The influence of Ca2+ and Nitroprusside on the opening kinematics of the mitral valve

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The Influence of Ca

2+

and Nitroprusside on the

Opening Kinematics of the Mitral Valve

Charlotte Oom

2006-01-20

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The Influence of Ca

2+

_{and Nitroprusside on the}

Opening Kinematics of the Mitral Valve

Examensarbete utfört i Medicinsk Teknik

vid Tekniska högskolan i Linköping

av

Charlotte Oom

LITH-IMT/BMS20-EX–06/417–SE

Handledare: Katarina Kindberg

imt, Linköpings universitet

Examinator: Matts Karlsson

imt, Linköpings universitet

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Linköpings tekniska högskola

Institutionen för medicinsk teknik Rapportnr: LiTH-IMT/BMS20-EX--06/417--SE

Datum: 2006-01-20

Svensk titel

Påverkan av Ca

2+

och Nitroprussid på mitralisklaffens öppningskinematik

Engelsk titel

The Influence of Ca

2+

and Nitroprusside on the Opening Kinematics of the Mitral

Valve

Författare

Charlotte Oom

Uppdragsgivare:

IMT

Rapporttyp:

Examensarbete

Rapportspråk:

Engelska

Sammanfattning (högst 150 ord). Abstract (150 words)

During a cardiac cycle the cardiac walls change between contracted and relaxed and the

valves open and close in response to pressure changes. This master thesis is a study of the

changes in heart movement pattern caused by intravenous injections of Ca

2+

or

Nitroprusside. At Stanford University radiopaque markers have been surgically implanted

in the walls and in the mitral valve of ovine hearts and 3D coordinates for each marker have

been constantly measured during the cardiac cycle. By using MatLab, the volume and

pressure of the left ventricle and several parameters related to the opening kinematics of the

mitral valve have been analyzed. The results show, among others, that both Ca

2+

and

Nitroprusside reduce the volume and pressure of the left ventricle and that both substances

decrease the size of the mitral annular ring. It was also shown that Ca

2+

delays the opening

of the mitral valve.

Nyckelord (högst 8)

Keyword (8 words)

mitral valve, opening, calcium, nitroprusside

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Abstract

During a cardiac cycle the cardiac walls change between contracted and relaxed and the valves open and close in response to pressure changes. This master thesis is a study of the changes in heart movement pattern caused by intravenous injec-tions of Ca2+ _{or Nitroprusside. At Stanford University radiopaque markers have}

been surgically implanted in the walls and in the mitral valve of ovine hearts and 3D coordinates for each marker have been constantly measured during the cardiac cycle. By using MatLab, the volume and pressure of the left ventricle and several parameters related to the opening kinematics of the mitral valve have been ana-lyzed. The results show, among others, that both Ca2+_{and Nitroprusside reduce}

the volume and pressure of the left ventricle and that both substances decrease the size of the mitral annular ring. It was also shown that Ca2+_{delays the opening of}

the mitral valve.

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Acknowledgements

There have been many people supporting and encouraging me during the work with this thesis. First of all I would like to thank my supervisor, Katarina Kindberg, who, with great knowledge in the area, has always been available for discussion and support. I would also like to thank my enthusiastic and helpful examinator, Matts Karlsson, for giving me a great number of new ideas and also for making me feel like a part of the larger research project. A third person that has been important in this work is Carl-Johan Carlhäll MD, PhD, who has contributed with valuable information on the cardiac anatomy and physiology and helped me finding relevant literature.

Thanks to all my friends also doing their master theses at IMT, my days have been filled with joy and laughter and therefore they deserve to be mentioned here too. Finally, I want to thank my boyfriend, Erold, for encouraging me in my work and helping me when needed.

Charlotte Oom

Linköping, January 2006

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Introduction

During a cardiac cycle action potentials in the cardiac walls cause the muscle fibres in the myocardium to contract, the space surrounded by the contracting wall decreases and blood is pushed through a valve into the next chamber. Leaflets in the valves open and close in response to pressure changes in order to let the blood through.

1.1 Aims of this Master Thesis

The purpose of this thesis work is to, by the use of surgically implanted radiopaque markers, study the effect that Ca2+_{and Sodium Nitroprusside (NIP) have on the}

opening kinematics of the mitral valve in an ovine heart. Parameters such as left ventricular pressure and volume, end-systolic-pressure-volume relationship, the curvature of the leaflets and different angles during opening will be analyzed and compared with negative controls.

The normal behavior of the mitral valve during opening has previously been stud-ied using this array of markers [9], but no study has previously been made on the effect of Ca2+ _{and NIP using marker technique and hence these results might be}

important for future research.

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Chapter 2

Anatomy and Physiology

2.1 Anatomy

The heart has four chambers, two atria and two ventricles (fig. 2.1). The right atrium receives blood from three veins, the superior vena cava, the inferior vena cava and the coronary sinus, all bringing deoxygenated blood back from the tis-sues. Blood passes from the right atrium through the tricuspid (=three leaflets) valve into the right ventricle and further through the pulmonary valve into the pulmonary trunk. Via the pulmonary trunk the blood reaches the lungs where it is reoxygenated before it returns to the left atrium via four pulmonary veins. From the left atrium the oxygenated blood passes through the mitral valve (also called the bicuspid (=two leaflets) valve) into the left ventricle and further through the aortic valve into the aorta. The aorta divides into smaller arteries which carry the blood to all different tissues in the body. The valves connecting atria and ventricles are called atrioventricular, AV, valves whereas the valves connecting the ventricles with aorta (left) or the pulmonary trunk (right) are called semilunar, SL, valves.

The thickness of the myocardium of the four chambers varies according to the function of each chamber. The walls of the ventricles are thicker than the walls of the atria because the ventricles pump the blood a greater distance. Also, since more force is required to pump blood to all other parts of the body than is required to pump blood to the lungs, the myocardium of the left ventricle is thicker than that of the right ventricle. The valves of the heart are composed of dense con-nective tissue covered by endocardium. The cusps of the bi- and tri-cuspid valves are connected to tendon-like cords, called chordae tendineae, which, in turn, are connected to the top of cone-shaped trabeculae carneae, called papillary muscles. The root of the papillary muscles are attached to the inside of the walls of the ventricles (see fig. 2.1). There are two major sets of chordae; first order chordae, which insert on the leaflet edges, and second order chordae, which are larger and attach to the anterior leaflet belly [16].

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4 Anatomy and Physiology

PSfrag replacements

Aortic valve Aorta

Pulmonary Trunk

Left Atrium (LA) Mitral valve Chordae Tendineae Papillary muscle Left Ventricle (LV) Apex Pulmonary valve Right ventricle (RV) Tricuspid valve Right atrium (RA)

Figure 2.1. Anatomic map of the heart [1].

