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I Course Biomedical Applications of Mathematics Elements of cardiocirculatory physiology Roberto Bonmassari S. C. di Cardiologia APSS-Ospedale Santa Chiara Trento

Preamble A Course of Biomedical Applications of Mathematics …… when the Hospital goes out and meet the University I’m not a physiologyst I am a clinician, a cardiologist

Agenda Four lessons: 18 - 25 september, 2 – 11 october • Aspects of cardiac anathomy • The cardiac and circolatory function: phisiologic aspects • Examples of clinical application of a phisiologic application in a pathologic condition: coronary stenosis and aortic stenosis

The heart is costituted from 4 chambers: 2 atria (right and left) 2 ventricles (right and left)

Atria recive blood, Ventricles eject blood

POLMONE Scambio Gassoso Piccolo Circolo CUORE Grande Circolo ORGANI Funzione di Pompa Consumo di Ossigeno

The Heart is a pump • The cardiac pump is the ground of the circulation • The are two circulation system that works in series: systemic and pulmonary circulation • The cardiac pump has the primary function of insurance an adeguate amount of blood flow through the systemic and the pulmonary vessel bed • The cardiac pump works with two mechanisms : blood aspiration and pushing

The Heart is a pump The cardiac pump produce a mechanical result (the circulation of the bood) due to the contraction and relaxation of the muscolar wall of the cardiac chambers (ventriculi and atria) • • But what is the primum movens of the cardiac function? • Upstrem the mechanical function is necessary the electric function: the electric excitation

The conduction system: Physiology and pathology Nodo del seno Nodo atrioventricolare Fascio di His Branca destra Branca sinistra Fibre di Purkinje

The Heart is a pump • The cardiac electrical activity is an automatic activity • Is only marginally influenced by nervous system • These are the basis of the electro-mechanical coupling partneship

The cardiac cycle Arterial Pressure Curve Fasi 1 contrazione Vs 2 rilasciamento Vs 3 riempimento Vs Ciclo di Wiggers 1915 Pressure (mm Hg) Atrial Systole 120 100 80 60 40 10 0 Ventricular Ejection Phase Isovolumetric Contraction Relaxation Semi-Lunar Valve Closes Semi-Lunar Valve Opens AV Valve Closes 1 Electrocardiogram T Q S Atrial Systole 0 Ventricular Pressure 3 R P Approx. Time Arterial Pressure AV Valve Opens 2 3 Ventricular Filling 0. 1 Ventricular Systole 0. 2 0. 3 0. 4 Diastole 0. 5 0. 6 0. 7 0. 8

Atrial Systole Pressure (mm Hg) 120 100 Ventricular Ejection Phase Isovolumetric Contraction Isovolumetric Relaxation Ventricular Filling Semi-Lunar Valve Closes Semi-Lunar Valve Opens Arterial Pressure 80 60 40 AV Valve Closes 10 AV Valve Opens Ventricular Pressure 0 R Q S Atrial Systole Approx. Time 0 Electrocardiogram T P 0. 1 Diastole Ventricular Systole 0. 2 0. 3 0. 4 0. 5 0. 6 Arterial Pressure Curve 0. 7 0. 8

The cardiac cycle pressure/volume V sin ratio

Ventricular Ejection Phase Atrial Ventricular Systole Filling Isovolumetric Contraction. Relaxation Pressure (mm Hg) 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 40 AV Valve 10 AV Valve Opens Closes Ventricular Pressure 0 R T P Electrocardiogram Q S Atrial Ventricular Diastole Systole Approx. Time 0. 1 0. 20. 30. 40. 50. 60. 70. 8 0 0. 20. 30. 40. 5 0. 60. 70. 8 Ventricular Filling Arterial Pressure Curve

Ventricular Ejection Phase Atrial Ventricular Systole Filling Isovolumetric Contraction. Relaxation Pressure (mm Hg) 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 40 AV Valve 10 AV Valve Opens Closes Ventricular Pressure 0 R T P Electrocardiogram Q S Atrial Ventricular Diastole Systole Approx. Time 0. 1 0. 20. 30. 40. 50. 60. 70. 8 0 0. 20. 30. 40. 5 0. 60. 70. 8 Atrial Systole Arterial Pressure Curve

