Age-related left ventricular function in the mouse: analysis based on in vivo pressure-volume relationships

¹ Arizona Prevention Center and ² Sarver Heart Center and Department of Surgery, University of Arizona, Tucson, Arizona 85724

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES APPENDIX

Our study compared left ventricular (LV) function between senescent and young adult mice through in situ pressure-volume loop analysis. Two groups of mice (n = 9 each), 6-mo-old and 16-mo-old (senescent) mice, were anesthetized with urethan and -chloralose, and their LV were instrumented with a Millar 1.4-Fr conductance micromanometer catheter for the acquisition of the pressure-volume loops. The senescent mice had a significantly decreased contractile function related to load-dependent parameters, including stroke volume index, ejection fraction, cardiac output index, stroke work index, and maximum derivative of change in systolic pressure over time. The load-independent parameters, preload recruitable stroke work and the slope (end-systolic volume elastance) of the end-systolic pressure-volume relationship, were significantly decreased in the senescent mice. Heart rate and arterial elastance were not different between the two groups; however, the ventricular-to-vascular coupling ratio (ratio of elastance of artery to end-systolic volume elastance) was increased by threefold in the senescent mice (P < 0.001). Thus there were significant decreases in contractile function in the senescent mouse heart that appeared to be related to reduced mechanical efficiency but not related to arterial elastance.

senescence; conductance catheter; end-systolic pressure-volume relationship; preload recruitable stroke work

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES APPENDIX

ELUCIDATING THE BASIC mechanisms of senescent heart dysfunction has become increasingly important due to the increased aging population and the increased incidence of age-related heart failure. There are numerous reports relating age to functional (41), biochemical, and electrical performance alterations of the isolated heart, using papillary muscle preparations and in human studies (29, 48). Cardiac senescence has been described to be associated with a cardiac isomyosin shift from - to -myosin heavy chain (50) and with expression of fibrosis-related genes (1). Alterations of growth controlling factors have been described as potential mechanisms for senescent dysfunction through expression of the serum response element gene and induction of c-fos (37), reduced endocrine factor and nerve growth factor (46), response to insulin (28), and increased expression of ANG II receptors (8, 18). Numerous reports have characterized impairment of excitation-contraction coupling (26, 30) and calcium homeostasis (2, 48). There are also engaging reports relating to cardiac senescent changes in nitric oxide synthase expression (25) and increased rate of myocyte apoptosis (22, 34). In summary, a unifying mechanism accounting for cardiac senescence remains to be described. Discovery of the mechanism(s) is complicated by functional measurements of ventricular mechanics in the aging subsequent to prolonged hypertension and pathological conditions such as coronary artery disease. For the above reasons, we set forth to compare the in situ ventricular mechanical properties of healthy young and senescent murine hearts.

Much of the reported research related to senescent heart function has been in humans or in rat models (2, 6, 9, 41). However, the use of a mouse model appears to be justified because of the ability to genetically engineer this species. Furthermore, in immunologically mediated myocardiopathy models, the mouse has many advantages because the murine immune response can be precisely defined. Together, use of the murine model appears to be justified when examining left ventricular (LV) dysfunction related to aging or acquired myocardopathies. No reports have been published regarding senescent murine heart function. Furthermore, because the murine cardiovascular system is similar to that of humans (12, 14), the murine model provides a valid way to define age-related alterations in ventricular mechanics and the associated molecular mechanisms. However, the size of the mouse limits the analytical tools available for measurement of LV function in vivo. The conductance-micromanometer system can provide quantification of LV systolic and diastolic performance in the mouse under both load-dependent and load-independent conditions (12). Thus we applied the conductance-micromanometer system to quantify the LV pressure-volume relationships of the young adult heart and the senescent murine heart.