All the valves in the heart open and close in response to pressure changes. When the pressure in the blood-containing compartment exceeds that of the next com-partment the valve will open and let the blood through. When the AV valves (mitral and tricuspid) are open the cusps point into the ventricle. When the valve is open the papillary muscles are relaxed and the chordae tendineae are slack. When the ventricle contracts the cusps are forced to close due to the pressure of the blood. The papillary muscles contract and the chordae tendineae become taut to prevent the cusps from opening into the atrium. [12, 17]

2.2 Physiology

2.2.1 The Cardiac Conduction System

The electrical activity in the heart is due to specialized cardiac muscle fibres that excite themselves, called autorythmic fibres. These fibres repeatedly generate ac-tion potentials that propagate through the conducac-tion system and trigger heart contractions. The propagation sequence starts with cells in the sinoatrial (SA) node, located in the right atrial wall, depolarizing spontaneously to the threshold value. The depolarization triggers an action potential which propagates through both atria via gap junctions in the intercalated discs of atrial muscle fibres and causes the atria to contract. The action potential continues into the AV node in the septum between the two atria and enters the AV bundle, which is the only place where it can conduct from the atria to the ventricles. In the ventricles it enters both right and left bundle branches and propagates through the bundles in

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2.2 Physiology 5

the septum towards the apex of the heart (see fig. 2.1). Next, large Purkinje fibres conduct the action potential from the apex upward to the rest of the ventricular myocardium, which causes the ventricles to contract.

The atrial and ventricular fibres that are excited by the action potentials in the SA node are called contractile fibres. Contractile fibres have a stable resting mem-brane potential close to -90 mV. The onset of an action potential in a contractile fibre is caused by a rapid depolarization to about 20 mV due to Na+ _{inflow when}

voltage gated fast Na+ _{channels open. Next, voltage-gated slow Ca}2+ _channels

open and some K+_{channels close which cause Ca}2+_{to flow in and thus}

depolariza-tion is maintained for a short period until K+_{flows out through K}+_{channels and}

repolarization occurs. In a cardiac muscle the refractory period (the period during which a second contraction cannot be triggered) lasts longer than the contraction itself. This prevents tetanus. [17]

2.2.2 Volumes in the Heart

In a normal human heart the atrial systole contributes a final 25 mL of blood to the volume already in each ventricle (about 105 mL). At the end of atrial systole (and ventricular diastole) each ventricle contains about 130 mL. This is the end-diastolic volume, EDV, and the pressure in the ventricle at this time is called the end-diastolic pressure, EDP. At the beginning of the ventricular systole both the SL and the AV valves are closed. This is a period of isovolumetric contraction. When the pressures in the left and right ventricles exceed that of the aorta (80 mmHg) and pulmonary trunk (20 mmHg) respectively, the SL valves open and the ventricular ejection period starts. The pressures in the left and right ventricles keep rising to about 120 mmHg and 25-30 mmHg respectively. The volume remaining in each ventricle at the end of systole is the end-systolic volume, ESV, about 60 mL. The pressure at this point is called the end-systolic pressure, ESP. The volume ejected per beat is called the stroke volume, SV, and is calculated according to equation 2.1.

SV = EDV − ESV (2.1)

Cardiac output, CO, is the volume of blood ejected from the ventricle to the aorta or pulmonary trunk during each minute.

CO [mL/min] = SV [mL/beat] ∗ HR [beats/min] (2.2) (HR = Heart rate)

Example 2.1: Ex. Cardiac output for a typical resting adult

A typical resting adult has a stroke volume of 70 mL/beat and a heart rate of 75 beats/min. Hence the cardiac output for a typical resting adult is 5.25 L/min.

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There are three factors that regulate the stroke volume and ensure that the left and right ventricles eject equal volumes of blood. These are preload, contractility and afterload. The preload is the degree of stretch of the cardiac muscle fibres before they contract, the contractility is the forcefulness of the contraction of individual muscle fibres and the afterload is the pressure that must be overcome before the SL valves can open [17].

2.2.3 Cardiac Muscle Contraction and its Dependence on

Ca

2+

Each cardiac muscle is like a Russian doll where division into smaller units always seems to be possible. The muscle itself is composed of a large number of muscle cells called muscle fibres or myocytes. In turn each muscle fibre is built up by many myofibrils, a cylindrical structure often as long as the muscle itself. The myofibril consists of a chain of short contractile units called sarcomeres. A sar-comere is formed by an array of parallel and overlapping thin and thick filaments. The thin filaments are composed of actin and the thick filaments are composed of a specific muscle form of myosin II (see fig. 2.2).

All kinds of muscle contraction (skeletal muscle, smooth muscle and cardiac mus-cle) depend on the ATP-driven sliding of actin filaments against myosin II fila-ments. When an action potential reaches the plasma membrane of a muscle cell the electrical excitation spreads rapidly into the T-tubules, a series of membra-nous folds that extend inward from the membrane and around each myofibril. When voltage-sensitive proteins in the T-tubule membrane are activated by the incoming action potential, they trigger the opening of Ca2+_{-release channels in the}

sarcoplasmatic reticulum, which surrounds each myofibril like a web. Ca2+_starts

flooding into the cytosol and initiates contraction of all the myofibrils at the same time. The Ca2+ _{is then actively pumped back into the sarcoplasmatic reticulum}

by an ATP-dependent Ca2+_{-pump. The Ca}2+ _{dependence is due to a set of}

spe-cialized accessory proteins, tropomyosin and troponin in particular. Tropomyosin is a long molecule that binds along the groove of the actin helix whereas troponin is a complex of three polypeptides, T, I and C (T = Tropomyosin-binding, I = inhibiting, C = Ca2+_{-binding). Troponin I binds to actin and to troponin T. In a}

resting muscle the I-T-complex binds to tropomyosin and pulls it into a position along the actin filament in which it blocks the binding sites for myosin heads and thereby makes contraction impossible. When the level of Ca2+_{is raised troponin C}

binds up to four molecules of Ca2+_{and causes troponin T to let go of tropomyosin.}

Tropomyosin slides back into its groove, the myosin head binding sites are revealed and the myosin heads can walk along the actin filaments. [5, 17]

2.2.4 The Effect of Sodium Nitroprusside (NIP) on the Heart

Because of their ability to increase coronary blood flow, and hence increase oxy-gen supply to all parts of the heart, nitrates have been used to treat patients with chest pain (angina pectoris) due to coronary artery disease for over 100 years

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2.2 Physiology 7 PSfrag replacements Fibre Fibre Fibre Whole muscle Fibril

Myosin (thick) filament

Actin (thin) filament Sarcomere

Figure 2.2. A cardiac muscle is like a Russian doll where division into smaller units always seems to be possible. Muscle contraction occurs when the myosin filaments slide along the actin filaments in the sarcomeres.

[2]. The pharmacological action of Sodium Nitroprusside is relaxation of vascular smooth muscle which causes peripheral veins and, to a smaller extent, also arteries to dilate. When the peripheral veins are dilated their blood storing capacity is increased and there will be a reduction in the amount of blood returning to the heart and hence a decreased preload. Thus intervention of Sodium Nitroprusside is expected to cause a volume and pressure reduction in each chamber of the heart. The arteriolar dilation reduces systemic vascular resistance and hence decreases the afterload [3]. The consequence of a reduced afterload is an increase in stroke volume. Since NIP also affects the preload the stroke volume is not expected to increase when NIP is added but the ejection fraction (SV/EDP) is expected to increase.

