deformations are assumed to be small unless otherwise stated. A change in length ΔL is produced when a force is applied to a wire or rod parallel to its length L0, either stretching it (a tension) or compressing it. Experiments have shown that the change in length (ΔL) depends on only a few variables. As already noted, ΔL is proportional to the force F and depends on the substance from which the object is made. Additionally, the change in length is proportional to the original length L0 and inversely proportional to the cross-sectional area of the wire or rod. For example, a long guitar string will stretch more than a short one, and a thick string will stretch less than a thin one. We can combine all these factors into one equation for ΔL: 𝟏𝑭 ∆𝑳 = 𝑳 𝒀𝑨 𝟎 where ΔL is the change in length, F the applied force, Y is a factor, called the elastic modulus or Young’s modulus, that depends on the substance, A is the cross-sectional 21  Introduction to biophysics Dr. Alaa Hassan Said area, and L0 is the original length. Table lists values of Y for several materials—those with a large Y are said to have a large tensile stiffness because they deform less for a given tension or compression. Material Young’s modulus Sheer modulus S Bulk (tension– (109N/m2) modulus B compression) Y (109N/m2) (109N/m2) Aluminum 70 25 75 Bone – tension 16 80 8 Bone – compression 9 Brass 90 35 75 Brick 15 Concrete 20 Glass 70 20 30 Granite 45 20 45 Hair (human) 10 Hardwood 15 10 Iron, cast 100 40 90 Lead 16 5 50 Marble 60 20 70 Nylon 5 Polystyrene 3 Silk 6 Spider thread 3 Steel 210 80 130 Tendon 1 Acetone 0.7 Ethanol 0.9 Glycerin 4.5 22  Introduction to biophysics Dr. Alaa Hassan Said Mercury 25 Water 2.2 Example: The Stretch of a Long Cable Suspension cables are used to carry gondolas at ski resorts. Consider a suspension cable that includes an unsupported span of 3020 m. Calculate the amount of stretch in the steel cable. Assume that the cable has a diameter of 5.6 cm and the maximum tension it can withstand is 3x106N. Strategy The force is equal to the maximum tension, or F=3×106 N. The cross-sectional area is πr2=2.46×10−3m2. To find the change in length, we can use the equation: 𝟏𝑭 ∆𝑳 = 𝑳 𝒀𝑨 𝟎 Solution All quantities are known. Thus, 𝟏 𝟑𝒙𝟏𝟎𝟔 𝑵 ∆𝑳 = ( )( ) (𝟑𝟎𝟐𝟎𝒎) 𝟐𝟏𝟎𝒙𝟏𝟎𝟗 𝑵/𝒎𝟐 𝟐. 𝟒𝟔𝒙𝟏𝟎−𝟑 𝒎𝟐 =18 m The equation for change in length is traditionally rearranged and written in the following form: 𝑭 ∆𝑳 =𝒀 𝑨 𝑳𝟎 𝐹 The ratio of force to area, is defined as stress (measured in N/m2and the ratio of the 𝐴 ∆𝐿 change in length to length, is defined as strain (a unitless quantity). In other words, 𝐿0 stress = Y ×strain. In this form, the equation is analogous to Hooke’s law, with stress analogous to force and strain analogous to deformation. If we again rearrange this equation to the form ∆𝐿 𝐹 = 𝑌𝐴 𝐿0 we see that it is the same as Hooke’s law with a proportionality constant 23  Introduction to biophysics Dr. Alaa Hassan Said 𝑌𝐴 𝐾= 𝐿0 This general idea—that force and the deformation it causes are proportional for small deformations—applies to changes in length, sideways bending, and changes in volume. STRESS 𝑭 The ratio of force to area, is defined as stress measured in N/m2 𝑨 STRAIN ∆𝑳 The ratio of the change in length to length, is defined as strain (a unitless 𝑳𝟎 quantity). In other words, stress=Y× strain Sideways Stress: Shear Modulus The following figure illustrates what is meant by a sideways stress or a shearing force. Here the deformation is called Δx and it is perpendicular to L0, rather than parallel as with tension and compression. Shear deformation behaves similarly to tension and compression and can be described with similar equations. The expression for shear deformation is 𝟏𝑭 ∆𝒙 = 𝑳 𝑺𝑨 𝟎 where S is the shear modulus and F is the force applied perpendicular to L0 and parallel to the cross-sectional area A. Again, to keep the object from accelerating, there are actually two equal and opposite forces F applied across opposite faces, as illustrated in the figure. The equation is logical—for example, it is easier to bend a long thin pencil (small A) than a short thick one, and both are more easily bent than similar steel rods (large S). 