Relationship between Experiment and the Computational Model

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Comparison of Stress Development between Left and Right Trabeculae in the Rat Heart

Trabeculae carneae are the smallest intact units of functional myocardium and have advantages for experimentation in that the production of force is uniaxial and the small radii of trabeculae enable the avoidance of anoxic conditions. The contractile performance (i.e. force-production) of trabeculae carneae is generally normalized to the cross-sectional area of the contractile machinery to yield estimates of muscle stress, which are impossible to measure in the whole heart due to technical limitations. In vivo heart rate range or loaddependent effects can be performed in the isolated trabeculae, more easily than in isolated myocytes.

Stress-Frequency Relationships

In order to compare the SFR between LV and RV trabeculae, a range of stimulus frequencies was applied to muscles equilibrated at optimal length. To ensure stability, I returned to the reference frequency of 5 Hz after each varying stimulus frequency. The original recordings of the developed stresses measured at different frequencies. When the frequency was changed, the initial stress was quite different, but at steady-state the developed stress levels converged to a constant value. The change in diastolic stress between the intermediate reference frequency (5 Hz) and each test frequency was usually obvious.

β-Adrenergic Response

Next, I investigated the effect of ISO (β-adrenergic stimulant) on SFR (peak stress). Increasing heart rate is expected to be accompanied by sympathetic activation in vivo. To clarify this anticipated β-adrenergic regulation of SFR, I treated the trabeculae with ISO and proceeded to measure the SFR. The cumulative concentration-response curve obtained by raising the ISO concentration in semi-log steps from 1 nmol·L^-1 to 1 μmol·L^-1; EC₅₀ was 22.5 nmol·L^-1 ± 16.6 nmol·L^-1 (n = 3).

Non-selective Adrenergic Response

To elucidate the effect of NE on the SFR, I measured the stress at 20 nmol·L^-1 NE, which is the concentration required to produce measurable hemodynamic or metabolic changes in vivo in the rat (Watanabe et al., 2003). The effect of NE on SFR was somewhat different from that of ISO. NE showed a similar increase in developed stress against the identical control trace in both trabeculae.

Discussion

The main findings of the present study are: (1) stress did not differ significantly between LV and RV trabeculae and the SFR in both groups was flat in the range of physiological frequencies applied at 37°C; (2) β-adrenergic stimulation resulted in a positive SFR with significant reduction in the twitch time constants and increase in the maximum rate of stress development in both groups in the range of physiological frequencies at 37°C; and (3) nonspecific adrenergic stimulation produced increased stress, but unchanged flattened SFR and twitch time constants in both groups in the range of physiological frequencies at 37°C.