Nitroprusside in the blood is metabolized to nitric oxide gas (NO) [15]. NO is also naturally released by endothelial cells when the hormone acetylcholine is se-creted. Since NO is gaseous it easily passes across membranes and into neighboring cells such as endothelial cells and underlying smooth muscle cells. Within the cells NO activates the enzyme guanylyl cyclase, stimulating it to convert GTP to cyclic GMP (cGMP). cGMP in turn causes phosphorylation of protein kinase, which de-creases cytosolic Ca2+ _{and produces smooth muscle relaxation in the walls of the}

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2.2.5 The Frank-Starling Mechanism (Length-Dependent

Ac-tivation)

"The heart has the intrinsic capability of increasing its force of contraction and therefore stroke volume in response to an increase in venous return. This is called the Frank-Starling mechanism." [10]. This characteristic is very unique for heart muscle as neither skeletal nor smooth muscle are able to alter their intrinsic in-otropic state. An increased venous return means an increased preload (i.e increased left-ventricular end-diastolic pressure (LVEDP) which causes the muscle fibres to stretch and thereby increases the length of the sarcomeres (see sec. 2.2.3). When the sarcomeres stretch the troponin-C-Ca2+_{-sensitivity will increase and hence the}

muscle fibres are caused to develop a larger tension. This effect is called

length-dependent activation. A Frank-Starling curve for a particular heart is a plot of

the stroke volume versus the left ventricular end-diastolic pressure (LVEDP). As stated by Frank-Starling an increased LVEDP gives an increased stroke volume, which holds true for all healthy ventricles. However the slope of the curve varies with the existing conditions on afterload and inotropy. For a given preload and increased afterload (higher pressure in aorta) the SV decreases. Inotropy has the opposite effect on the SV, a heart with high inotropy will be capable of producing a larger SV than a heart with low inotropy for a given preload. Figure 2.3 shows the variation of the mean Frank-Starling Curves for blocked control, Ca2+ _and

NIP (for an explanation on the interventions see sec. 3.1).

Figure 2.3.Variations in the Frank-Starling curve for blocked control, calcium and NIP. All curves are average for animals 8, 9, 10, 11, 14, 17, 18 and 21.

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Chapter 3

Material

3.1 Data Acquisition

In this study data has been acquired with an invasive method called marker track-ing. 36 radiopaque markers have been surgically implanted in chamber walls, leaflets and papillary muscles of 20 ovine (sheep) left ventricles and atria accord-ing to figure 3.1. This was done at Falk Cardiovascular Research Center, Stanford University School of Medicine, Stanford, CA, USA. Markers were surgically im-planted in 20 sheep, 9 of which who died either during or after the operation. 10 of the remaining 11 animals have been used for this study. In some of the animals in the study one or more markers have been lost and hence those animals were not suitable to use when studying parameters which depended on the position of a lost marker. (For example the distance between markers 34 and 35 (D3435) cannot be measured if marker 34 is missing.) Although those animals have still been used when studying other parameters. Hence different sets of animals have been used depending on the parameter.

The ovine heart was chosen for this project because of its anatomic similarity to the human heart and its highly consistent, reproducible anatomy, function, and patterns of dysfunction [9]. After the operation the sheep were allowed to rest for a couple of weeks before data acquisition started. For detailed information on the surgery and data acquisition see [9]. By X-ray video tracking of the markers from two different angles every 16.7 ms 3D coordinates for each marker was obtained at 60 Hz. During data acquisition of the marker coordinates the LVP and the sur-face lead electrocardiogram, ECG, were also analogously acquired on two channels. The first recorded set of data for each sheep is a control which shows the nor-mal state of the heart after implanting the markers. Next beta blockers (Esmolol, UL-FS 49 and Atropin 1_{) have been added in order to slow down the heart rate}

1_{Carljohan Carlhäll MD, PhD., Div. Clinical Physiology, Dept. of Medicine and Care, Center}

for Medical Image Science and Visualization, Linköping University Hospital, S-581 85 Linköping, Sweden; Private communication

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10 Material

and hence facilitate further observations. In this work the set of data where beta blockers have been added is called a blocked control. During the rest of the day each sheep was subjected to a series of interventions to the heart according to table A.1 in the appendix. After each new intervention some time was allowed to pass before a negative control was made and a new intervention could be carried out. Ca2+ _{was added intravenously to the animals by bolus injection of CaCl}

(15mg/kg) [13]. Sodium Nitroprusside was intravenously infused during afterload reduction (0.5-8 µg/kg/min depending on the condition of the sheep) [11]. The negative control that was made before intervention with Ca2+ _{has been called}

control Ca2+_{etc. In this study 5 sets of data have been used; blocked control (blk}

ctrl), control Ca2+_{(ctrl Ca), Ca}2+ _{(Ca), control NIP (ctrl NIP) and NIP (NIP).}

At each of the interventions mentioned above four runs of data collection were made. During the second, third and fourth runs the heart was subjected to Vena Cava occlusions which means that the blood flow through the Vena Cava is de-creased. With these four runs it is possible to study a large number of parameters involved in the opening of the mitral valve. One of them is the distance between the leaflet edges (markers 34 and 35) which is plotted for a typical animal in fig. 3.2.

(a) Left ventricle (1-3, 5-7, 9-10 and 12-13) and atrium (4, 8, 11, 14) and the mitral annular ring (15-22).

(b) The mitral annular ring (15-22) and the anterior (31-34) and posterior (35-36) leaflets.

Figure 3.1. Schematic picture of the positions of the markers in the left ventricle and atrium and in the mitral annulus.

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3.2 Parameter Calculations 11

Figure 3.2. Distance between leaflet edges (markers 34 and 35) for animal 12. (Opening of the valve occurs at t=0, see sec. 4.1.)

3.2 Parameter Calculations

All parameter calculations have been made in MatLab 7.0.1 (the MathWorks, Inc.) and Mathematica 5.2 (Wolfram Research, Inc).

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Chapter 4

Method

4.1 Setting the Interval

To reduce the amount of data a time interval of 333 ms was chosen for the study. Because several of the main parameters of interest are related to the opening of the mitral leaflets the interval was chosen to include the time of opening. It was of great importance to choose the sample points in the interval in a way so that the intervals from different beats become comparable. This was done using the LVP as a reference and will be described below.

In order to determine the time at which opening of the mitral leaflets occurs the LVP and the LAP were plotted in the same plot (fig. 4.1). Since no common reference level had been used when collecting these data some modification was required. As previously mentioned (sec. 2.1) the leaflets open when the pressure in the atrium rises above that of the ventricle and close when the atrial pressure has decreased enough to be exceeded by the ventricular pressure. For each animal the level of the atrial pressure curve was modified according to known models of how the two pressures are supposed to interact [17]. By studying LVP and LAP for each animal it was assumed that the LVP at the time of opening can be esti-mated using LV Pmax and LV Pminfor each beat and computing a quantity called

LV Plow.

LV Plow= LV Pmin+ 0.15(LV Pmax− LV Pmin) (4.1)

The time sample immediately following LV Plow in each beat was assigned t = 0

and 10 sample points on each side of t = 0 were included in the interval (see fig. 4.1).

There are several other ways that t = 0 could have been chosen. The reason for choosing the sample immediately following LV Plowas opposed to that immediately

preceding LV Plow was that the pressure curve after LV Plow is flatter, i.e. the

values of the pressure differ less between two adjacent samples and the difference in the pressure in t = 0 will become more equal in two different beats. Another

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14 Method

choice would have been to assign t = 0 to the sample point that is closest in pressure to LV Plow, whether preceding or following. This would probably have

given a rather similar range of pressures in t = 0 as in the choice made and might be an option if the study is remade.

Figure 4.1. Left ventricular and atrial pressure and LV Plowfor animal 12.

4.2 Parameter Investigation

Each parameter has been investigated using the same scheme. The values of the chosen parameter were determined for each sample in the chosen interval (21 samples) and for all beats available (1-3 beats depending on the file). For each sample the "average beat behavior" was calculated using all beats available. The standard error of the average beat has not been taken into account. The average beat was computed for all animals and the "average animal behavior" was determined by calculating the mean of all animals in each sample. The standard error (SE) of the mean was calculated and plotted as error bars in the average animal curve. SD = q PN i=1(Xi− ¯X)2 N (4.2)

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4.2 Parameter Investigation 15

SE =√SD

N (4.3)

where Xi is the value for animal i, ¯X is the mean of all animals and N is the

number of animals used in the study.