24  Introduction to biophysics Dr. Alaa Hassan Said Shear deformation 𝟏𝑭 ∆𝒙 = 𝑳 𝑺𝑨 𝟎 where S is the shear modulus (see Table) and F is the force applied perpendicular to L0 and parallel to the cross-sectional area A. Examination of the shear moduli in Table reveals some telling patterns. For example, shear moduli are less than Young’s moduli for most materials. Bone is a remarkable exception. Its shear modulus is not only greater than its Young’s modulus, but it is as large as that of steel. This is why bones are so rigid. Example: Calculating Force Required to Deform: That Nail Does Not Bend much Under a Load. Find the mass of the picture hanging from a steel nail as shown in Figure, given that the nail bends only 1.80 μm. (Assume the shear modulus is known to two significant figures.) Strategy The force F on the nail (neglecting the nail’s own weight) is the weight of the picture w. If we can find w, then the mass of the picture is just w/g. The equation ∆𝑥 = 1𝐹 𝐿0 can be solved for F 𝑆𝐴 Solution 1𝐹 Solving the equation ∆𝑥 = 𝐿0 for F , we see that all other quantities can be found: 𝑆𝐴 25  Introduction to biophysics Dr. Alaa Hassan Said 𝑺𝑨 𝑭= ∆𝒙 𝑳𝟎 S is found in Table and is S=80×109N/m2. The radius r is 0.750 mm (as seen in the figure), so the cross-sectional area is A=πr2=1.77×10−6m2 The value for L0 is also shown in the figure. Thus, (𝟖𝟎𝒙𝟏𝟎𝟗 𝑵/𝒎𝟐 )(𝟏. 𝟕𝟕𝒙𝟏𝟎−𝟔 𝒎𝟐 𝑭= ( −𝟑 ) (𝟏. 𝟖𝒙𝟏𝟎−𝟔 𝒎) = 𝟓𝟏 𝟓𝒙𝟏𝟎 𝒎 This 51 N force is the weight w of the picture, so the picture’s mass is 𝒘 𝑭 𝒎= = = 𝟓. 𝟐 𝑲𝒈 𝒈 𝒈 Discussion This is a fairly massive picture, and it is impressive that the nail flexes only 1.80 μm an amount undetectable to the unaided eye. Changes in Volume: Bulk Modulus An object will be compressed in all directions if inward forces are applied evenly on all its surfaces as in the following figure. It is relatively easy to compress gases and extremely difficult to compress liquids and solids. For example, air in a wine bottle is compressed when it is corked. But if you try corking a brim-full bottle, you cannot compress the wine—some must be removed if the cork is to be inserted. The reason for these different compressibilities is that atoms and molecules are separated by large empty spaces in gases but packed close together in liquids and solids. To compress a gas, you must force its atoms and molecules closer together. To compress liquids and solids, you must actually compress their atoms and molecules, and very strong electromagnetic forces in them oppose this compression. 26  Introduction to biophysics Dr. Alaa Hassan Said We can describe the compression or volume deformation of an object with an equation. First, we note that a force “applied evenly” is defined to have the same stress, or ratio 𝐹 of force to area on all surfaces. The deformation produced is a change in volume ΔV 𝐴 , which is found to behave very similarly to the shear, tension, and compression previously discussed. (This is not surprising, since a compression of the entire object is equivalent to compressing each of its three dimensions.) The relationship of the change in volume to other physical quantities is given by: 𝟏𝑭 ∆𝑽 = 𝑽 𝑩𝑨 𝟎 𝐹 where B is the bulk modulus (see Table), V0 is the original volume, and is the force 𝐴 per unit area applied uniformly inward on all surfaces. Note that no bulk moduli are given for gases. 27  Introduction to biophysics Dr. Alaa Hassan Said Example: Calculating Change in Volume with Deformation: How much is Water Compressed at Great Ocean Depths? ∆𝑽 Calculate the fractional decrease in volume for seawater at 5.00 km depth, 𝑽𝟎 where the force per unit area is 5×107N/m2. Strategy 1𝐹 Equation ∆𝑉 = 𝑉 is the correct physical relationship. All quantities in the equation 𝐵𝐴 0 ∆𝑉 except are known. 𝑉0 Solution ∆𝑉 Solving for the unknown gives 𝑉0 ∆𝑽 𝟏 𝑭 = 𝑽𝟎 𝑩 𝑨 Substituting known values with the value for the bulk modulus B from Table, ∆𝑽 𝟓𝒙𝟏𝟎𝟕 𝑵/𝒎𝟐 = = 𝟎. 𝟎𝟐𝟑 𝑽𝟎 𝟐. 𝟐𝒙𝟏𝟎𝟗 𝑵/𝒎𝟐 Discussion Although measurable, this is not a significant decrease in volume considering that the force per unit area is about 500 atmospheres (1 million pounds per square foot). Liquids and solids are extraordinarily difficult to compress. 28  Introduction to biophysics Dr. Alaa Hassan Said Elasticity of the human organs Elasticity of the human bone and tendon Bones, on the whole, do not fracture due to tension or compression. Rather they generally fracture due to sideways impact or bending, resulting in the bone shearing or snapping. The behavior of bones under tension and compression is important because it determines the load the bones can carry. 29  Introduction to biophysics Dr. Alaa Hassan Said Bones are classified as weight-bearing structures such as columns in buildings and trees. Weight-bearing structures have special features; columns in building have steel- reinforcing rods while trees and bones are fibrous. The bones in different parts of the body serve different structural functions and are prone to different stresses. Thus, the bone in the top of the femur is arranged in thin sheets separated by marrow while in other places the bones can be cylindrical and filled with marrow or just solid. Overweight people have a tendency toward bone damage due to sustained compressions in bone joints and tendons. 