• PHYSICAL QUANTITY • DIMENSIONS: fundamental [M] [L] [t] [i] secondary • MEASURE UNITS:

IS – CGS – PRACTICAL S.

• FUNDAMENTAL CONSTANTS • SCALAR QUANTITIES • VECTOR QUANTITIES (modulus, direction, versus) • DISPLACEMENT:



 s



v = Δs /Δt  • VELOCITY: a = Δv / Δt • ACCELERATION: € • FORCE: from Principles of Dynamics €

  F = ma

newton (IS) dyna (CGS)

€ • MASS: kg (IS) g (CGS)

€

• DENSITY:

d = m/V

• PRESSURE:

p = Fn /ΔS

pascal (IS) baria (CGS) mmHg, atm (PRACTICAL S.)

€

• FLOW:

€

m3/s (IS)

Q = V/Δt cm3/s (CGS) liter/s (PRACTICAL S.)

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

• CARDIOVASCULAR SYSTEM € • DESCRIPTION of the CIRCULATORY SYSTEM: MEAN VELOCITY and MEAN PRESSURE behaviours in the subsequent districts of the circulatory system MEAN VELOCITY: • significant decrease towards capillaries • returning to heart high values are recovered

interpretation: STEADY FLOW MOTION Q = costante, v time independent (closed system, no holes/sources) Q = S v continuity equation (S1v1 = S2v2) • total section encreasing toward capillary system and decreasing returning to the heart MEAN PRESSURE: • decreases from 100 mmHg (aorta) to 1-2 mmHg (vena cava) interpretation: • necessary to study the details of liquid motion • definitions and formulas with different physical quantities STEADY MOTION of a REAL and UNIFORM LIQUID in a RIGID DUCT

⇓ BEATING MOTION of a REAL and NOT UNIFORM LIQUID in a DEFORMABLE DUCT • LAMINAR FLOW: viscosity coefficient (friction forces):

FA = η A v relative /δ

€

• Poiseulle formula Q ∝ Δp πr 4 Q = Δp € 8η • laminae velocity: parabolic velocity contour € • silent € DUCT’s MECHANICAL RESISTANCE : in laminar flow:

R =

8η πr 4 €

R = Δp / Q

above critical velocity

v > vc :

v c = ℜη / d r (empirical formula)

• TURBOLENT FLOW: • laminae velocity lines ⇒ vortexes € • noisy • Q ⇔ Δp high energy waste by friction   € L = F ⋅ s = F s cosα

• WORK # force fields # Energy forms

joule (J) (SI), erg (CGS)

€ ENERGY CONSERVATION PRINCIPLE • kinetic energy : Ek = ½ m v 2 • kinetic Energy theorem : L = ΔE k L A→B = U A – U B • conservative forces (potential energy U) : • dissipative forces (friction) € €

- POTENTIAL ENERGY U(x,y,z)€ • mechanical Energy conservation: U + Ek = constant applications   F = mg 1 – weight force

L A→B = U A – U B = mgh A – mgh B

U + Ek = m g h +

U= mgh €

€

1 m v 2 = constant 2

2 – liquid (ideal, η = 0) falling in a duct

L = ΔE k

ΔV = constant in same Δt

€

• Bernoulli € theorem:

€ • liquid zero viscosity • steady motion • rigid duct’s walls

€

p v h + + = constant d g 2g 2

consequences: • horizontal vessel with constant section friction dissipated energy A (per volume unit) • aneurism (worsening) • stenosis (worsening)

A = p1 – p2

• in turbulent flow: • Q ∝ Δp • mechanical resistance (in parallel in every districts): • Rcapillaries = RcT ⇔ Rarterioles = RaT R aT =

Ra Na

R cT =

Rc Nc

•

Rc > Ra

•

N c >> N a

€

Δp a Δp c > ⇒ Δp a > Δp c RaT > RcT Q Q € of flows € • graphical representations € • resistances evaluation • flow in the circulatory system: € laminar flow nearly always and € everywhere €

 BLOOD NOT A UNIFORM LIQUID:

• blood composition • haematocrit value • blood viscosity

• effects from not uniformity: a) axial buildup: decreased mean viscosity b) in capillaries: viscosity η = f (r) p = dgh • HYDROSTATIC PRESSURE: definition € of mmHg – cmH2O – atmosphere (practical S.)