Example 4.1: Investigation of the LVP

Figure 4.2 illustrates how each parameter is investigated using the LVP as an example. First LVP for each sample in the interval was calculated (fig. 4.2a). This run has three beats. The average behavior for the LVP was calculated using the three beats in fig. 4.2a, leading to fig. 4.2b. This was done for all animals (fig. 4.2c) and finally the average behavior and the standard error for LVP for all animals were calculated (fig. 4.2d).

These steps were carried out for the intervention as well as for the relevant con-trol. Their values in each sample point were compared by a Student’s t-test on a 5 % significance level, i.e. in each sample point the "average beat values" for all animals in the intervention run were tested against the "average beat values" for all animals in the control run. For those cases where the Student’s t-test returned ’true’ the difference between the intervention and the control run were said to be significant.

In addition to the sample-sample t-test, where the value of each sample in the control run was tested against the value of the same sample in the test run, some local changes during the interval were also sometimes studied, depending on the behavior of the parameter. Examples of local changes are the difference between the maximal and minimal value during the interval (called the total range) and the difference between the first and last sample in the interval (called the total

change). For one single parameter the difference between the maximal value and

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16 Method

(a) LVP for animal 10. Only the samples that are included in the relevant interval are shown. The sample in each beat that has been assigned t=0 is indicated with an arrow.(This particular file contains three beats.)

(b) Average left ventricular pressure for an-imal 10. Each sample in the average beat curve is the average of three samples from fig. a.

(c) LVP curves for all relevant animals. (Animals 7, 8, 9, 10, 11, 12, 14, 17, 18 and 21.)

(d) LVP for the animals in c (mean±SE)

Figure 4.2.Illustration of the investigation scheme using LVP as an example. All plots are for blocked control.

4.3 Statistics

The two-sample t-test is used to determine whether two population means are equal or different. In this study, the control group consists of the same animals as the test group and hence there was a one-to-one correspondence between the values in the two groups and a paired t-test was used. In a paired t-test the differ-ence in mean for the two groups is first calculated. The mean of the control group is written ¯X and the mean for the test group ¯Y . Hence the difference between the means, which is also called the signal, is ¯X − ¯Y .

For animal number i the values obtained in the control run (X) and the test run (Y) will differ from the mean with ˆXi and ˆYi respectively.

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4.4 End-Systolic Pressure-Volume Relationship (ESPVR) 17

ˆ

Xi= (Xi− ¯X) (4.4)

ˆ

Yi= (Yi− ¯Y ) (4.5)

The noise can then be calculated as: s

PN

i=1( ˆXi− ˆYi)2

N (N − 1) (4.6)

The test value, t, is then obtained simply by calculating the signal-to-noise ratio: t = r X − ¯¯ Y PN i=1( ˆXi₋Yˆi)2 N(N −1) (4.7)

where N is the number of parameters, i.e the number of runs that have been used for the t-test. (If, for example, a group of 7 animals were used N would be equal to 14 since each animal has been used twice.)

In order to interpret the test value the significance level on which the test is to be carried out has to be chosen. In this study p<0.05 has been used as significance level and p<0.08 has been regarded as near significant. The critical t, tc, can then

be obtained using statistical tables. If tc is smaller than the test value, t, the

difference between the two groups is significant on the selected significance level [14, 18]. The paired t-test was used to test the results from the negative control run against the results from the intervention.

4.4 End-Systolic Pressure-Volume Relationship

(ES-PVR)

Since each animal has undergone a series of different interventions during the day of observation it was of great importance to control the health of the hearts before each new test. In this case the contractility of the left ventricle was used as a mea-surement of the maintained health. In a completely healthy heart the contractility would remain constant throughout the day. Here, the end-systolic pressure-volume relationship (ESPVR), derived from left ventricular pressure-volume loops, has been used to measure the ventricular contractility [4].

When the pressure of a chamber is plotted against the volume of the same chamber a pressure-volume (PV) loop is achieved. For each animal and each intervention left ventricular PV loops for all the Vena Cava occlusions were plotted in the same figure (fig. 4.4). By using the MatLab function polyfit the end-systolic (ES) points of each PV loop were connected with a straight line. The slope of this line is the ESPVR for that particular animal after that particular intervention and the

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18 Method

average ESPVR for each intervention could be calculated1_.

From the LVP-plot the ES-point was calculated as follows: The LVP and its first and second derivatives were plotted in the same plot (see fig. 4.3). The deriva-tives were calculated with the MatLab function conv. For each beat there are two second derivative distinct minima, one before the top of the LVP curve and one after the top. The ES-point can be found immediately after the top and hence the second minima of the second derivative was used as an indicator. To make sure that the program picked the second minima and not the first a requirement of a negative first derivative was added. The sample point immediately before the sample point that gave the second minima of the second derivative was used as ES-point.

Figure 4.3. LVP, dLVP/dt and d2

LVP/dt2

plotted in the same figure in order to calculate the ES-point. Solid arrows indicate the second minima of d2

LVP/dt2

and dashed arrows indicate the calculated ES-point in each beat. The values shown are taken from animal 10.

1_{No ESPVR could be calculated for the blocked control run in animal 7 since no Vena Cava}

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4.5 Volume of the Left Ventricle (LVV) 19

Figure 4.4. Pressure-Volume loops for all 4 runs for animal 9, blocked control. The ES points have been connected with a straight line.

4.5 Volume of the Left Ventricle (LVV)

The volume of the left ventricle (LVV) was measured for each sample in the interval by adjusting a convex hull to the marker positions 1, 2, 3, 5, 6, 9, 10, 12, 13, 15, 16, 17, 18, 19, 20, 21 and 22 (see fig. 3.1a). This was done with the MatLab function convhulln. All those markers are located in the outer wall of the left ventricular and in the annulus. Marker 7 has been left out because of its uncertain position in the aortic root. Three of the animals used in the study had lost one of the relevant markers (see tab. A.1 in the Appendix). However, since this study does not focus on measuring the exact volume but rather on studying changes in volume in the individual animals, those animals with lost markers will be used when studying the volume.

4.6 Distance Between Two Markers

A program was designed to measure the 3D distance between two markers, i.e. the shortest way between the two. This program was used to calculate two distances across the annulus; using markers 18 and 22 (D1822) or markers 16 and 20 (D1620), and the distance between the leaflet edges using markers 34 and 35 (D3435). The distance, d, between point 1, (x1, y1, z1), and point 2, (x2, y2, z2), has been

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20 Method

d =p(x1− x2)2+ (y1− y2)2+ (z1− z2)2 (4.8)

4.7 Defining Moment of Opening

In this study two different methods have been used in order to define the moment when the leaflets open. The first method was used when the mean moment of opening for many animals was to be calculated, whereas the second method was used when the exact moment of opening for one beat was required. The distance between markers 34 and 35 was used to define the moment of opening in both methods.

4.7.1 Method 1 - Mean Moment of Opening

The leaflets were regarded as closed for all samples where there was no significant difference between the distance D3435 of one sample compared to the immediately preceding sample. To avoid errors caused by local random changes in D3435 that occur before the actual opening the significance level used here was set to 1%.