30  Introduction to biophysics Dr. Alaa Hassan Said Brittle Bones Brittle materials have a small plastic region and they begin to fail toward fracture or rupture almost immediately after being stressed beyond their elastic limit. Bone, cast iron, ceramic, and concrete are examples of brittle materials. Materials that have relatively large plastic regions under tensile stress are known as ductile. Examples of ductile materials include aluminum and copper. 31  Introduction to biophysics Dr. Alaa Hassan Said The following figure shows how brittle and ductile materials change shape under stress. Even the cartilage that makes up tendons and ligaments is relatively brittle because it behaves less like example (c) and more like examples (a) and (b). Luckily, those tissues have adapted to allow the deformation required for typical movement without the brittle nature of the materiel coming into play. Tendon Another biological example of Hooke’s law occurs in tendons. Functionally, the tendon (the tissue connecting muscle to bone) must stretch easily at first when a force is applied but offer a much greater restoring force for a greater strain. The following figure shows a stress-strain relationship for a human tendon. Some tendons have a high collagen content so there is relatively little strain, or length change; others, like support tendons (as in the leg) can change length up to 10%. Note that this stress-strain curve is nonlinear, since the slope of the line changes in different regions. In the first part of the stretch called the toe region, the fibers in the tendon begin to align in the direction of the stress—this is called uncrimping. In the linear region, the fibrils will be stretched, and in the failure region individual fibers begin to break. A simple model of this relationship can be illustrated by springs in parallel: different springs are activated at different lengths of stretch. 32  Introduction to biophysics Dr. Alaa Hassan Said Typical stress-strain curve for mammalian tendon. Three regions are shown: (1) toe region (2) linear region, and (3) failure region. Unlike bones and tendons, which need to be strong as well as elastic, the arteries and lungs need to be very stretchable. The elastic properties of the arteries are essential for blood flow. The pressure in the arteries increases and arterial walls stretch when the blood is pumped out of the heart. When the aortic valve shuts, the pressure in the arteries drops and the arterial walls relax to maintain the blood flow. When you feel your pulse, you are feeling exactly this—the elastic behavior of the arteries as the blood gushes through with each pump of the heart. If the arteries were rigid, you would not feel a pulse. 33 Introduction to biophysics Dr. Alaa Hassan Said The heart is also an organ with special elastic properties. The lungs expand with muscular effort when we breathe in but relax freely and elastically when we breathe out. Our skins are particularly elastic, especially for the young. A young person can go from 100 kg to 60 kg with no visible sag in their skins. The elasticity of all organs reduces with age. Gradual physiological aging through reduction in elasticity starts in the early 20s. 34  Introduction to biophysics Dr. Alaa Hassan Said Example : Calculating Deformation: How Much Does Your Leg Shorten When You Stand on It? Calculate the change in length of the upper leg bone (the femur) when a 70.0 kg man supports 62.0 kg of his mass on it, assuming the bone to be equivalent to a uniform rod that is 40.0 cm long and 2.00 cm in radius. Strategy The force is equal to the weight supported, or F=mg=(62.0kg)(9.80m/s2)=607.6N, and the cross-sectional area is πr2=1.257×10−3m2. To find the change in length, we can use the equation: 𝟏𝑭 ∆𝑳 = 𝑳 𝒀𝑨 𝟎 Solution All quantities except ΔL are known. Note that the compression value for Young’s modulus for bone must be used here. Thus, 𝟏 𝟔𝟎𝟕. 𝟔 𝑵 ∆𝑳 = ( ) ( ) (𝟎. 𝟒𝒎) 𝟗𝒙𝟏𝟎𝟗 𝑵/𝒎𝟐 𝟏. 𝟐𝟓𝟕𝒙𝟏𝟎−𝟑 = 2x10-5 m Discussion This small change in length seems reasonable, consistent with our experience that bones are rigid. In fact, even the rather large forces encountered during strenuous physical activity do not compress or bend bones by large amounts. Although bone is rigid compared with fat or muscle, several of the substances listed in Table have larger values of Young’s modulus YY. In other words, they are more rigid. Strength of Human Bones The Femur “In human anatomy, the femur (thigh bone) is the longest and largest bone. Along with the temporal bone of the skull, it is one of the two strongest bones in the body. The average adult male femur is 48 cm (18.9 in) in length and 2.34 cm (0.92 in) in diameter and can support up to 30 times the weight of an adult.” 