Ventricular Ejection Phase Atrial Ventricular Systole Filling Isovolumetric Contraction. Relaxation Pressure (mm Hg) 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 40 AV Valve 10 AV Valve Opens Closes Ventricular Pressure 0 R T P Electrocardiogram Q S Atrial Ventricular Diastole Systole Approx. Time 0. 1 0. 20. 30. 40. 50. 60. 70. 8 0 0. 20. 30. 40. 5 0. 60. 70. 8 Isovolumetric Contraction Arterial Pressure Curve

Ventricular Ejection Phase Atrial Ventricular Systole Filling Isovolumetric Contraction. Relaxation Pressure (mm Hg) 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 40 AV Valve 10 AV Valve Opens Closes Ventricular Pressure 0 R T P Electrocardiogram Q S Atrial Ventricular Diastole Systole Approx. Time 0. 1 0. 20. 30. 40. 50. 60. 70. 8 0 0. 20. 30. 40. 5 0. 60. 70. 8 Ventricular Ejection Arterial Pressure Curve

Ventricular Ejection Phase Atrial Ventricular Systole Filling Isovolumetric Contraction. Relaxation Pressure (mm Hg) 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 40 AV Valve 10 AV Valve Opens Closes Ventricular Pressure 0 R T P Electrocardiogram Q S Atrial Ventricular Diastole Systole Approx. Time 0. 1 0. 20. 30. 40. 50. 60. 70. 8 0 0. 20. 30. 40. 5 0. 60. 70. 8 Isovolumetric Relaxation Arterial Pressure Curve

Left 300 Coronary 200 Blood Flow (ml/min) 100 0 Right Systole Diastole Slide courtesy of A. C. Guyton, MD, Textbook of Medical Physiology, Sixth Edition, 1981 W. B. Saunders Company

How is the Cardiac function? Cardiac output and pressure CO= Pr / R= SV x HR Legenda 1. 2. 3. 4. Pr = systemic pressure R = systemic resistance SV = stroke volume (amount of blood eject every beat) HR = number of beats per minute

Cardiac function = CO Determinants • Cardiac rate • Inotropic condition = contractility • Venus return (RV): influenced from neuroumoral factors (Frank-Starling law) • Peripheric resistance = CARDIAC OUTPUT 4 -6 l/min CARDIAC INDEX 1. 6 -2. 5 l/min/m²

Cardiac output = CO CO= Pr / R= SV x HR examples : 1. Increase of FC -> does not increase GC, decrease of the VOLUME SYSTOLESV (if Rv does not increase) 2. Increase of RV -> oncreases GC 10 -20% (increase of Pa A dx 10 mm. Hg) 3. Increase of FC + Increase of RV -> increases GC with = SV 4. Stirring adrenergethic -> increases RV + increse of the function of the pump (FC, contract? ) = INCREASES GC 5. Important reduction of FC or alteration of V dx -> increase of Pa A dx = barrier for the venous comeback Organs are able to change their flow working on the oppositions; they are able to regulate the distribution of the CARDIAC RANGE.

Cardiac function: Frank-Starling mechanism

Cardiac function: CO-CI & R ; Conduttance= 1/R

diastolica Difetto di riempimento sistolica Difetto di espulsione

Cardiac power output Ventricular function index Cardiac Power output = MAP x CO = SW X HR

Cardiac power output

Function of blood circulation TRANSPORT • substrates and cathabolism products to and from organs and tissues • in a changeable measure and in proportion of her requirements and necessities GOAL • to maintain an optimal composition of the interstitial fluid necessary for the cellular function

VASO ARTERIOSO TONACA INTIMA = ENDOTELIO TONACA MEDIA TONACA AVVENTIZIA PLACCA ATEROSCLEROTICA

Distribution of blood flow • It is necessary to give at any time to organs and tissues a blood flow distribution based on requirements • There are two control mechanisms in a close correlation • Central Autoregulation • Local Autoregulation

Distribuzion of blood flow Central Autoregulation GOAL: TO MAINTAIN COSTANT perfusion pressure of the organs (independently from the flow: Fl= P/R) Mechanism: neuro-ormonal central control on R e Fl Local Autoregulation GOAL: TO MAINTAIN ADEQUATE flow for each organ for the metabolic erquirements (independently from systemic pressure) Mechanism: regulation of local vascular resistance due to metabolism activity