• effects from hydrostatic pressure € • invasive pressure measurement (U manometer) • not invasive pressure measurement (sfigmomanometer) • HEART (general description) • MECHANICAL POWER:

W= L /Δt watt (IS)

• EFFICIENCY: η = L/E

TOTAL

-heart parameters: frequency, period, pulsation ejection volume -muscle contractions isotonic, isometric € -time correlation between pVS, VVS, paorta, ECG, FCG • HEART WORK: ◊ L VS

≈ p VSΔVVS ≈ 0.8joule

 DISTENSIBLE

◊ L TOT

€ VESSELS

≈ 1joule

◊W

≈ 1watt

€

◊

€

• cohesion forces • cohesion forces in liquids ⇒ surface tension forces F = τ  → τ = F/ ↔ τ = L/ΔS L = τ ΔS = U i – U f ⇒ U = τ S € • detergents • τ = τ (temperature) • flottation € € • tensioactive liquids • capillarity phenomena 2τcosθ = d r h g • gas embolism Δp' = Δp – Δpτ

• cohesion forces in € deformable materials • elasticity € phenomena : Hooke law (V, S,  bodies) deformation ∝ applied force volume-pressure curves aorta/vena cava

€

€ formula (sphere): • Laplace equilibrium

Δp =

2τ r

τ • Laplace equilibrium formula (cylinder): Δp = R • tension-radius curves €

• vessel’s equilibrium radius:

{€ττ == τΔp(R)R

with active tension τ = Δp R – τ A : (stable equilibrium radius REs, unstable REi ) €

η ≈ 15%

 BEATING

MOTION

Q = Q(t) = Q(t + T)

• HYDRODYNAMICAL EFFECTS of VESSEL’s DISTENSIBILITY

• BEATING FLOW:  elastic deformation travelling in the walls with velocity • u >> v • u ∝ 1/v • u ∝ vessel' s stiffness  flow ≈ steady E ⇒ U ⇒ E' ⇒ U' ⇒ E" ⇒ €.......  pulse € stiffness → hypertension in old subjects  wall’s € € € • beating flow and MECHANICAL IMPEDANCE k

elastic

k

elastic

 u

k

€ cavity:  extensible beating

FA + FE + Fp = m a ⇓

dx dx kS m + RS + x = SΔp cosωt dt dt V 2

2

2

o

2

€

⇓

x = x(t) €

⇒

Q = Sv = S

€

dx(t) = Q(t) dt

⇓ €

Q(t) =

€ € mechanical impedance Z:

€

Δp o cos[ωt + φ ] Z

mω k 2 – ) 2 S ωV € –––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Z =

R2 + (

• VISCOUS FLOW TRANSPORT    FA = – f v

F + F =0 €A F - transfer velocity v t =

f

Stokes:

f = 6πηr

- Archimede bouyant force SA = m g [m = moved liquid mass] • SEDIMENTATION:

v = Vg t

(d – d') f

2 r 2 g (d – d') sphere: v t = 9 η

€

  F = q E • ELECTROPHORESIS:

v = t

qE =µ E f

q with µ = € f

e

sphere: v = t

e

qE 6πηr

€

• CENTRIFUGATION: - circular uniform motion ⇒ ω = Δθ , v = ω R, a = ω R (centripetal) €Δt 2 - ‘apparent’ forces → centrifugal force Fc = m ω R 2

2ω r sphere: v = r (d – d') € 9 η 2

€ ω r v = (d – d')V f 2

t

t

€

€

- Einstein-Stokes formula: - sedimentation coefficient S:

2

o

o

f =

€

RT N oD

S =

v (d – d') = V ωr f t

2

o

€

• analitical centrifuge • preparation centrifuge

€

RT 1 v ω r (1 – d ) D d' ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

- molecular weight M measurement:

M =

t

2

o

BIOMECHANICS

  M = F∧r • torque vector: Nxm (IS) € • translational and rotational balance conditions:     F = R = 0 e M = M =0 ∑ ∑ • constraints € and levers • gravity center –––––––––––––––––––––––––––––––––––––––––––––––––––––––––– € i

i

T

• THERMOLOGY and THERMODYNAMICS

– temperature: (indicative of a body thermal state) °C K (IS) T = t + 273° – thermodynamic system (No) – thermodynamic parameters: p, V, t, …. – thermodynamic equilibrium • INTERNAL ENERGY U (state function) – heat: calorie (cal), Calorie = 1 kcal ◊