4.7.2 Method 2 - Moment of Opening for one Animal

In this method it has been assumed that opening does not occur in any of the first 10 samples in the interval. (This assumption has been justified by the graphs of the average distance between markers 34 and 35 which show that D3435 is always constant during the first 10 samples for control Ca2+_{, Ca}2+_{, control NIP, and NIP}

(fig. 5.10)). For each beat the mean D3435 for the first 10 samples in the interval was calculated. Starting at sample 11 the leaflets were defined open in the first sample where the distance was larger than 1.4 times the calculated average, i.e. 40% longer than for the closed state.

4.8 Movement Pattern of the Leaflets

During a cardiac cycle the annulus changes position. In order to be able to study the movement of the leaflets as if the annulus was not moving a moving internal Cartesian reference system was introduced (fig. 4.5). First the origin was placed at the midpoint of the line joining markers 22 and 18. A line was drawn between the origin and the apical marker 1; this line became the y-axis with positive direction towards the base of the heart (away from the apex). Markers 18 and 22 were projected onto the y=0-plane and a line between these two projections constituted the x axis with its positive direction towards the projection of marker 18. The z axis was defined by taking the cross product of the x and y axes. By doing this markers 18 and 22 will always be in the z=0-plane. In each time frame a new reference system was calculated and the original coordinates of the leaflet markers 18, 22 and 31-36 were translated and plotted in the xy- and xz-plane respectively.

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4.8 Movement Pattern of the Leaflets 21 X Z 18 22 1 Y

Figure 4.5. The new moving cartesian reference system. The white point indicates the origin of the new coordinate system.

4.8.1 Curvature (κ) in the xy-plane

One way of studying the movement pattern of the leaflets was by calculating the curvature for three markers at a time. The leaflets were divided into three sets of markers; upper anterior leaflet (markers 22, 31 and 33), lower anterior leaflet (markers 32, 33, 34) and posterior leaflets (markers 18, 36, 35), see fig. 3.1b. For each set the radius of curvature (RoC) was calculated at each time frame. The RoC is defined as the radius of an imaginary circle that the three points lie on. Calculation of the RoC was done using the new moving coordinate system. For each set the markers in the order mentioned above will be referred to as point 1, 2 and 3. (Eg. for the upper anterior leaflet marker 22 is point 1, marker 31 is point

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22 Method

2 and marker 33 is point 3.)

The new moving coordinate system was regarded as 2D, using only the x and y coordinates (i.e. projecting each point on the z=0-plane). The first step was to find the center of the imaginary circle. Using the fact that the distances from each of the three points to the center are equal renders two equations with two unknown parameters - the x- and y-coordinate of the center point (see eq. 4.9 and 4.10).

x = x

2

3(y1− y2) + (x21+ (y1− y2)(y1− y3))(y2− y3) + x22(−y1+ y3)

2(x3(y1− y2) + x1(y2− y3) + x2(−y1+ y3)) (4.9) y = −x 2 2x3+ x21(−x2+ x3) + x3(y12− y22) 2(x3(y1− y2) + x1(y2− y3) + x2(−y1+ y3))+ + x1(x 2 2− x23+ y22− y23) + x2(x23− y21+ y23) 2(x3(y1− y2) + x1(y2− y3) + x2(−y1+ y3)) (4.10)

By solving the equations the coordinates of the center could be determined and the size of the RoC was described by the distance from either of the three points to the center.

In order to determine the direction of the RoC, i.e. whether the curve was bent towards the other leaflet (positive direction) or away from the other leaflet (nega-tive direction) the "right hand rule" was used (fig. 4.6). Two vectors were created, vector ¯a pointing from point 2 towards point 1 and vector ¯b pointing from point 2 towards point 3. To the 2D vectors, ¯a and ¯b, a z-coordinate =0 was added and the cross product between the two was calculated. The "right hand rule" says that if the z-coordinate of the cross product is positive the closest way of turning vector ¯a into vector ¯b is in the anti-clockwise direction and if the z-coordinate is negative the closest way is the clockwise direction. Hence a positive z-coordinate indicates a negative direction of RoC if calculated for either of the two anterior leaflet sets and a positive direction of RoC for the posterior leaflet set, whereas a negative z-coordinate indicates a positive direction for the anterior sets and a negative direction for the posterior set.

Since a plot of the radius versus time would "jump" from positive infinity to neg-ative infinity (or the other way around) each time the imaginary center shifts side of the curve, the inverse, the curvature, κ, was plotted against time instead.

κ = 1/RoC (4.11)

A large value of κ indicates a large curvature and hence the plot becomes continuous, without jumps.

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4.8 Movement Pattern of the Leaflets 23 1 3 2 3 2 1

Negative z-coordinate Positive z-coordinate

PSfrag replacements ¯ a ¯ a ¯b ¯b

Figure 4.6. Illustration of the direction of the radius of curvature. Left: Negative z-coordinate, ¯ax¯b points in to the picture. If this was the anterior leaflet the direction of the RoC would be positive and if it was the posterior leaflet the direction would be negative. Right: Positive z-coordinate, ¯ax¯b points out of the picture. If this was the posterior leaflet the direction of the RoC would be positive and if it was the anterior leaflet the direction would be negative.

4.8.2 Angles Between Leaflet Markers and Septal-Lateral

Axis (θ

31−34

and θ

35−36

)

As a second way of studying the movement of the leaflets during opening six different angles were calculated at each time frame (fig. 4.7). Marker vectors were constructed joining each marker in the anterior leaflet (31-34) with marker 22 and joining each marker in the posterior leaflet (35-36) with marker 18. By measuring the 3D angle between a vector connecting markers 18 and 22 (the septal-lateral axis) and each one of the marker vectors six angles were obtained; θ31, θ32, θ33

and θ34for the anterior leaflet and θ35and θ36for the posterior leaflet. The angles

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24 Method 22 31 33 34 32 18 35 36 16 20 PSfrag replacements θ31 _θ 32 θ33 θ34 θ35 θ36

Figure 4.7. Illustration of how θ31−36 were calculated.

4.8.3 Angular Velocity for Marker 34 around Marker 32,

dα/dt

A third parameter that was used to study the opening pattern of the leaflets was the angular velocity of the tip of the anterior leaflet. Marker 32 was used as a pivot point and the velocity with which marker 34 moved around marker 32 was measured. To be able to do this the coordinate system once again had to be shifted. A new 3D moving coordinate system was arranged where marker 32 was always in the origin and where the x-, y- and z-axes kept the same directions as the axes in the coordinate system used when data was collected. One vector joining markers 32 and 34 was created for the closed state, ¯c, using the coordinates of markers 32 and 34 in the first sample of the interval. Similarly vectors between markers 32 and 34 were created for each one of the samples where the leaflets were defined open according to method 2 (section 4.7.2), denoted ¯d1, ¯d2, ¯d3, etc. For

each one of the time frames with open values the angle α between vectors ¯c and ¯

di was defined according to equation 4.12.

α = arccos(¯c · ¯di) = arccos(

¯ c ¯di

| ¯c || ¯di|

) (4.12)

By using the α(t)-curve for one animal the angular velocity could be estimated as dα/dt. A positive angular velocity is obtained when the leaflets are opening and a negative angular velocity is obtained when they are closing.

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Chapter 5

Results

Here the results from all parameters mentioned in the method section will be presented. In order to facilitate interpretation of the graphs the left ventricular pressure during the interval has been plotted as a third curve in all figures.