35  Introduction to biophysics Dr. Alaa Hassan Said Compression When you place an object on top of a structure, the object’s weight tends to compress the structure. Any push that tends to compress a structure is called a compressive force. The average weight among adult males in the United States is 196 lbs (872 N). According to the statement that the femur can support 30x body weight, the adult male femur can support roughly 6,000 lbs of compressive force! Such high forces are rarely generated by the body under its own power; thus motor vehicle collisions are the number one cause of femur fractures. Tension When you hang an object from a structure the object’s weight will tend to stretch the structure. The structure responds by providing a tension force to hold up the object. Tension forces are restoring forces produced in response to materials being stretched. Non-rigid objects like ropes, cables, chains, muscles, tendons, can effectively provide tension forces only, while rigid object can supply compression and tension forces. For example, the biceps muscle is providing a tension (T) force on the thumb-side forearm bone (radius bone). 36  Introduction to biophysics Dr. Alaa Hassan Said Stress The maximum compression or tension forces that a bone can support depends on the size of the bone. More specifically, the more area available for the force to be spread out over, the more force the bone can support. That means the maximum forces bones, (and other objects) can handle are proportional to the cross-sectional area of the bone that is perpendicular (90°) to the direction of the force. For example, the force that the femur can support vertically along its length depends on the area of its horizontal cross- section which is roughly circular and somewhat hollow (bone marrow fills the center space). These cross sections show the midshaft of the femur of an 84-year-old female with advanced osteoporosis (right), compared to a healthy femur of a 17-year-old female (left). Larger bones can support more force, so in order to analyze the behavior of the bone material itself we need to divide the force applied to the bone by the minimum cross-sectional area (A). This quantity is known as the stress on the material. Stress has units of force per area, so the SI units are (N/m2) which are also known as Pascals. Units of pounds per square inch (PSI, lbs/in 2) are common in the U.S. 𝑭 𝒔𝒕𝒓𝒆𝒔𝒔 = 𝑨 37  Introduction to biophysics Dr. Alaa Hassan Said Ultimate Strength of the Femur The maximum stress that bone, or any other material, can experience before the material begins fracture or rupture is called the ultimate strength. Notice that material strength is defined in terms of stress, not force, so that we are analyzing the material itself, without including the effect of how much material is present. For some materials the ultimate strength is different when the stress is acting to crush the material (compression) versus when the forces are acting to stretch the material under tension, so we often refer to ultimate tensile strength or ultimate compressive strength. For example, the ultimate compressive strength for human femur bone is measured to be 205 MPa (205 million Pascals) under compression along its length. The ultimate tensile strength of femur bone under tension along its length is 135 MPa. Along with bone, concrete and chalk are other examples of materials with different compressive and tensile ultimate strengths. Transverse Ultimate Strength So far, we have discussed ultimate strengths along the long axis of the femur, known as the longitudinal direction. Some materials, such as bone and wood, have different ultimate strengths along different axes. The ultimate compressive strength for bone along the short axis (transverse direction) is 131 MPa, or about 36% less than the 205 MPa longitudinal value. Materials that have different properties along different axes are known as anisotropic. Materials that behave the same in all directions are called isotropic. 