The purpose of this study was to compare the LV functions in young adult and senescent mice. The parameters used for comparison were those that distinguished between load-dependent and load-independent functions. We found that there was a significant decrease in LV contractile function in the senescent mouse heart that was independent of load.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES APPENDIX

Animals

All animal studies were performed after approval by our animal review committee. Guidelines for the Care and Use of Laboratory Animals [DHEW Publication No. (NIH) 85-23, Revised 1985, Office of Science and Health Reports, DRR/NIH, Bethesda, MD 20205] and Principles of Laboratory Animal Care (published by the National Society for Medical Research) were followed in this study. Before the study, the mice were conditioned for 1 wk in the animal facility.

Eighteen C57BL/6 female mice purchased from Charles River Laboratories (Wilmington, DE) were divided into two equal groups: group 1, consisting of 6-mo-old mice (young adult), and group 2, consisting of 16-mo-old mice (senescent). C57BL/6 female mice were used due to their common application in immunologic and genetic engineering studies. The mice were anesthetized with urethan (1,000 mg/kg ip) and -chloralose (50 mg/kg ip). Respiration was controlled through a tracheostomy cannula connected to a pressure-controlled respirator (RSP 1002, Kent, CT) with a rate of 120 times/min, and FI_O2 of 1.0. The external jugular vein was cannulated for volume administration, which was limited to 200 µl of hetastarch. A substernal transverse incision was made to expose the apical portion of the heart and the inferior vena cava (IVC). Electrical cautery was used to ensure minimal blood loss. The Millar conductance catheter (1.4 Fr) was inserted through a 25-gauge apical stab wound into the LV, and the pericardium was left as intact as possible. The catheter was positioned along the cardiac longitudinal axis with the distal electrode in the aortic root and the proximal electrode in the LV apex.

Conductance Catheter System

The Millar 1.4 Fr catheter (SPR-719) is a composite of four conductance electrodes and a micromanometer. The distance between the conductance sensor electrodes is 4.5 mm, which is equal to the distance between the apex and the aortic valve of the mouse heart. The Millar conductance system controller (Millar MCS-100) was set with the frequency at 20 kHz, the low-pass cutoff frequency at 50 Hz, the full scale current selected at 30 µA, and the pressure transducer (TCB-600) at 1 V/100 mmHg. The signals of the conductance and pressure were digitized by BioBench software (National Instruments, Austin, TX).

All steady-state and caval occlusion pressure-volume loops were acquired with the computer data acquisition system while the ventilation was momentarily turned off. To acutely change the cardiac preload, caval occlusion was produced over a 3-s period using a nonmetallic occluder applied to the IVC. The data were recorded as a series of pressure-volume loops (10-20 loops).

Postmortem Quantification of LV Volume

After completion of the study, the heart was arrested at diastole with hypertonic potassium chloride (1 M). Two methods were used to determine the end-diastolic volume (V_ed). The LV was flushed with isotonic saline through the mitral valve until all air was purged, and then the aorta was clamped. The LV was filled with saline to a LV end-diastolic pressure of 5 mmHg and weighted with an analytical balance. After gentle compression and blotting, the empty heart was again weighed. The difference between the weights was regarded as the V_ed. A second volumetric measurement was made with a casting mixture of resin and catalyst (Biopolymerization Products, Tucson, AZ) at a ratio of 1:0.5. This material was injected into the LV, in a manner similar to the saline method to achieve a LV end-diastolic pressure of 5 mmHg to make a polymer cast of the LV chamber. The heart was suspended by the aorta in a humidified chamber for 48 h to permit complete polymer curing. The LV polymer volume, which was also regarded as the V_ed of the LV, was calculated by the mass of the cast divided by the polymer density.

Conductance Catheter Calibration for Volume

The most critical element in the application of this conductance system was the volume calibration. We applied two methods to achieve this: calibration with a volume calibration line (VCL) and parallel volume (V_p) and calibration with the experimental slope coefficient () and V_p.