5.1 End-Systolic Pressure-Volume Ratio, ESPVR

The average ESPVR for control Ca2+_{, Ca}2+_{, control NIP and NIP are shown in}

table 5.1 and figure 5.1. As expected, according to the Frank Starling mechanism (see sec. 2.2.5), ESPVR increased significantly when the inotropic agent Ca2+_was

added. No significant change was seen under the intervention of NIP.

Figure 5.1. Graphical illustration of tab. 5.1: Average End-Systolic Volume-Pressure Ratio, ESPVR (mean±SE) for animals 8, 9, 10, 11, 14, 17, 18 and 21. *p<0.05

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26 Results

Ctrl Ca2+ _Ca2+ _{Ctrl NIP} _NIP

ESPVR [mL/mmHg] 4.4 ± 1.0 6.7 ± 2.6 * 4.3 ± 1.0 4.8 ± 1.1 Table 5.1. Average End-Systolic Pressure-Volume Ratio, ESPVR (mean±SE) for ani-mals 8, 9, 10, 11, 14, 17, 18 and 21. *p<0.05

5.2 Left Ventricular Pressure (LVP)

Figure 5.2 shows the LVP for Ca2+_{, NIP and their controls. When Ca}2+_{was added}

to the heart there was no significant change in the LVP during the first half of the interval. Starting at sample 12, however, the pressure in the calcium affected ventricle was constantly significantly lower than its control until the end of the interval. When NIP was added the left ventricular pressure was significantly lower in each sample during the whole interval, except in the last sample. According to fig 5.2 b, the average maximum pressure for the NIP affected ventricle is only about 70 % of that of the normal state. When the total change of pressure for Ca2+ _{and NIP were compared with their controls (see tab. 5.2 and fig. 5.2) a}

significant difference from the control run was seen for the intervention with NIP but not for Ca2+_{. (For a review on total change and total range of volume see}

sec. 4.2.)

(a) LVP for ctrl Ca2+

and Ca2+

(b) LVP for ctrl NIP and NIP Figure 5.2. LVP (mean±SE) for animals 7, 8, 9, 10, 11, 14, 17, 18, 21.

Tot. change -124.0 ± 5.0 -135.3 ± 11.6 -127.6 ± 5.9 -94.3 ± 3.3 * [mmHg]

Table 5.2. Total change of LVP (mean±SE) for control Ca2+_{, Ca}2+_{, control NIP and}

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5.3 Left Ventricular Volume (LVV) 27

Figure 5.3. Graphical illustration of tab. 5.2: Total change of LVP (mean±SE) for control Ca2+

, Ca2+

, control NIP and NIP. Animals 7, 8, 9, 10, 11, 14, 17, 18 and 21. *p<0.05.

5.3 Left Ventricular Volume (LVV)

Addition of either Ca2+_{or NIP caused the volume in the left ventricle to become}

significantly smaller in each sample of the interval (fig. 5.4). For both interventions there was also a clear difference in the total change of volume (tab. 5.3 and fig. 5.5). During the interval the LVV of the negative controls increased 4.1±1.1 and 4.5±1.1 mL respectively, whereas the LVV under intervention of NIP increased only with 1.0±1.1 mL and the LVV under intervention of Ca2+ _{decreased. The total range}

in each run was calculated and is also shown in table 5.3. The total range was significantly lower for NIP but not for Ca2+_.

(a) LVV for ctrl Ca2+

and Ca2+

(b) LVV for ctrl NIP and NIP Figure 5.4. LVV (mean±SE) for animals 7, 8, 9, 10, 11, 14, 17, 18, 21.

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28 Results

Tot. change [mL] 4.1 ± 1.1 -2.9 ± 1.5 * 4.5 ± 1.1 1.0 ± 1.1 * Tot. range [mL] 17.0 ± 0.8 18.7 ± 0.8 18.8 ± 0.8 17.1 ± 0.9 * Table 5.3. Total change and total range of LVV (mean±SE) for control Ca2+_{, Ca}2+_,

control NIP and NIP. Animals 7, 8, 9, 10, 11, 14, 17, 18 and 21. *p<0.05.

Figure 5.5. Graphical illustration of the LVV total chance in tab. 5.3. Control Ca2+_,

Ca2+

, control NIP and NIP. Animals 7, 8, 9, 10, 11, 14, 17, 18 and 21. *p<0.05.

5.4 Size and Shape of the Mitral Annulus

The distance between markers 18 and 22 (D1822) (fig. 5.6) proved to be signif-icantly shorter at each single time frame in the interval when Ca2+ _{was added}

and when NIP was added than for their controls. According to table 5.4 the to-tal change in D1822 during the interval became negative under intervention with Ca2+_{, which was a significantly different result from the positive value in the}

con-trol run. No significant difference in the total change was observed when NIP was added.

Just like D1822 the distance between markers 16 and 20 (D1620) (fig. 5.7) was significantly shorter during the whole interval when NIP was added compared to the normal state. When Ca2+ _{was added the distance was significantly shorter}

during the latter half of the interval (from sample 10). For both interventions the total change during the interval also decreased significantly (table 5.4).

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5.4 Size and Shape of the Mitral Annulus 29

(a) D1822 for ctrl Ca2+

and Ca2+

(b) D1822 for ctrl NIP and NIP Figure 5.6. Distance between markers 18 and 22 (mean±SE). Animals 7, 8, 9, 10, 11, 14, 17, 18 and 21.

(a) D1620 for ctrl Ca2+

and Ca2+

(b) D1620 for ctrl NIP and NIP Figure 5.7. Distance between markers 16 and 20 (mean±SE). Animals 7, 8, 9, 10, 11, 14, 17, 18 and 21.

The area of the annulus was significantly smaller at each time frame when Ca2+_or

NIP was added (fig. 5.8) and a significant decrease in the total change of the area during the interval was also observed for both interventions (table 5.4). These findings were expected since both D1822 and D1620 were shorter for both inter-ventions.

The shape, or ovality, of the mitral annulus was measured by calculating D1822/D1620. The closer to 1 the value of D1822/D1620, the more circular the annulus. For both controls D1822/D1620 was below one, i.e D1620 was longer than D1822. Adding Ca2+_{further decreased D1822/D1620 significantly in all samples and consequently}

the annulus became more oval. Adding NIP did not affect the ovality as much as adding Ca2+_{did, there was however a significant increase in ovality in the middle}

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dif-30 Results

ferent between either normal state and Ca2+ _{or normal state and NIP (table 5.4).}

(a) Area of annulus for ctrl Ca2+_{and Ca}2+ _{(b) Area of annulus for ctrl NIP and NIP}

Figure 5.8. Area of annulus. Animals 7, 8, 9, 10, 11, 14, 17, 18 and 21.

(a) Shape of annulus for ctrl Ca2+ _and

Ca2+

(b) Shape of annulus for ctrl NIP and NIP

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5.5 Distance Between Leaflet Edges, D3435 31 Ctrl Ca2+ _Ca2+ _{Ctrl NIP} _NIP D1822 [cm] 0.06 ± 0.03 -0.12 ± 0.03 * -0.02 ± 0.05 -0.13 ± 0.03 D1620 [cm] 0.14 ± 0.03 0.02 ± 0.05 * 0.11 ± 0.04 -0.02 ± 0.05 * An. area [cm2_] _{0.47 ± 0.04} _{-0.28 ± 0.05 *} _{0.19 ± 0.07} _{-0.38 ± 0.04 *} D1822/D1620 -0.01 ± 0.04 -0.04 ± 0.00 * -0.28 ± 0.00 -0.03 ± 0.00 Table 5.4. Total change of D1822, D1620, annular area and D1822/D1620 (mean±SE). Animals 7, 8, 9, 10, 11, 14, 17, 18 and 21. *p<0.05.