38  Introduction to biophysics Dr. Alaa Hassan Said An interesting fact to finish up this section: when a person stands the femur actually experiences compressive and tensile stresses on different sides of the bone. This occurs because the structure of the hip socket applies the load of the body weight off to the side rather than directly along the long axis of the bone. Both tension and compressive stresses are applied to the Femur while standing. Body Levers A lever is a rigid object used to make it easier to move a large load a short distance or a small load a large distance. There are three classes of levers, and all three classes are present in the body. 39  Introduction to biophysics Dr. Alaa Hassan Said For example, the forearm is a 3rd class lever because the biceps pull on the forearm between the joint (fulcrum) and the ball (load). The elbow joint flexed to form a 60° angle between the upper arm and forearm while the hand holds a 50 lb ball. Lever Classes Using the standard terminology of levers, the forearm is the lever, the biceps tension is the effort, the elbow joint is the fulcrum, and the ball weight is the resistance. When the resistance is caused by the weight of an object, we call it the load. The lever classes are identified by the relative location of the resistance, fulcrum and effort. First class levers have the fulcrum in the middle, between the load and resistance. 40  Introduction to biophysics Dr. Alaa Hassan Said Second class levers have resistance in the middle. Third class levers have the effort in the middle. For all levers the effort and resistance (load) are actually just forces that are creating torques because they are trying to rotate the lever. In order to move or hold a load the torque created by the effort must be large enough to balance the torque caused by the load. Remembering that torque increases as the force is applied farther from the pivot, the effort needed to balance the resistance must depend on the distances of the effort and resistance from the pivot. These distances are known as the effort arm and resistance arm (load arm). One way to remember the classes of lever is to think “FRE” or “free,” as in: “I want to be free of confusion about levers.” The F stands for fulcrum, in the middle of a class 1 lever (e.g., seesaw). The R stands for resistance (which is the same thing as the load), and it is in the middle of a class 2 lever (e.g., wheelbarrow). The E stands for effort, which is in the middle of a class 3 lever (e.g., broom). 41  Introduction to biophysics Dr. Alaa Hassan Said Mechanical advantage Mechanical advantage is a measure of the force amplification attained by the machine. Translation, how much easier does the machine make the work? MA = the ratio of the effort arm to the resistance arm MA = effort arm /resistance arm MA is used to measure the efficiency of the lever A lever operates at a mechanical advantage when the effort is farther from the fulcrum than the load A lever operates at a mechanical disadvantage when the effort is nearer to the fulcrum than the load Characteristics of class 1 levers First-class levers always change the direction of the force. In other words, if the effort is “down,” the load moves “up.” First-class levers can be used to affect the force on the load, the distance through which the load moves, and the speed with which it moves. If the fulcrum is close to the load and far from the effort, the force is increased but the effort must move through a greater distance or with a greater speed to move the load. If, on the other hand, the fulcrum is close to the effort, the force is not as much increased, but the load moves through a greater distance or with a greater speed. The mechanical advantage of a first-class lever can be greater than 1 or less than 1, depending on the location of the fulcrum relative to the load and effort. 42  Introduction to biophysics Dr. Alaa Hassan Said Characteristics of class 2 levers A second-class lever does not change the direction of the force (if the effort force points “up,” the load moves “up”). The second-class lever always confers a mechanical advantage because the “effort arm” or distance from the fulcrum to the effort is greater than the “load arm” or distance from the fulcrum to the load. Characteristics of class 3 levers Like a second-class lever, a third-class lever does not change the direction of the force. The interesting thing about third-class levers is that they do not confer a mechanical advantage. The mechanical advantage of a third-class lever is less than 1! What, then, is the use of third-class levers? They always produce a gain in the speed (or distance covered per unit time) of the load. Sometimes the gain in speed of the load is useful in itself. 