L = J Q con J = 4.18 J cal–1

– ideal gas: – real gas:

pV = n R T (p +

◊

Q = c m (t2 – t1)

with

R =

gas: cp > cV

p oVo 273°

a )(V – b) = n RT V2 €

Tc = critical temperature € • I PRINCIPLE of THERMODYNAMICS st

energy conservation: ΔU = JQ – L (signs convention for L, Q) • ENTHALPY H (p = constant) (state function) H = U + pV € ΔH = JQ reactions eso/endo thermal (ΔH < 0 / ΔH > 0) • efficiency η of a thermal machine

→

• IInd PRINCIPLE of THERMODYNAMICS - limits in spontaneous energy transfers (heat) - thermostat definition statements: ◊ Clausius ◊ Kelvin • ENTROPY S (state function) dQ = dS ◊ from Clausius inequality T ◊ S(B) > S(A)

∫

dQ A T B

rev

≡ S(A) – S(B)

• GIBBS FREE ENERGY G (state function) G = H – T S (constant pressure and temperature (as human body)) - insulated system ◊ ΔS > 0 - S ∝ disorder of the system ◊ increase of disorder (insulated system) ΔG = ΔH – TΔS > 0 or < 0: endoergonic or esoergonic processes (spontaneous direction of the process/transformation) • HEAT TRANSMISSION - conduction (by contact) Q ∝ ΔT - convection (with matter displacement) Q ∝ ΔT - radiation (electromagnetic waves emission) I = σ T4 • Stefan law: € –1 • Wien law: λImax ∝ T € - evaporation (one way only, dependent on water vapour pressure) –––––––––––––––––––––––––––––––––––––––––––––––––––––––––– €

€ • MEMBRANE’ PHYSICS • DIFFUSION gradC (from thermal agitation) Ist Fick law: (solutions) α partition coefficient IInd Fick law

J sM = –DM α

ΔC ΔC = –D εα = –P ΔC Δx Δx

ε hindrance coefficient p

€

same for gas: C ⇒ RT (ideal gas)

- gas-liquid diffusion: Henry law Vi = si p i (si = gas-i solubility) € - biological gases: O2, N2, CO2, H2O (saturated in alveoli) - example: inadequate O2 transport from Henry law € - capture from haemoglobin) (active biochemical mechanism • FILTRATION gradp (Δp – change in hydraulic pressure) - JVM = – Lp Δp - diffusion + filtration

J sM total = –PΔC – αε

C1 + C 2 L p Δp 2

• OSMOSIS gradπ (Δπ – change in osmotic pressure)

-

liquid recall: osmotic pressure π Vant’Hoff laws (for dilute solutions) state equation (for dilute solutions): πV = δ n R T JVM = +Lp Δπ osmole, osmolarity (1 osm = 22,4 atm) osmotic work L = nRT lnC1 – nRT lnC2 chemical potential energy: µ = nRT lnC + µ o • osmotic equilibrium: - blood - oncotic π - membrane balances: JVM = – Lp (Δp – Δπ) ⇓

microcirculation €

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

• ELECTRICITY PHENOMENA - electric charge Q, q - Coulomb force

 F =

 1 qQ r 4 π εoεr r 2 r

con εr > 1

  F E = - electric field q € - conservative force LAB = U(A) – U(B) U = electrical potential energy qQ 1 € U = pointlike charge: 4 π εoεr r

- electric potential V:

V =

€ - electric dipole/dipolar layer: Q

U q

volt (V) (IS)

 pr pSΩ V(P) = = 4 π εoεr r 3 4 π εoεr

- electric capacity€ C: C = V farad (F, µF) (IS) - plane and cylindrical condenser € - electric current i, electric current density J 2 i (ampere), J = i/S (ampere/m ) (IS) € - Ohm law:

• generalized Ohm law: • 2 Ohm laws:

J = σ E – the same as:

e R = ρ  /S where ρ = 1/σ

VA – VB = R i

V e - condenser charge and discharge i = R o

–

t τ

where τ = RC

- electrolitic dissociation (3 steps) € ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

• ELECTRIC FIELD E = – grad V MECHANISM € C –C V –V - electrochemical flows

J

=µ

EsM

1

s

2

2

where ε = 1 – φ

ε

1

2

Δx

equivalent/liter ⇒ C(Eq/liter) = Z C(osmole) € -€ electrochemical potential:

