THE AUSTRALIAN NATIONAL UNIVERSITY Overview of Physical Principals in Physiology Christian Stricker Associate Professor for Systems Physiology ANUMS/JCSMR - ANU Christian.Stricker@anu.edu.au http://stricker.jcsmr.anu.edu.au/Physical_principles.pptx

At the end of this lecture students should be able to Aims At the end of this lecture students should be able to state what the elementary SI units are; explain the concept of SI units and give examples; interpret relevant symbols for multiples/fractions of units; define frequency, temperature, distance, velocity, acceleration, volume, mass density, concentration, force, weight, tension, pressure, torque, lever, energy and power and assign the correct units; state which special dimensions are used in medicine; and name and estimate some different forms of energy.

Contents Importance of the concepts covered SI units, and derived dimensions Multiples and fractions of units Frequency, Temperature Distance, velocity, acceleration Volume, density, concentration Force, weight, tension, pressure Torque and lever types Energy and power

Importance How to document a patient’s state? Patient data Inspection History Measurements Become more and more important as “objective”. Examples: BP, Temperature, pH, cardiac output, hearing sensitivity, … Without unit, a number is meaningless! Patient data We have to refresh units / dimensions

Elementary Units (SI) SI units refer to Système international d'unités”. kg is special case as it has a “multiple” in front (see next). Follows “meter-kilogram-seconds” system (MKS).

Some Derived Dimensions List incomplete (some physiologically relevant ones…) It is possible to describe all measurements using the 7 elementary SI units. Dependency often established via the energy associated.

Multiples and Fractions of Units Multiples are typically upper, fractions lower case. Because of inability to print Greek character µ, sometimes people use ‘mu’ or ‘u’ for it.

How Often Does Your …? Frequency (f) [Hz] used to describe a periodic event. In medicine, as 1 s is mostly too short, the base is often 1 min (beats per min; bpm). Useful to determine the time interval between the events: 1/f 10 Hz → 100 ms 80 bpm → 0.75 s = 750 ms (60/bpm)

Temperature Kelvin is SI unit. Conversion: ºC = K - 273.15 0 K = absolute zero (in space…) Conversion: ºC = K - 273.15 In medicine, typically ºCelsius. 0º: triple point of water (solid, fluid, gaseous) at sea level 100º: boiling point at sea level 37º: average body temperature

Distance, Velocity Distance [m] = length or equivalent Velocity [m/s] = distance travelled per unit time. How fast does a pulse wave travel? Distance (heart → wrist) in m: 1.50 m. Delay to periphery: 210 ms V = 1.50 / 0.21 = 7.1 m/s. You are going to measure this in context of the ECG in Block 2. Similarly for nerve conduction velocity in Block 6. Modified from Nam et al. (2013), Sensors 13:4714

Distance, Velocity, Acceleration Acceleration = change in velocity per unit time [m/s2]. Acceleration +-ve; deceleration –-ve. Velocity can be inferred from acceleration as area under that curve. Distance can be inferred from velocity as area under that curve. Acceleration can be inferred from the velocity as its differential in time.

Volume - Density Volume in SI units [m3], however this is an impractical size. Volume is typically in litres; i.e. 1000 (l or L) = 1 m3. In medicine, it is customary to abbreviate litre in L instead of l as the latter could be mistaken as number. Density [kg / L] = mass per volume. At 4ºC, H2O density is 1 kg/L. At this density, 1 mL = 1 g

Concentration Molar concentration [ ] = amount of substance s per unit volume [mol/L ≡ M] = molarity. Molal concentration = amount of substance per unit mass of solvent [mol/kg H2O]. At 4ºC molar conc. = molal conc. Otherwise molar conc. ≈ molal conc. Deviations at high concentrations 1 mol contains 6.022∙1023 molecules Mass of a molecule expressed in daltons (Da)

Force – Weight – Tension Force equals mass * acceleration [N]. Because acceleration has a direction, force is directional (vector). Weight is a special case, where accele-ration is caused by gravity (9.81 m/s2). For every force (“action”), there is a counter force (“reaction”, resistance, etc.) Tension is a special force that develops in a muscle (string, cable, vessel wall, etc.) after a force has been applied to it (muscle contraction,…).