43  Introduction to biophysics Dr. Alaa Hassan Said Levers in the body The bones in the human body act as levers, with the joints fulfilling the role of pivot points. The muscles provide the effort, and the weights of segments of the body — or external weights — provide the load. The human body provides examples of first, second, and third-class levers. First and third-class levers are the most common in the body. 44  Introduction to biophysics Dr. Alaa Hassan Said As we saw in the last section, a characteristic of third-class levers is that they confer no mechanical advantage. And the first-class levers in the body often operate with a mechanical advantage less than 1. The human body is built for speed, rather than mechanical advantage! First-class levers in the human body An example of a first-class lever is provided by the head, top of the spine, and neck muscles. The fulcrum of this system is the joint between the occipital bone at the base of the skull and the atlas, the first vertebra of the neck. The weight of the head is like the load, tending to rotate the head forward and down (as one might move if looking through a microscope or writing at a desk). The neck extensor muscles exert the effort to hold the head up. Second-class levers in the human body When you do a press-up from the floor, your head, neck, trunk, and legs form a lever that has the balls of the feet as fulcrum. The action of the arms raises the load. This is an example of a second-class lever, with the effort at one end, the load in the middle, and the fulcrum at the other end. Third-class levers in the human body A biceps curl is an example of a third-class lever. The load is the weight held in the hand, the fulcrum is the elbow joint and the effort is provided by the bicep muscles of the arm. The contraction of the muscles in the upper arm pulls the lower arm up. The muscles move a short distance compared to the end of the lever (the lower arm). The speed of movement in the lower arm is helpful for throwing a ball or swinging a tennis racket. Pressure Pressure is an important physical quantity—it plays an essential role in topics ranging from thermodynamics to solid and fluid mechanics. As a scalar physical quantity (having magnitude but no direction), pressure is defined as the force per unit area applied perpendicular to the surface to which it is applied. Pressure can be expressed in a number of units depending on the context of use. 45  Introduction to biophysics Dr. Alaa Hassan Said Units, Equations and Representations In SI units, the unit of pressure is the Pascal (Pa), which is equal to a Newton / meter 2 (N/m2). Other important units of pressure include the pound per square inch (psi) and the standard atmosphere (atm). The elementary mathematical expression for pressure is given by: where p is pressure, F is the force acting perpendicular to the surface to which this force is applied, and A is the area of the surface. Any object that possesses weight, whether at rest or not, exerts a pressure upon the surface with which it is in contact. Pressure in Liquids and Gases: Fluids Just as a solid exerts a pressure on a surface upon which it is in contact, liquids and gases likewise exert pressures on surfaces and objects upon which they are in contact with. The pressure exerted by an ideal gas on a closed container in which it is confined is best analyzed on a molecular level. Gas molecules in a gas container move in a random manner throughout the volume of the container, exerting a force on the container walls upon collision. Taking the overall average force of all the collisions of the gas molecules confined within the container over a unit time allows for a proper measurement of the effective force of the gas molecules on the container walls. Given that the container acts as a confining surface for this net force, the gas molecules exert a pressure on the container. For such an ideal gas confined within a rigid container, the pressure exerted by the gas molecules can be calculated using the ideal gas law: 𝒏𝑹𝑻 𝑷= 𝑽 where n is the number of gas molecules, R is the ideal gas constant (R = 8.314 J mol -1 K-1), T is the temperature of the gas, and V is the volume of the container. 46  Introduction to biophysics Dr. Alaa Hassan Said Variation of Pressure with Depth Pressure within static fluids depends on the properties of the fluid, the acceleration due to gravity, and the depth within the fluid. P = hρg The pressure exerted by a static liquid depends only on the depth, density of the liquid, and the acceleration due to gravity. Pressure within a gas: The force contributing to the pressure of a gas within the medium is not a continuous distribution as for liquids. Where p0 is the pressure at h = 0, M is the mass of a single molecule of gas, g is the acceleration due to gravity, k is the Boltzmann constant, T is the temperature of the gas, and h is the height or depth within the gas. Gauge Pressure and Atmospheric Pressure Pressure is often measured as gauge pressure, which is defined as the absolute pressure minus the atmospheric pressure. Atmospheric Pressure An important distinction must be made as to the type of pressure quantity being used when dealing with pressure measurements and calculations. Atmospheric pressure is the magnitude of pressure in a system due to the atmosphere, such as the pressure exerted by air molecules (a static fluid) on the surface of the earth at a given elevation. 