Calibration with VCL and V_p. The principle of the conductance catheter system (CCS) is a simple cylindrical equation: V = (L²/) · G, where V is absolute volume, L is the interelectrode distance,  is conductivity of the blood, and G is conductance (3, 43). We therefore calibrated our system with a known volume of fresh heparinized whole murine blood loaded in a series of seven cylinders to derive the VCL.

A system for conductance catheter volume calibration was devised to relate known volumes of mouse blood to conductance signals. Seven cylindrical holes in a lucite block 1 cm deep and with diameters ranging from 2 to 5 mm were filled with fresh whole blood, and the conductance of each was determined with the conductance catheter. An interelectrode distance of 4.5 mm was used to compute the absolute volume measured by the conductance catheter in each cylinder, using V =  · r² · L.

According to the principle of the conductance system, volume was directly proportional to the conductance. Therefore, regression of the volume vs. the conductance was linear. Regression of the calculated volume vs. the corresponding conductance signal produced the regression line shown in Fig. 1. We used this volume-conductance regression line as the VCL and the regression formula as the volume calibration formula (VCF), which was V = 22.103 · G + 6.6; r² = 0.995, P < 0.001 (Fig. 1). All the raw signals of conductance acquired by the conductance catheter were put into this formula (VCF) to calculate the raw volume (V_cc). The V_cc acquired from the mice was 25-55 µl and in the midrange of the VCL.

View larger version (14K): [in this window] [in a new window]   Fig. 1.   Volume calibration line (VCL). Calculated cylinder volume (µl) was plotted against the corresponding conductance measured by the conductance catheter system. The regressed line was considered the VCL. Regression formula, V = 22.103 · G + 6.6 (r2 = 0.995, P < 0.001), was used to calculate the raw volume and parallel volume, where V is volume and G is conductance.

The raw conductance signals included both the conductance of LV blood volume and the conductance of the volume of the surrounding myocardium and thoracic tissues. That is, the V_cc translated from the raw conductance signals included the volume of blood in the LV [V(t)] and V_p calculated from the signal error of the parallel conductance (G_p) of the surrounding tissues. Therefore, the instantaneous LV volume was expressed by the relationship V(t) = V_cc  V_p.

The calibration of V_p required use of a hypertonic saline dilution method, as described by others (4, 7, 20). In our experiments, 10 µl of hypertonic saline (15%) were injected into the external jugular vein. Passage of the hypertonic saline through the LV causes the conductance waveform to expand proportionally to the volume and the conductivity of the blood in LV. The difference between the end-systolic conductance (G_es) and the end-diastolic conductance (G_ed) increased by about twofold after hypertonic saline injection. A regression line was constructed for the series G_es vs. G_ed. The intersection between this regression and the identity line (y = x) was defined as the G_p. The V_p was calculated from the G_p with the VCF (V_p = 22.103 · G_p + 6.6).

In summary, after applying the VCF to calculate V_cc from the raw signal conductance and V_p from G_p, we computed the instantaneous LV blood volume as shown by V(t) = V_cc  V_p.

Calibration of . The principle of the CCS is
In this expression, L is the distance between the sensor electrodes,  is the conductivity of the blood, and  is the experimental slope coefficient for the relationship between V(t) and G(t) (24). G(t) is the instantaneous raw conductance signal.

The volume calibration of  was performed by the ratio of the raw stroke volume (SV_cc) measured by the CCS divided by the stroke volume (SV) measured by a descending aortic flow probe (Transonics, Ithaca, NY) according to the formula  = SV_cc/SV (12, 24). The descending aortic flow probe measurements in the mouse are 74% of the total stroke volume (M. Feldman, Department of Cardiology, University of Texas, San Antonio, TX, personal communication); therefore, all reported SV measurements were fractionally corrected to account for aortic arch blood flow.

The calibration of VCL and V_p was confirmed by the comparison of SV_cc with SV from the flow probe and of the V_ed measured by CCS with the V_ed measured by saline displacement and LV polymer casting.