5.5 Distance Between Leaflet Edges, D3435

The variation in distance between markers 34 and 35 is shown in figure 5.10. The distances in samples 15 and 16 in the Ca2+_{run were significantly shorter than in}

the control. The maximum distance for the control run is reached at sample 16, whereas the maximum distance for the Ca2+ _{run is not reached until at sample}

17, i.e there is a time lag. For the NIP run there were no samples with significant difference from the control and they both reached their maximum D3435 in sample 16.

(a) Distance between leaflet edges for ctr Ca2+_{and Ca}2+

(b) Distance between leaflet edges for ctr NIP and NIP

Figure 5.10. Distance between leaflet edges (markers 34 and 35). Animals used are 7, 8, 9, 11, 14, 18 and 21.

5.5.1 Maximum Distance Between Leaflet Edges, max D3435

Since the values of D3435 between the samples are unknown it is impossible to know whether there really is a time lag for Ca2+_{or if the real maximum for both}

runs might be reached between sample 16 and 17. As a way to overcome this problem the maximum separation of markers 34 and 35 was calculated according to the normal scheme (see sec. 4.2). One average maximum separation with SE for

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32 Results

each intervention was achieved. The time for the maximum separation tmax₋sep

for each beat was stored and by using the defined moment of leaflet opening for the same beat (see sec. 4.7.2) a new variable, topen was defined as

topen= tmax−sep− tmoment−of−opening (5.1)

The maximum separation of the leaflet edges was plotted against topen for each

intervention and its control run (fig. 5.11). No significant difference were seen neither in topennor D3435maxfor any of the two interventions, but D3435maxwas

near significantly shorter for Ca2+ _{than for its control (see tab. 5.5).}

Even though there was no significant difference in topen at significance level 5%

there is a possibility that there is a significant difference in the time it takes from the start of the interval until the maximum separation of markers 34 and 35. By performing a t-test on tmaxsep it was however proved that the difference between

each intervention and their control was negligible, see table 5.5.

D3435max [cm] 2.58 ± 0.13 2.46 ± 0.13 ** 2.62 ± 0.14 2.56 ± 0.13

topen [sec] 0.03 ± 0.00 0.03 ± 0.00 0.03 ± 0.00 0.03 ± 0.00

tmax₋sep [sec] 0.25 ± 0.10 0.26 ± 0.38 0.25 ± 0.13 0.25 ± 0.25 Table 5.5. Maximum separation of leaflet edges, moment of opening and moment of maximum separation of leaflet edges (mean±SE). Animals 7, 8, 9, 11, 14, 18 and 21. **p<0.08.

(a) Ctrl Ca2+_{and Ca}2+ _{(b) Ctrl NIP and NIP}

Figure 5.11. Maximum separation of leaflet edges plotted against the time that has passed since opening when the maximum separation is reached (mean±SE). Animals 7, 8, 9, 11, 14, 18 and 21.

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5.6 Maximum Pressure Drop (-dP/dt|max) 33

5.6 _{Maximum Pressure Drop (-dP/dt|}

max

)

The maximum pressure drop, (-dP/dt|max), in the interval changed significantly

due to interventions with both Ca2+ _{and NIP (see tab. 5.6). Ca}2+ _{increased the}

maximum pressure drop with 14% whereas addition of NIP resulted in a large decrease with as much as 27%.

−dP/dt|max −61.3 ± 3.5 −69.7 ± 4.6* −67.9 ± 4.0 −49.3 ± 1.1*

[mmHg/sec]

Table 5.6. Maximum pressure drop, −dP/dt|max (mean±SE). Animals 7, 8, 9, 10, 11,

14, 17, 18 and 21. *p<0.05.

5.7 Movement of the Leaflets

In figure 5.12 the positions of the markers in the xy- and xz-plane in the new moving coordinate system are shown for four different sample points. It is clear that during opening the leaflets do not only move in the xy-plane but also in the

plane. However the main changes occur in the xy-plane and therefore the

xz-plane will be left out in the following comparisons.

(a) xy-plane (b) xz-plane

Figure 5.12. Movement of the mitral leaflets in four samples immediately after opening (mean±SE). Positions i,ii,iii and iv are samples 13, 14, 15 and 16 respectively (mean±SE). a, Movement in the xy-plane. b, Movement in the xz-plane. Animals 8, 9, 11, 14, 18 and 21.

Figures 5.13 and 5.14 a-d show the positions of the leaflets for an average Ca2+

affected heart and its control run. No regular significant difference between the two was observed by looking at the markers for one time frame at a time. However,

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34 Results

comparing the behavior of the anterior leaflets of the two during the whole sequence showed that the tip (markers 33 and 34) of the Ca2+ _{affected leaflet was lagging}

compared to the control. The control reached its fully open state in sample 16 whereas the Ca2+_{affected leaflet was not maximally open until in sample 17. The}

same phenomenon was observed after the fully open state is reached, the Ca2+

anterior leaflet again lagged behind the control towards the closed state. The same behavior was observed for the NIP affected leaflet (figures 5.15 and 5.16), but to a smaller extent. Another interesting observation is that for all runs there seems to be a joint in the anterior leaflet at marker 32.

(a) sample 13 (b) sample 14

(c) sample 15 (d) sample 16

Figure 5.13.Movement of leaflets during opening for ctrl Ca2+_{and Ca}2+_(mean±SE).

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5.7 Movement of the Leaflets 35

Figure 5.14. Movement of leaflets during opening for ctrl Ca2+

and Ca2+

(mean±SE). Samples 17-20 (samples 13-16 are shown in fig. 5.13). Animals 8, 9, 11, 14, 18, 21.

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36 Results

Figure 5.15. Movement of leaflets during opening for ctrl NIP and NIP (mean±SE). Samples 13-16 (samples 17-20 are shown in fig. 5.16). Animals 8, 9, 11, 14, 18, 21.

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5.8 Curvature (κ) in the xy-plane 37

Figure 5.16. Movement of leaflets during opening for ctrl NIP and NIP (mean±SE). Samples 17-20 (samples 13-16 are shown in fig. 5.15). Animals 8, 9, 11, 14, 18, 21.

5.8 Curvature (κ) in the xy-plane

Figures 5.17 and 5.18 show the curvature (κ) of the different predefined sections (marker sets 1, 2 and 3 according to sec. 4.8.1) of the leaflets at each time frame in the interval. No significant difference was observed in any time frame for any of the three sections when comparing the two interventions with their controls at one time frame at a time. However the time lag that was observed for both the Ca2+

and NIP affected leaflets when studying the movement of the leaflets (see section 5.7) was clearly visible in the figures for the curvature as well. In each one of the three marker sets for both Ca2+ _{and NIP the most curved state, either positively}

or negatively, is reached first by the control and about one time frame (1/60 sec) later by the intervention. (Marker set 2 affected by NIP is an exception).

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38 Results

(a) Anterior leaflet: Curvature (κ) for markers 22, 31 and 32 (marker set 1).

(b) Anterior leaflet: Curvature (κ) for markers 32, 33 and 34 (marker set 2).

(c) Posterior leaflet: Curvature (κ) for markers 18, 36 and 35 (marker set 3). Figure 5.17. Curvature for Ca2+

and ctrl Ca2+

(mean±SE). Animals 8, 9, 11, 14, 18, 21.