47  Introduction to biophysics Dr. Alaa Hassan Said In most measurements and calculations, the atmospheric pressure is considered to be constant at 1 atm or 101,325 Pa, which is the atmospheric pressure under standard conditions at sea level. Gauge Pressure For most applications, particularly those involving pressure measurements, it is more practical to use gauge pressure than absolute pressure as a unit of measurement. Gauge pressure is a relative pressure measurement which measures pressure relative to atmospheric pressure and is defined as the absolute pressure minus the atmospheric pressure. Most pressure measuring equipment give the pressure of a system in terms of gauge pressure as opposed to absolute pressure. For example, tire pressure and blood pressure are gauge pressures by convention, while atmospheric pressures, deep vacuum pressures, and altimeter pressures must be absolute. Hydrostatic Based Barometers Early barometers were used to measure atmospheric pressure through the use of hydrostatic fluids. Hydrostatic based barometers consist of columnar devices usually made from glass and filled with a static liquid of consistent density. The columnar section is sealed, holds a vacuum, and is partially filled with the liquid while the base section is open to the atmosphere and makes an interface with the surrounding environment. As the atmospheric pressure changes, the pressure exerted by the atmosphere on the fluid reservoir exposed to the atmosphere at the base changes, increasing as the atmospheric pressure increases and decreasing as the atmospheric pressure decreases. This change in pressure causes the height of the fluid in the columnar structure to change, increasing in height as the atmosphere exerts greater pressure on the liquid in the reservoir base and decreasing as the atmosphere exerts lower pressure on the liquid in the reservoir base. The height of the liquid within the glass column then gives a measure of the atmospheric pressure. Pressure, as determined by hydrostatic barometers, is often measured by determining the height of the liquid in the barometer column, thus the torr as a unit of pressure, but can be used to determine pressure in SI units. Hydrostatic based barometers most commonly use water or mercury as the static liquid. While the 48  Introduction to biophysics Dr. Alaa Hassan Said use of water is much less hazardous than mercury, mercury is often a better choice for fabricating accurate hydrostatic barometers. The density of mercury is much higher than that of water, thus allowing for higher accuracy of measurements and the ability to fabricate more compact hydrostatic barometers. Aneroid Barometer Another type of barometer is the aneroid barometer, which consists of a small, flexible sealed metal box called an aneroid cell. The aneroid cell is made from beryllium-copper alloy and is partially evacuated. A stiff spring prevents the aneroid cell from collapsing. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction are amplified by mechanical mechanisms to give a pressure reading. Such pressure measuring devices are more practical than hydrostatic barometers for measuring system pressures. Many modern pressure measuring devices are pre-engineered to output gauge pressure measurements. While the aneroid barometer is the underlying mechanism behind many modern pressure measuring devices, pressure can also be measured using more advanced measuring mechanisms. 49  Introduction to biophysics Dr. Alaa Hassan Said Pressure and Cardiovascular System The cells of the body act like individual engines. In order for them to function they must have: Fuel from our food to supply energy. O2 from the air we breathe to combine with the food to release energy. A way to dispose of the by-products of the combustion (mostly CO2, H2O, and heat). Since the body has many billions of cells an elaborate transportation system is needed to deliver the fuel and O2 to the cells and remove the by-products. The blood performs this important body function. Blood represents about 7% of the body mass or about 4.5 kg (~ 4.4 liters) in a 64 kg person. The blood, blood vessels, and heart make up the cardiovascular system (CVS). Major components of the cardiovascular system The heart is basically a double pump; it provides the force needed to circulate the blood through the two major circulatory systems: - 1. The pulmonary circulation in the lungs. 