Pressure Pressure = Force per unit area Does not have a direction, but if in a container (vessel), exerts force in all directions. = fluid column height. Unit Pa = N/m2; unfortunately area is very big. In medicine, mostly kPa for most, except body fluids, which are in torr (mmHg; BP) or cmH2O (for small pressures like CSF, lung). 1 torr = 0.133 kPa. Mercury manometers are unsafe.

Force – Torque – Lever Types Head on spinal column. Triceps on ulna Achilles tend. / forefoot Molar crushing Biceps, biting with incisives, etc. To explain, torque is introduced: Torque = Force * radius. Torque causes a rotation / movement. Fulcrum / pivot is at center of rotation. Applies to muscles and sesamoid bodies, like patella, etc.

Muscle Tension Modified after Rhodes & Pflanzer 2003 Large forces at work equivalent to weights of masses of several 100 kg.

Energy – Work – Power Energy = Work [J] Energy can take different forms Heat (“internal” work) Kinetic energy Potential energy Electrical energy PV work Chemical energy … Different forms sum to total energy; can be converted into other forms. Metabolic energy in medicine still often measured in cal (old…) 1 cal = 4.185 J Power = Work per time unit [W]

Take-Home Messages Numbers without dimensions have little meaning. In medicine, frequency is often based on minute. Weight is a special force caused by mass * gravity. Tension is a force that develops in a muscle. Pressures are measured in kPa, except body fluids. Torque is the product of radius and force to causes rotation. Muscles produce large forces when contracting. Energy takes different forms, summing to the total and can be converted into others.

MCQ The force of 1 N on a standard mass causes which of the following accelerations? 9.81 m/s2 0.981 m/s2 10 m/s2 1 m/s2 0.1 m/s2 How large is the energy of 1 mg of blood moving at a speed of 20 µm/min? 20·10-12 kg*m2/s2 5.6·10-12 kg*m2/s2 5.6·10-20 kg*m2/s2 0.56·10-15 kg*m2/s2 5.6·10-20 kg*m/s2

That’s it folks…

MCQ The force of 1 N on a standard mass causes which of the following accelerations? 9.81 m/s2 0.981 m/s2 10 m/s2 1 m/s2 0.1 m/s2 How large is the energy of 1 mg of blood moving at a speed of 20 µm/min? 20·10-12 kg*m2/s2 5.6·10-12 kg*m2/s2 5.6·10-17 kg*m2/s2 0.56·10-15 kg*m2/s2 5.6·10-20 kg*m/s2

Elementary Units (SI) Dimension Unit Abbreviation Length meter m Mass kilogram kg Time second s Amount of substance mole mol Current ampere A Temperature kelvin K Luminous intensity candela cd SI units refer to Système international d'unités”. Follows “meter-kilogram-seconds” system (MKS). kg is special case as it has a “multiple” in front (see next).

Some Derived Dimensions Unit Abbrev. Frequency Hertz / … Hz / bpm s-1 / min-1 Force Newton N kg·m·s-2 Pressure Pascal / torr Pa N·m-2 = kg·m-1·s-2 Heat / Energy / Work Joule J N·m = kg·m2·s-2 Power Watt W J·s-1 = kg·m2·s-3 Electric potential Volt V W·A-1 = kg·m2·s-3·A-1 Electric resistance Ohm Ω V·A-1 = kg·m2·s-3·A-2 Conductivity Siemens S Ω-1 = kg-1·m-2·s3·A2 … List incomplete (some physiologically relevant ones…) It is possible to describe all measurements using the 7 elementary SI units. Dependency often established via the energy associated.

Multiples and Fractions of Units Factor Prefix Symbol 101 deca- da 10-1 deci- d 102 hecto- h 10-2 centi- c 103 kilo- k 10-3 milli- m 106 mega- M 10-6 micro- µ 109 giga- G 10-9 nano- n 1012 tera- T 10-12 pico- p 1015 peta- P 10-15 femto- f 1018 exa- E 10-18 atto- a Multiples are typically upper, fractions lower case. Because of inability to print Greek character µ early on, sometimes people use ‘mu’ or ‘u’ for it.