µ = RT lnC + Z e NoV + µ o (n = 1) RT C € V –V = ln - Nernst equation: where F = e No ZF C - Donnan-Gibbs formula: {Na}1 {Cl}1 = {Na}2 {Cl}2 kC - oncotic pressure: π = π proteins + π ΔΣ with π ΔΣ = 2C € 2

1

2

1

2

2

1

2

APPLICATIONS

€ mV • CAPILLARY MEMBRANE: (OK) ΔV = –1.5 • CELL’s MEMBRANE: - passive mechanisms gradC and gradV: Na e K (KO) - active mechanism: pump Na-K model:

JNa(total) + JK(total) = 0 ⇓ RT P {K} + P {Na} ln - Goldman equation: V = ZF P {K} + P {Na} K

e

Na

e

K

i

Na

i

m

€ P = f (t) → V = f '(t) - action potential: P € - axon cable properties Na

K

(membrane condenser charge/discharge Cm and dumpening with distance) constant τ and λ - action potential propagation: • active (amyelinic fibers) • activa and passive (myelinic fibers) → jumping propagation - electric potential from  excitable cells: pr pΩ V(P) = = € 4π ε ε r 4 π ε ε S

3

o

r

o

r

- ECG - EEG – EMG –––––––––––––––––––––––––––––––––––––––––––––––––––––––––– €

• MAGNETIC FIELD

    - Laplace law: F = Δ i ∧ B magnetic field B µ i - Biot and Savart law: B = 2π d where µ = magnetic permeability € B: tesla (IS) = 104 gauss µ ⇒ magnetic properties of matter: € diamagnetism µ 1 ferromagnetism µ >>1 €€    - Lorentz force: F = € qv ∧ B - Ampere equivalence: coil € ≡ magnet solenoid → B = µ i € n  - B not conservative € € • ELECTROMAGNETIC INDUCTION  € ΔΦ(B) € - Faraday-Neumann law: V = – Δt   where Φ(B) = B • nS = magnetic field flow tesla m2 = weber (IS)   B ↔ E - Maxwell equations: € - self-inductance: → inductance L (henry in IS) € 2

1

induced

€

- RLC circuit alternating current:

ΔV = ΔV sin(ωt) da cui I = I sin(ωt + φ ) o

€

o

• impedance Z:

Z =

ΔVo 1 2 = R 2 + [ωL – ] Io ωC

- Electromagnetic waves:   E⊥B E >> B

λν = c

€ –––––––––––––––––––––––––––––––––––––––––––––––––––––––––– • WAVE PHENOMENA € - periodic function: f (t) = f (t + T) T = period 2π 2π - f (t) = A sin( t + φ ) where = 2πν = ω T T • longitudinal waves € • transverse waves ∝A • energy transfer: E E • intensity: I = watt m–2 in IS ΔtΔS 2

€

TOTAL

€ analysis – periodic function: - harmonic (Fourier) f (t) = €f (t + T) = ∑ [S sin(nωt) + C cos(nωt)] t x - propagation: S(t) = A sin[2π ( – )] T λ - spherical waves: A ∝ 1 r - principles: Huygens – Malus –waves overlap € - reflection n v n= = - refraction€and total reflection: refraction index n v - Doppler effect (relative motion source–observer) - polarization - interference (coherence necessary): € phase concordance (constructive) phase opposition di (destructive) ∞

n =0

€

n

n

2

2

1

1

2

• stationary waves (going in opposing direction) • beats (small frequency difference) - directional beam waves at high frequencies ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

• ACUSTICS - sound: properties

Δp = 2I v d ΔI - sound sensation levels σ: Δσ = I I with I = 10 Wm from which → σ –€σ = Log I resulting: € I I σ (bel) = Log e σ (decibel) = 10 Log I I € - hearing: hear external–medium–internal - ultrasound (in Medicine ≈ 1 MHz) : • Doppler flowmeter: ±2u cosθ Δν = ν [ ] for v >> u €v with v sound velocity and u source-observer relative velocity o

–12

o

–2

o

o

o

o

S

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––– €

• OPTICS

- electromagnetic waves (spectrum) - atomic and molecular transitions E = hν - light intensity • PHYSICAL OPTICS

λ ≈ D with D optical system dimensions €

• GEOMETRICAL OPTICS λ