Stress and Frequency

The SFR in trabeculae or correspondingly the force-frequency relationship (FFR) in whole heart, with the Frank-Starling law, is well-known as one of the most important intrinsic factors responsible for control of cardiac contractility in physiological conditions (Holubarsch et al., 1996). The Frank-Starling law is based on a length-tension relationship, and is quite clearly manifest in the LV, which is far more preload dependent than the RV (Santamore and Dell’Italia, 1998). Wall thickness is far less and elastance is lower in the RV than the LV; therefore, the RV is far more afterload-dependent than the LV (Walker and Buttrick, 2009). In addition, the structural and mechanical properties of the RV are distinct from those of the LV. Despite these differences, to immediately meet the demand of vital organs, the ventricles should contract synchronously with identical cardiac output under various circumstances. In this study, for any given frequency, each trabecula has mostly similar steady-state stress regardless of marked differences in the initial stress. Also there was no difference in inherent stress between trabeculae from the LV and the RV; however, RV trabeculae had a shorter time to peak force and relaxation time than LV trabeculae. These results are supported by other studies. Rouleau et al. (1986) demonstrated that RV muscles shortened faster and their time to attain peak total tension was shorter than that of LV muscles in dogs (Rouleau et al.(1986). Suga et al. (1973) provided evidence that increases in the paced heart rate proportionally shorten the time to peak systole without any effect on the peak value of endsystolic elastance (Suga et al., 1973). Under normal circumstances, the right chamber pressure presents a lower load against which the RV ejects blood than does the left chamber, and also shows an earlier systolic peak and more rapid pressure decline (Dell’Italia and Walsh, 1988b). In support of this, a model of pulmonary hypertension showed adaptation of the RV by decreasing muscle shortening velocity and by increasing the time to attain peak total tension to eject against a high pressure system (Alpert and Mulieri, 1982). The above results suggest that mechanical differences exist between LV and RV myocardium in term of either cellular components or Ca²⁺ regulating mechanisms. The mechanisms involved in SFR have been suggested to centre primarily on increased Ca²⁺ availability to the contractile proteins as consequence of the following: the increased number of APs per minute leads to increase SR Ca²⁺ storage with augmented Ca²⁺ transients through the activation of LCCs (Borzak et al., 1991; Wier and Yue, 1986); reduced Ca²⁺ efflux through the NCX in diastole leads to increase cytosolic Ca²⁺ accumulation (Subramani et al., 2005; Vila Petroff et al., 2003). Recently, Ca²⁺/calmodulin-dependent protein kinase IIδ (CaMKIIδ) phosphorylation of RYR2 has been suggested to play an important role in mediating positive FFR in the heart, with defective regulation of RYR2 by CaMKIIδ-mediated phosphorylation being associated with the loss of positive FFR in failing hearts (Kushnir et al., 2010). Changes in the time to attain peak total tension and the velocity of muscle shortening have a close relationship with changes in AP duration. For example, an increase in AP duration occurs in hypertrophied myocardium in response to an increase in afterload, which leads to an increase in the time to attain peak total tension, and a decrease in the velocity of muscle shortening (Keung and Aronson, 1981). Furthermore, Watanabe et al. (1983) showed that the shorter AP duration of the RV as compared to the LV is accompanied by a shorter time to attain peak total tension and by a slower velocity of muscle shortening in rats.  The differences observed in muscle mechanics in my study, as well as in other studies, may be related to differences in the expression and activity of Ca²⁺ modulation-related proteins.  Some differences in cellular calcium kinetics between RV and LV myocardium have been described (Saari and Johnson, 1980) and I examined these further to compare Ca²⁺ handling between LV and RV myocytes . Brooks et al. (1987) showed that the force generation of RV papillary muscle per unit mass is similar to that of LV papillary muscle, although the shortening velocity of isolated RV muscle is greater than that of the LV. They measured the difference in myosin heavy chain isozyme expression that is associated with a higher ATPase activity in the RV and LV; that is, the level of α-myosin heavy chain isozyme in the RV is significantly higher than in the LV in both rats and rabbits. The SFR/FFR has an important effect when myocardial performance reduces as systolic volume decreases (Frank-Starling relation), because SFR leads to an increase in contractile strength and so compensates for the Frank-Starling effect. However, my observation of the SFR (relatively flattened), suggests that innate myocardial stress is independent of frequency, which does not agree with the biphasic or positive SFR results in previous studies (Kassiri et al., 2000; Layland and Kentish, 1999). This discrepancy could be due to differences in experimental conditions: in case of biphasic SFR, only RV trabeculae of rat heart were stimulated at 0.2, 0.5, 1, and 2 Hz at room temperature; in the case of positive SFR, the protocol to stimulate the trabeculae was repeated for successively increasing test frequencies (0.1 – 12 Hz) and then repeated with decreasing stimulation frequency. In this study, both groups of trabeculae showed a significant depression of stress beyond the maximal physiological range (12 Hz), in accordance with previous studies which demonstrated an increase of contractile force as heart rate increased, followed by a decline with excessive increase in heart rate (Alpert et al., 1998). In contrast, my results are different from a previous study (Wang et al., 2008) in which RV trabeculae in the mouse showed a positive SFR in the range of frequencies investigated (4 Hz – 14 Hz) .

Adrenergic Stimulation and SFR

Cardiac output is the product of stroke volume and heart rate. However, increased heart rates reduce diastolic filling time, which reduces stroke volume. For example, during exercise, tachycardia is accompanied by a decrease in end-diastolic volume despite a progressive increase in filling pressure, so that stroke volume is maintained by a decrease in end-systolic volume (Higginbotham et al., 1986). This suggests that positive FFR can prevent the reduction of stroke volume at faster heart rates and ensure an enhanced cardiac output. Under physiological conditions, increasing heart rate is accompanied by autonomic system input. Therefore, understanding the control mechanism for cardiac contractility requires the application of adrenergic stimulation to verify the regulation of SFR. When I explored the effect of -adrenergic stimulation, I found that the SFR of both LV and RV trabeculae showed a positive relationship. This finding is consistent with others in the literature (Kambayashi et al., 1992; Kassiri et al., 2000; Ross et al., 1995).

1. Introduction
1.1 Basic Cardiac Physiology
1.2 Left and Right Heart
1.3 Virtual Cardiac Cell
1.4 Relationship between Experiment and the Computational Model
1.5 Thesis Objectives
2. Methods
2.1 Experimental Animals
2.2 Solutions and Chemicals
2.3 Trabecular Contraction Experiments
2.4 Ca²⁺ Transient Experiments
2.5 Mathematical Modelling
3. Comparison of Stress Development between Left and Right Trabeculae in the Rat Heart
3.1 Stress-Frequency Relationships
3.2 β-Adrenergic Response
3.3 Non-selective Adrenergic Response
3.4 Discussion
4. Comparison of Ca²⁺ Handling between Left and Right Ventricular Myocytes
4.1 Ca²⁺ Transients
4.2 Discussion
5. Biophysical Whole Cell Modelling
5.1 Development of Whole Cell Model
5.2 Simulation results
5.3 Discussion
5.4 Chapter Summary
6. Thesis Summary
6.1 Main Findings
6.2 Limitation and Prospective
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Multi-scale Electromechanics of the Heart