2. The systemic circulation in the rest of the body. The blood in a normal individual circulates through one system before being pumped by the other section of the heart to the second system. 50  Introduction to biophysics Dr. Alaa Hassan Said Circulation Let us start with the blood in the left side of the heart and follow its circulation through one complete loop. The blood is pumped by the contraction of the heart muscles from the left ventricle at a pressure of about 125 mm Hg into a system of arteries that subdivided into smaller and smaller arteries (arterioles) and finally into a very fine meshwork of vessels called the capillary bed. During the few seconds it is in the capillary bed the blood supplies O 2 to the cells and picks up CO2 from the cells. After passing through the capillary bed the blood collects in small veins (venules) that gradually combine into larger and larger veins before it enters the right side of the heart via two main veins-the superior vena cava and the inferior vena cava. The returning blood is momentarily stored in the reservoir (the right atrium). And during a weak contraction (5-6 mm Hg) the blood flows into the right ventricular. On the next ventricular contraction this blood is pumped at a pressure of about 25 mm Hg via the pulmonary arteries to the capillary system in the lungs, where it receives more O2 and where some of the CO2 diffuses into the air in the lungs to be exhaled. The freshly oxygenated blood then travels via the main veins from the lungs into the left reservoir of the heart (left atrium); during the weak atrial contraction (7-8 mmHg) the blood flows into the left ventricle. On the next ventricular contraction this blood is again pumped from the left side of the heart into the general circulation. 51  Introduction to biophysics Dr. Alaa Hassan Said The heart has a system of valves that, if functioning properly, permit the blood to flow only in the correct direction. If these valves become diseased and do not open or close properly the pumping of the blood becomes inefficient. The blood volume is not uniformly divided between the pulmonary and systemic circulation, but it is: - 52  Introduction to biophysics Dr. Alaa Hassan Said Q) Calculate the mass of blood in all circulation of a person his body mass is 80kg. Mass of Blood ( 80 × 7/100 = 5.6 kg ) Mass of Blood in Systemic Circulation Mass of Blood in Pulmonary Circulation 5.6 × 80/100 = 4.48 kg 5.6 × 20/100 = 1.12 kg Arteries Capillaries Veins Arteries Capillaries Veins 4.48 × 4.48 × 4.48 × 1.12 × 1.12 × 1.12 × 15/100 10/100 75/100 46.5/100 7/100 46.5/100 = 0.672 kg = 0.448 kg = 3.360 kg = 0.521 kg = 0.078 kg = 0.521 kg Q) The mass of the pulmonary blood of a person is 1.5 kg, find: - 1) The mass of this person. 2) The mass of his systemic blood. Pulmonary Mass = Blood Mass x 20/100 1.5 = Blood Mass x 20/100 Blood Mass = 7.5 kg 1) The mass of this person: - Blood Mass = Body Mass x 7/100 7.5 = Body Mass x 7/100 Body Mass = 107 kg 2) The mass of his systemic blood: - Systemic Mass = Blood Mass x 80/100 Systemic Mass = 7.5 x 80/100 ======== Systemic Mass = 6 kg To the eye blood appears to be a red liquid slightly thicker than water. When examined by various physical techniques it is found to consist of several different components. 53  Introduction to biophysics Dr. Alaa Hassan Said The red color is caused by the red blood cells (erythrocytes). A nearly clear fluid called blood plasma accounts for the other 55%. The combination of red blood cells and plasma causes blood to have flow properties different from those of a fluid like water. Beside red blood cells and plasma, there are some important blood components, such as the white blood cells (leukocytes), present in small amounts. The blood also contains platelets. Platelets are involved in the clotting function of blood. Typical Pressures in Humans Body system Gauge pressure in mm Hg Blood pressures in large arteries (resting) Maximum (systolic) 100–140 Minimum (diastolic) 60–90 Blood pressure in large veins 4–15 Eye 12–24 Brain and spinal fluid (lying down) 5–12 While filling 0–25 When full 100–150 Chest cavity between lungs and ribs −8 to −4 Inside lungs −2 to +3 Esophagus −2 Stomach 0–20 Intestines 10–20 Middle ear