Circulation modelling • • ORGANS in parallelo if we consider AORTA with different metabolic, vascular, anathomic characteristics (f. e. heart, abdominal argans, muscols, brain…) • VASCULAR SYSTEM: determinate from a segments sequence in serie similar in each organ Arterie – arteriole – capillari – venule – vene

The Vascular System: segments 1) Aorta e great proximal arteries • Elastic matrix tessue prevalent HISTOLOGY • Improve distention of vascular wall during sistole PHISIOLOGY • cinetic energy of stroke volume (during systole ) is storaged as elastic energy released during diastole (partecipate at the diastolic value of BP) • modulation of suddenly variations of BP : dynamic sistolic reserve • pressure wave downstream is delayed • Riduction of elastic properties PATHOLOGY • reduction of dynamic sistolic reserve • increase differential blood pressure even if a costant stroke volume • increase of afterload of left ventricle • increase of the rate of propagation of the pressure wave

The Vascular System: segments 2) Muscolar small arteries • Arteries with a thick muscolar medium tonaca: are the junction betweengreat arteries and organs and tessues – Thick medium muscolar tonaca ( high thickness/lumen ratio ) – COSTANT STRESS of the wall (PR x radius/ thickness) – COSTANT DIAMETER with variations due to neuro-horrmonal control – Regulatory mechanims : metabolics production and myogenic control • Play a central role in the vascular resistance control = control and persistance of an adequate flow to organs and tessues FL= P / R – Is the principal location of the flow resistance (aortic pressure 100 mm. Hg, small arteries pressure 30 mm. Hg, vein pressure 15 mm. Hg) • The pressure gradient between small arteries and veins (about 15 mm. Hg) permits – The capillar filtration – The distal reabsorbtion

The Vascular System: segments 3) Capillars • In this segments is present the most importanti function of circulation = SUBSTRATES AND OXIGEN EXCHANGE BETWEEN BLOOD/TESSUES WIT H AN FOUDAMENTAL ROLE IN OMEOSTASIS OF THE INTERSTITIAL FLUID – The walls are very smooth , sometimes in certein organs fenestrates – Little diameter = little transmural stress (Stress= D x P/spessore) with a better tolerance of the transmural pressure – There is a significant flow resistance with a fall of pressure (from 30 mm. Hg to 15 mm. Hg) – At the arteriolar portion happen THE FILTRATION at the venular portion THE REABSORBTION – In any time not in all THE CAPILLARS there is perfusion: the density of the perfused capillars is important in terms of exchange between the tessues – The exchange happen due to: • Pressure gradients (FLUIDS): hydrostatic pressure (proximal side) and colloido osmotic pressure (distal side) • Diffusion: liposoluble gas and yhdrosoluble substances – The amount of not reabsorbed fluids returns to the systemic circulation through an alternative circulation : THE LINFATIC SYSTEM = 4 -5/L in a day-> 1/4 -1/2 TOTAL PLASMATIC ALBUMIN

The Vascular System: segments 3) Capillars CAUSES OF INCREASE OF FILTRATION 1. Increase of the exchanges surface (due to the increase of number of the perfused capillars) 2. Increase of the pre-capillar pressure (more diffusion) 3. Increase of the postcapillar pressure (less reabsorbtion)) 4. Increase of the permeability per surface unit (increase of holes) INTERCAPILLAR DISTANCE = less distance = more opend capillars = more fast the exchange

The Vascular System: segments 4) Venule and veins • EMODYNAMIC: – Pressure = 15 mm. Hg in orizzontal position – Prefusion pressure for the veins heart return • HISTOLOGY: –Thin wall – Very strechable –Muscolar portion very thin • FUNCTION: – Return of blood from tissue sto the heart – Storage of blood able to control the return to the heart – Influence to the capillar pressure • LEGS: superficial and deep veins – Muscolar wall more thick – Unidirectional valves (distribution of the Hydrostatic pressure in orthostatisms)

Vascular resistance • Not uniform distribution a long the segments of circulation 1. 2. 3. 4. Arteries Small arteries Capillars Veins 5% 60% 20% 15% • Medium vascular resistence-> integrated values of organs and tissues in parallelo respect the aorta

Vascular resistance The vascular regulation is a local methabolic process in all organs, a part in kidney and skin. In fact even if in a denervation condition these organs are able to matain a adequate vascular tone modificated by methabolic influences. Flow depend closely by the radius R = L x h 8/ x r 4 10% in reduction diameter vessel = 50% in increase resistance

