Fluid dynamics: Human transport system. Pulmonary Hypertension Treatment with Epoprostenol: A Riddle. Preliminary Questions

Transcription

1 Human transport system Fluid dynamics: Blood flow in the human body Solving a medical enigma by physics Credit: Dr. ir. Th.J.C. Faes Dept. Physics & Medical Technology VU University Medical Centre, Amsterdam, tjc.faes@vumc.nl, Credit: Th.J.C. Faes, VUmc. Oct. Tel.: vrije Universiteit amsterdam Ventilatory & Circulatory System: Aim: Get O in and CO out Components: Airways Lungs Blood vessels Heart Source: Despopulos (1986) p.69 Pulmonary Hypertension Treatment with Epoprostenol: A Riddle Preliminary Questions Roeleveld et al. Chest (004) 57-9 Walking distance in 6 min right ventricular stroke volume (1) What is pulmonary hypertension? () What is blood pressure, how is it measured () What are the energies involved No change in blood pressure No effect of epoprostenol Patient is fitter Significant effect of epoprostenol 4 What is pulmonary hypertension? Ventilatory & Circulatory System: Aim: Get O in and CO out Components: Airways Lungs Blood vessels Heart Pressures Pulmonary Pressure Systemic Pressure Lungs Source: Despopulos (1986) p.69 5 What is pulmonary hypertension? mpap rest (mmhg) Normal 9-15 < 0 Seriousness of Pulmonary Hypertension small mild severe > 40 Hilvering in Sluiter 199, pp

2 How much Pascal (Pa) is 1 mmhg? Six-minute walking test 1mmHg 1 bar bar 760 1mmHg bar 1.5Pa 7 Distance patients walk (not running) in a six-minute period. Measure of fitness of: 1) circulation, ) ventilation, ) locomotion ( bewegingsapparaat ) Heart acts as a pump. Stroke volume ( slag volume ): volume of blood pumped by each ventricle every heart beat ( ml) Cardiac output (hart-minuut-volume) = stroke volume x heart rate volume of blood pumped by each ventricle in one minute (about 5 litre ) 8 Amount of Blood Pumped in a Life Time Calculate the amount of blood pumped by the heart in a life time of 80 years. Assume that stroke volume is 80 ml and heart rate is 75 beats a minute. y d/y h/d m/h b/m N V N V volume of supertanker 9 Beats beats 9 Beats s m Cardiac Energy Delivered in a Life Time Calculate the amount of energy delivered by the heart in a life time of 80 years. Assume that stroke volume is 80 ml mean pressure is 100 mmhg and heart rate is 75 beats a minute. E e p g h 1 v V N E N pv see previous page 1 for each heart beat E pv gmh mv 9 Beats beats Beats s 600 kg jam J 9 10 Some Anatomy & Physiology Heart & Circulation: Systemic part Pulmonary (low pressure) circulation Systemic (high pressure) circulation Left & right side of the heart Ventricle (1,) and atria (10,9) Cardiac output Source: Despopulos (1986) p.69 From large aorta to capillaries to vena Vessel diameter & joint cross-sectional area Source: Despopoulos (001) p

3 Pressures in the Circulation Pulmonary part Systemic part Differences in Systemic & Pulmonary Circulation Source: Rushmer (1976) pp.9 Source: Rushmer (1970) pp Pressure and Orthostatic Pressure Measuring blood pressure in situ Given: mean pressure at heart level is 100 mmhg 1 mmhg = 1.5 Pa Calculate: Pressure at feet and head Extra-vascular pressure sensor system Flushed with heparinized saline solution Pressure to be measured Pressure actually measured PHead g h 4.9 kpa=7 mmhg PFeet g h 5 kpa=190 mmhg 100 mmhg mmhg Important where to put your blood pressure meter!! 15 catheter Problems: Transfer properties catheter Hydrostatic pressure Source: Webster (1998) p Hydrostatic Pressure Errors Source: Working group Pulmonary hypertension PHead Orthostatic Hypotension due to acceleration 100 mmhg a h with : a 7 m / s g 1 10 kg / m,1 mmhg 1.5 Pa Hydrostatic pressure error: P = P 1 ρgh 1 cm difference corresponds to 0.75 mmhg Feasible accuracy 1- mmhg Observed errors up to 15 mmhg 17 18

4 Bernoulli Recap Fluid flow Streamlines path traced out by massless particle in the fluid Δm 1 1 ΔV 1 1 A 1 Δx 1 1 A 1 v 1 Δt Δm A v Δt 1 A 1 v 1 A v Continuity equation dm dm Fluid flow 1 A 1 v 1 A v incompressible: const en A 1 v 1 A v fast through small diameter, slow through big ones Work P 1 ΔW FΔx PAΔx P ΔW P 1 A 1 Δx 1 P A Δx ΔW P 1 A 1 v 1 Δt P A v Δt Also ΔW ΔKE ΔPE ΔW 1 Δmv Δm gy 1 Δmv 1 Δm gy 1 Work ΔW 1 Δmv Δm gy 1 Δmv 1 Δm gy 1 ΔW P 1 A 1 v 1 Δt P A v Δt Δm 1 A 1 v 1 Δt A 1 v 1 Δt Δm 1 ΔW P 1 Δm 1 P Δm P 1 1 P 1 v gy 1 v 1 gy 1 P v 1 gy 1 P 1 v gy const Bernoulli Equation (~ 1740) Pulmonary Hypertension Treatment with Epoprostenol: A Riddle No change in blood pressure No effect of epoprostenol Roeleveld et al. Chest (004) 57-9 Walking distance in 6 min right ventricular stroke volume Patient is fitter Significant effect of epoprostenol 4 4

5 Application of Bernoulli s equation e p g h v 1 constant 5 Application of Bernoulli s equation e p g h v Resting cadiac output velocity 1 constant kinetic pressure gravit. kinectic pressure energy energy energy energy energy density pressure density heightdensity density density m/s J/m mmhg Pa = J/m m J/m total % of total % of Conclusion: Kinetic energy << Pressure Gravitational energy < Pressure gravit. energy density % of total aorta mean arteries mean capillaries venae cavae and atria pulmonary artery mean only if is constant! 6 Measurement of flow rate: Thermodilution Bronzion (1995) p 114 Khandpur (005) 49 Vascular Resistance: Poiseuille s law Model of lung Measure heat profile Injection of cold liquid dm a4 8 P P 1 L P P 1 dm 8 L a 4 Total Peripheral Resistance 7 P arterial P venous dm cardiac R TPR 8 Pressures in Pulmonary Hypertension P arterial P venous Unchanged PAP *) (mmhg) Cardiac Output (l/min) dm cardiac R TPR Total Peripheral Resistance Larger X Smaller nice nice Baseline After 1 year Ratio (year/baseline) 5 ± ± ± ± TPR 1065 ± ± (dynes s cm -5) *) Pulmonary Arterial Pressure Roeleveld et al. found in PPH (N=9) 9 Pulmonary Hypertension Treatment with Epoprostenol: A Riddle No change in blood pressure No effect of epoprostenol Roeleveld et al. Chest (004) 57-9 Walking distance in 6 min right ventricular stroke volume Patient is fitter Significant effect of epoprostenol 0 5

6 Conclusion Vasodilatory drug: Decreased pulmonary resistance (0 %) Increased cardiac output with (0 %) and with that oxygen supply and six-minute-walking distance Pressure constant: Poiseuille s law: pressure = flow x resistance Physics (Poiseuille s law) explained the results 1 6