Eindhoven University of Technology Model based Cardiovascular Pathophysiology (8VB20) June 30, 2014, 9.00 12.00 h Surname and initials : Indent. nr. : This exam consists of 4 exercises. Each exercise contributes equally to your final score. Answers may be given in English or Dutch. Motivate your answers. Answer exercises 3 and 4 on a separate page.
1. Figure A below shows left ventricular pressure-volume loops recorded in a patient with coronary artery disease: the right-most loop reflects a normal loop, the other loops were obtained upon vena cava constriction (Kass et al, Circ Res 1990). The heart rate equalled 60 beats per minute. p lv [mmhg] figure A p lv [mmhg] figure B V lv [ml] V lv [ml] We model the systemic circulation of the patient with a lumped parameter model that includes a time-varying elastance model of the ventricle, a constant-pressure preload, and a three-element windkessel afterload. a. Draw the model of the systemic circulation. b. Give the constitutive equation for the left ventricle. Estimate the ventricular model parameters using figure A. c. Give the constitutive equations for the elements in the afterload model. Estimate the parameter values using figure A. In the patient, the diseased coronary artery was opened in a PTCA ( dotter ) procedure. During this procedure, temporarily the flow through this artery is blocked completely. During the phase of complete block, the pressure-volume loops in figure B were recorded. d. Explain the change observed in these pressure-volume loops, as compared to the initial normal loop. To better describe the time-varying nature of pressure and flow, the three element windkessel afterload model is often extended with an inertance element. e. Give the constitutive equation for this element. Derive, using Newton s second law, an expression for the constitutive parameter involved, for a vessel segment with length l, radius a, filled with blood with density ρ.
2. An important regulatory feedback mechanism is the baroreflex. In our model of the baroreflex, the signal r(t), generated by the baroreceptor, is translated into a setting of a receptor parameter value E(t), that may deviate from the reference setting E r. The model involves intermediate parameters x(t), y(t) and z(t) that are related according to: x(t) = r(t τ D ) (1) dy(t) = 1 (x(t) y(t)) dt τ L (2) z(t) = Ky(t) (3) E(t) = E r (1+z(t)) (4) a. What is the mathematical meaning of parameter τ D in equation (1)? What physiological process does it represent? b. What is the mathematical meaning of parameter τ L in equation (2)? What physiological process does it represent? The figure below shows the change in time of arterial pressure (left panel), the receptor signal r(t) (middle panel) and four effector signals z(t) (right panel) in response to blood loss between 30 s and 90 s. The baroreflex is switched on at 150 s. 120 art 0 baro 0.4 E 1 100 0.1 0.3 E 2 R p pressure [mmhg] 80 60 40 receptor [ ] 0.2 0.3 0.4 0.5 effector [ ] 0.2 0.1 0 0.1 E 4 20 0.6 0.2 0 0 100 200 300 time [s] 0.7 0 100 200 300 time [s] 0.3 0 100 200 300 time [s] c. Use the figure to estimate the value of the parameter K in equation (3) for the case of the peripheral resistance R p. d. Explain the response of the peripheral resistance R p at t = 300s. e. Which effector could be represented by E 2 in the right panel? Explain your answer. f. Give one effector that could be represented by E 1 or E 4 in the right panel. Explain your answer.
answer questions 3 and 4 on a separate page 3. The figure below shows some hemodynamic signals of a normal healthy heart and of a heart with acute aortic insufficiency of 10% (i.e., the leakage area is 10% of the valves normal opening area). In both hemodynamically steady-state situations, venous return is 5.1 L/min, mean arterial pressure 92 mmhg, and heart rate is 70 beats per minute.
a. Sketch the missing blood flow velocity signal through the mitral valve of the normal heart in panel A of the figure. Explain the shape of your drawing. b. Calculate left ventricular ejection fraction during both normal hemodynamic function and during 10% aortic valve insufficiency. c. Sketch the missing aortic pressure signal during 10% aortic valve insufficiency in panel B of the figure. Explain the shape of your drawing and the potential differences with the normal signal. d. Patients with acute aortic insufficiency often suffer from pulmonary oedema (= longoedeem). Explain how acute aortic insufficiency can cause pulmonary oedema. Make use of the pressure signals in panel B. e. Sketch the missing blood flow velocity signal through the insufficient aortic valve in panel C of the figure. Explain the shape of your drawing. f. Calculate how much blood leaks back into the left ventricle per cardiac cycle in the heart with 10% aortic valve insufficiency. g. Strike out what does not apply: Aortic valve insufficiency primarily increases preload/afterload of the left ventricle.
4. Omdat het linker ventrikel de grootste massa heeft, wordt in deze opgave het hele hart samen als een afgeknotte ellipsoïde beschouwd. Voor de elektrische activatie van dit hart nemen we aan dat er slechts twee spierlagen zijn van elk één cel dik. De activatie van de binnenlaag is gelijktijdig. Dit geldt ook voor de buitenlaag. Hieronder vind je het verloop van de actiepotentialen van de binnen- en buitenlaag. a. Benoem de fasen in een actiepotentiaal. b. Geef de fasen aan in de tekening. c. Geef per fase aan wat de belangrijkste ion-stromen zijn. d. Reconstrueer in de onderste grafiek het ECG-signaal in afleiding II (in tijd kwantitatief, in voltage kwalitatief). e. Beargumenteer hoe je tot de reconstructie in d. bent gekomen. end of the exam