Peripheric distribution of CO and oxygen consumption

Myocardial ischemia Fractional Flow Reserve – FFR

Coronary circulation: anatomic aspects • Coronary tree = vascular system with dicotomyc regular ramification with a diameter progressively smaller • 2 distinct section in term of anatomic and functional characteristics - 1 Epicardic portion - 2 Microcirculation section

Coronary Circulation: segments Epicardial segment Microcirculation)

Coronary circulation: anatomic aspects • Epicardic portion (diameter 4 -5 - 0. 5 mm) - “Conduttance” vessel : not able to influence the vascular resistance - are visible using contrast media • Microcirculation (diameter < 0. 5 mm) - “ Resistance” vessel site of autoregulation process - Are able to modify vascular resistance up to 6 times - Incomplitely visible with contrast media (cause of “myocardial blush”)

Coronary Circulation physiologyc aspects • • • Coronary Flow = Pressure/Resistance = 300 -600 ml/min 5 -10% of cardiac output (4 -6 l/m) Can increase up to 5 -6 times (Resistance can change up to 6 times) Pulsed flow (not continue) with a prevalent diastolic component Cardiac methabolism: exclusively aerobic - O 2 dependent with a very high O 2 extraction from the arterial blood (10 ml/100 gr/min vs 0. 5 ml/100 gr/min in the skelectric muscle) and with 30% O 2 saturation the blood of coronary sinus = more oxigen demand request more oxigen supply it is mandatory an increase of coronary flow it is not possible oxigen extraction

Left 300 Coronary Blood Flow (ml/min) 200 Right 100 0 Systole Diastole Slide courtesy of A. C. Guyton, MD, Textbook of Medical Physiology, Sixth Edition, 1981 W. B. Saunders Company

PLACCA ATEROSCLEROTICA

Physiopathology ischemia Supply Demand MVO 2 Supply: stenosi spasmo riserva coronarica Demand: FC PAO e contrattilità, ipertrofia

Coronary stenosis: physiopathology concept of coronary flow reserve • A coronary stenosis (> 40%) determine a reduction in perfusion pressure without a concomitant flow reduction due to contemporary microcirculation resistance reduction FL= P/R, if decrease P and R contemporary = FL remain stable • Stenosis upper a limit level (80 -85% diameter) run out the dilatation possibilities of the microcirculation: in this condition every other reduction of pressure means reduction of flow because the incapacity of reduction of resistance = ischemia RUN OUT OF THE CORONARY FLOW RESERVE

IVUS - INTERMEDIATE LESION RCA

FFR and CFR: What Do They Investigate? FFR CFR (E TEST NON INVASIVI)

Fractional Flow Reserve (FFR) Pa Pd S Qmax FFR = N Qmax Pd = Pa During maximal hyperemia FFR = the ratio of maximal myocardial flow in the stenotic territory to maximal myocardial flow in that same territory if the stenosis were absent

FFR: a Flow Index Derived from Pressures sten FFR = Q Q N = Pd P a

Normal Value of Myocardial Fractional Flow Reserve Pa Pd Pd FFR = Pa Normal FFR = 1

Myocardial Fractional Flow Reserve: Definition Pa Pd FFR = Pv S Qmax N = FFR Qmax Pd / R myo Pa / R myo = Pd Pa

During Maximal Vasodilatation Q Pa Pv 100 Pa 0 Pd 100 70 Pv 0 Q 100 Q 70 70 100 Pd FFR = Pa = 0. 70 P

R. E. 50 -y-old man. Aborted sudden death. LV angiogram: mild hypokinesia of the anterior wall.

Coronary Pressure Measurements 1979 2001 Pa Pd HYPEREMIA FFR = Pd /Pa = 56/80 = 0. 70

Coronary Pressure Measurements: Prerequisits 1. Pressure Measuring Guide Wire 2. Maximal Hyperemia 3. FFR instead of P

Pressure Monitoring Guide Wires 0. 014” 3 cm

Pa = Guiding Cathet 100 50 0 Pd = Pressure Wir

Coronary Pressure Measurements: Prerequisits 1. Pressure Measuring Guide Wire 2. Maximal Hyperemia 3. FFR instead of P

Hyperemia - administration • Hyperemic stimuli – Intravenous Adenosine 140 -160 g/kg/min – Intracoronary Adenosine LCA: 20 -40 g RCA: 15 -30 g – Intracoronary Papaverine LCA: 15 mg RCA: 10 mg – Adenosine Triphosphate (ATP) (ic. or iv) (same dosages as for Adenosine)