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5.8 Curvature (κ) in the xy-plane 39

(a) Anterior leaflet: Curvature (κ) for markers 22, 31 and 32 (marker set 1).

(b) Anterior leaflet: Curvature (κ) for markers 32, 33 and 34 (marker set 2).

(c) Posterior leaflet: Curvature (κ) for markers 18, 36 and 35 (marker set 3).

Figure 5.18. Curvature for NIP and ctrl NIP (mean±SE). Animals 8, 9, 11, 14, 18, 21.

For each marker set κmin, κmaxand the total range of curvature for the control and

the intervention were calculated. There was no significant difference in κdif f or

κmaxbetween neither control Ca2+and Ca2+nor between control NIP and NIP. A

significant difference was observed in κmin for marker set 1 between control Ca2+

and Ca2+_{, shown in table 5.7. Under the influence of Ca}2+ _{this section seems to}

be able to stretch out, become straight and even curve slightly negatively, whereas the unaffected leaflet stays positively curved.

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40 Results ctrl Ca2+ _Ca2+ _{ctrl NIP} _NIP Ms 22,31,32 κmax 1.39 ± 0.15 1.33 ± 0.15 1.36 ± 0.17 1.35 ± 0.15 κmin -0.00 ± 0.06 -0.33 ± 0.06 * -0.49 ± 0.08 -0.18 ± 0.13 Tot. range 1.40 ± 0.12 1.66 ± 0.15 1.84 ± 0.23 1.53 ± 0.15 Ms 32,33,34 κmax 1.46 ± 0.04 1.73 ± 0.07 1.49 ± 0.09 1.40 ± 0.05 κmin -1.09 ± 0.07 -0.92 ± 0.14 -1.07 ± 0.10 -0.88 ± 0.13 Tot. range 2.55 ± 0.07 2.65 ± 0.15 2.56 ± 0.08 2.27 ± 0.11 Ms 18,35,36 κmax 1.37 ± 0.08 1.28 ± 0.08 1.00 ± 0.13 1.40 ± 0.08 κmin -0.24 ± 0.18 -0.35 ± 0.22 -0.12 ± 0.17 -0.32 ± 0.22 Tot. range 1.61 ± 0.13 1.63 ± 0.17 1.11 ± 0.08 1.71 ± 0.18 Table 5.7.Maximal curvature (κmax), minimal curvature (κmin) and total range of

cur-vature for the three marker sets during the interval (mean±SE). All values are measured in cm−1_{. Ms = markers. Animals 8, 9, 11, 14, 18, 21. *p<0.05}

5.9 Leaflet Angles, θ

i

Figures 5.19 and 5.20 show the behavior of the angles θ31−36 during the interval.

Ca2+ _{seems to affect angles θ}

32−34 (fig. 5.19 b-d), i.e the middle part and tip of

the anterior leaflet. The effect of Ca2+ _{on these angles is the previously observed}

time lag. The widest open state of markers 32, 33 and 34 (the largest angle for θ32,33,34) for the control run is reached approximately one time frame (1/60 sec)

before that of the Ca2+ _{run and thereafter the angles of the Ca}2+_{affected leaflets}

follow the behavior of the control run, but still with a time lag. Ca2+ _{does not}

seem to have any equally obvious time lagging influence on θ31(fig. 5.19 a). Ca2+

does not have any time lagging effect on the angles in the posterior leaflet (θ35

and θ36) (fig. 5.19 e,f), but after θ has reached its maximal angle both posterior

angles close more slowly under the influence of Ca2+_{. This will be discussed later}

in this section.

The plots of the theta angles for NIP and its control (fig. 5.20) show no differ-ence for the anterior leaflet (θ31−34). The small time lag that was observed when

looking at the movement of the NIP affected leaflets in sec. 5.7 is not visible here. The posterior leaflet θ35−36, on the other hand, seems to behave a little differently

under the influence of NIP. Just as was observed for Ca2+ _{both θ}

35 and θ36 close

more slowly for the NIP run than for the control run and at the last sample in the interval θ35 is significantly larger for NIP than for its control and θ36 is near

significantly larger.

In order to study the behavior of the leaflets after maximal opening the difference between the maximum θ obtained during the interval and the value of θ in the last

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5.9 Leaflet Angles, θi 41

sample was calculated. A t-test was then performed between each intervention and its control (see tab. 5.8). The difference for θ35 under the influence of NIP

was significantly lower than that of the control run on a 5 % significance level. On an 8% significance level the difference for θ35and θ36were significantly lower also

for Ca2+_.

(a) θ31 (b) θ32

(c) θ33 (d) θ34

(e) θ35 (f) θ36

Figure 5.19. θ-angles for markers 31-36 for ctrl Ca2+ _{and Ca}2+_{(mean±SE). Animals}

(58)

42 Results

(a) θ31 (b) θ32

(c) θ33 (d) θ34

(e) θ35 (f) θ36

Figure 5.20. θ-angles for markers 31-36 for ctrl NIP and NIP (mean±SE). Animals 8, 9, 11, 14, 18, 21.

The influence of Ca2+ and Nitroprusside on the opening kinematics of the mitral valve

The Influence of Ca

2+

and Nitroprusside on the

Opening Kinematics of the Mitral Valve

Charlotte Oom

2006-01-20

The Influence of Ca

and Nitroprusside on the

Opening Kinematics of the Mitral Valve

Examensarbete utfört i Medicinsk Teknik

vid Tekniska högskolan i Linköping

av

Påverkan av Ca

och Nitroprussid på mitralisklaffens öppningskinematik

The Influence of Ca

and Nitroprusside on the Opening Kinematics of the Mitral

Valve

Charlotte Oom

IMT

Examensarbete

Engelska

During a cardiac cycle the cardiac walls change between contracted and relaxed and the

valves open and close in response to pressure changes. This master thesis is a study of the

changes in heart movement pattern caused by intravenous injections of Ca

or

Nitroprusside. At Stanford University radiopaque markers have been surgically implanted

in the walls and in the mitral valve of ovine hearts and 3D coordinates for each marker have

been constantly measured during the cardiac cycle. By using MatLab, the volume and

pressure of the left ventricle and several parameters related to the opening kinematics of the

mitral valve have been analyzed. The results show, among others, that both Ca

and

Nitroprusside reduce the volume and pressure of the left ventricle and that both substances

decrease the size of the mitral annular ring. It was also shown that Ca

delays the opening

of the mitral valve.

mitral valve, opening, calcium, nitroprusside

Abstract

Acknowledgements

Contents

List of Figures

List of Tables

Chapter 1

Introduction

1.1

Aims of this Master Thesis

Chapter 2

Anatomy and Physiology

2.1

Anatomy

2.2

Physiology

2.2.1

The Cardiac Conduction System

2.2.2

Volumes in the Heart

2.2.3

Cardiac Muscle Contraction and its Dependence on

Ca

2.2.4

The Effect of Sodium Nitroprusside (NIP) on the Heart

2.2.5

The Frank-Starling Mechanism (Length-Dependent

Ac-tivation)

Chapter 3

Material

3.1

Data Acquisition

3.2

Parameter Calculations

Chapter 4

Method

4.1

Setting the Interval

4.2

Parameter Investigation

4.3

Statistics

4.4

End-Systolic Pressure-Volume Relationship

_{and Nitroprusside on the}

_{Maximum Pressure Drop (-dP/dt|}