Influence of Systemic Pressure on Transstenotic Gradient 200 Aortic Pressure = 122 mm Hg 200 P = 70 mm. HG 100 P = 49 mm. HG 100 Coronary Pressure = 52 mm Hg 0 Aortic Pressure = 89 mm Hg FFR = 52/122 = 0. 43 Coronary Pressure = 40 0 mm Hg FFR = 40/89 = 0. 45

Coronary Pressure Measurements: Prerequisits 1. Pressure Measuring Guide Wire 2. Maximal Hyperemia 3. FFR instead of P

Fractional Flow Reserve in Clinical Practice Baseline 100 Adenosine IC Hyperemia Pa Pa 80 60 40 20 0 Pd d P FFR = Pd /Pa (during hyperemia) = 58/79 = 0. 73

Fractional Flow Reserve in Clinical Practice REST HYPEREMIA 150 112 100 Proximal to the lesion 58 50 Crossing the lesion 0 Distal to the lesion FFR=58/112=0. 52

QCA vs Pressure-derived FFRmyo

FFR and CFR: What Do They Investigate? P R R s m FFR CFR F=R

Coronary Pressure Measurements Clinical Applications 1. Diagnostic Setting: Is this lesion responsible for patient’s complaints? Should this lesion be revascularized? 2. Interventional Setting: Is a stent needed after balloon angioplasty? Is the stent well deployed? BDB 98/029

Clinical Applications of FFR 1. Before PTCA: when FFR > 0. 75 the prognosis is at least as good without than with an angioplasty. when FFR < 0. 75 an angioplasty is justified by a marked symptomatic improvement following revascularization.

Clinical Applications of FFR 2. After balloon: when FFR > 0. 90 and angio is OK, the longterm outcome after POBA is similar than what can be expected after additional stent implantation.

Clinical Applications of FFR 3. After stent: pullback maneuver : No pressure drop during hyperemia.

A FFR = 75 / 101 = 0. 74 B FFR = 90 / 106 = 0. 85 C FFR = 91 / 107 = 0. 85 D FFR = 98 / 100 = 0. 98

FFRmyo Myocardial Fractional Flow Reserve FFRmyo represents the true fraction of maximum flow which can still be maintained in spite of the presence of a stenosis. It is exactly that index which tells to what extent a patient is limited by his coronary disease.

FFRmyo Myocardial Fractional Flow Reserve FFRmyo = Max. myocardial blood flow in the presence of a stenosis normal maximum blood flow

In summary FFRmyo. . . is a lesion specific index is independent of hemodynamic parameters has a normal value of 1. 0 takes into account collateral flow has no need for a normal control artery can be easily obtained: FFRmyo = Pd / Pa

Courtesy of Charles Chan, M. D. National Heart Center, Singapore

Courtesy of Charles Chan, M. D. National Heart Center, Singapore

Aortic stenosis

AORTIC VALVE: tricuspid Valvola normale Valvola stenotica

Aortic stenosis: pathology

AORTIC STENOSIS: imaging

Aortic stenosis: pressure curves

Acquiring Hemodynamic Data *Accurate method of measuring CO, especially in patients with low cardiac output. • O 2 consumption measured from metabolic hood or Douglas bag; it can also be estimated as 3 ml/min/kg or 125 ml/min/m 2. • AVo 2 difference calculated from arterial – mixed venous (pulmonary artery) O 2 content, where O 2 content = saturation x 1. 36 x Hg

Aortic stenosis hemodynamic evaluation Gorlin equation CO/(SEP)(HR) Area in cm² = --------------------44. 3(C)(sq rt of pressure gradient) Where C = empirical constant For MV, C = 0. 85 (Derived from comparative data) For AV, TV, and PV, C = 1. 0 (Not derived, is assumed based on MV data)

Alternative to the Gorlin Formula *A simplified formula for the calculation of stenotic cardiac valves proposed by Hakki et al…Circulation 1981. Tested 100 patients with either AS or MS. *Based on the observation that the product of HR, SEP or DFP, and the Gorlin equation constant was nearly the same for all patients measured in the resting state (pt. not tachycardic). Values of this product were close to 1. 0. *Calculations somewhat comparable………

How measure stenosis severty? Echocardiography