Analysis of the Signals

Pvan software (Conductance Technologies, San Antonio, TX, and Millar, Houston, TX) was used to analyze all pressure-volume loop data. Regression analyses of multiple isochronal pressure-volume loop data were produced by IVC compression. From the baseline and IVC compression loops, comprehensive sets of hemodynamic parameters (defined in Table 1) were calculated as shown in Table 2. Only the loops with end-systolic pressures (P_es) >60 mmHg were chosen for analysis by IVC blocking. The parameters of contractility and stiffness of the LV were calculated, including end-systolic volume elastance (E_es), end-systolic pressure-volume relationship (ESPVR), preload recruitable stroke work (PRSW), the slope of end-diastolic pressure-volume relationship (EDPVR), and EDPVR. The ventricular-to-vascular coupling ratio was assessed by the arterial elastance-to-E_es ratio (E_a/E_es). These computations were performed according to those recently reported by Georgakopoulos et al. (12) and previously by others (13, 27, 49).

View this table: [in this window] [in a new window]   Table 1.   Hemodynamic parameters

View this table: [in this window] [in a new window]   Table 2.   Hemodynamics of young and old mice based on in vivo analysis of pressure-volume relationships

Statistical Analysis

All data are reported as means ± SE. The standard volume line was analyzed by simple linear regression. When appropriate, differences between young mice and senescent mice were compared by an unpaired Student's t-test or one-way ANOVA. P < 0.05 was used as criteria for statistical significance.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES APPENDIX

Hemodynamics of Young and Senescent Mice

Table 2 contrasts the hemodynamic function parameters of young adult to those of senescent mice. We found that the senescent mice had a significantly decreased contractile function compared with the young mice; parameters included stroke index (SI), cardiac index (CI), ejection fraction (EF), stroke work index (SWI), end-systolic pressure (P_es), and maximum derivative of change in systolic pressure over time (dP/dt_max) (P < 0.05). The diastolic function and minimum dP/dt were also significantly less in old mice (P < 0.01); however, there was no significant difference in the time constant of isovolumic relaxation () and the slope of EDPVR between the young and the senescent mice.

LV Contractility

Two typical pressure-volume loop sets generated by IVC compression are shown in Fig. 2. The ESPVR of the senescent mice demonstrated a markedly decreased slope in comparison to that of the young mice. More specifically, the E_es of the senescent mice decreased by threefold (12.02 ± 1.4 mmHg/µl) compared with that of the young mice (42.8 ± 7.6 mmHg/µl) (P < 0.01). PRSW computed by regression of stroke work (SW) to the V_ed (r² = 0.99, P < 0.001) is the slope of the regression line and is shown in Fig. 3. Consistent with the ESPVR data, Table 2 shows that there was about a 28% decrease in the PRSW relationship in the senescent mice (58.8 ± 4.4 mmHg) compared with young mice (83.6 ± 5.7 mmHg) (P < 0.01).

View larger version (66K): [in this window] [in a new window]   Fig. 2.   A: end-systolic pressure-volume relationship (ESPVR) of young adult mice. B: ESPVR of senescent mice. Response to ramping of the preload by occlusion of inferior vena cava produced the corresponding pressure-volume loop changes. End-systolic pressure (Pes) was plotted with end-systolic volume (Ves) to derive the ESPVR (dotted line). Slope of the regression line (ESPVR) is ventricular end-systolic elastance (Ees). Ees of young mice was 3-fold greater than that of senescent mice, which supports the observation that the left ventricular contractility of senescent mice was significantly decreased.

View larger version (15K): [in this window] [in a new window]   Fig. 3.   Comparison of the preload recruitable stroke work (PRSW) relationship between young adult and senescent mice. Stroke work was plotted against end-diastolic volume (Ved), which was acquired from a series of pressure-volume loops during inferior vena cava occlusion. Regression line is the PRSW relationship, and slope of this line is PRSW. Two representative linear PRSW relationships are shown. , Old mice (y = 49.8 · x  167.39, r2 = 0.998). , Young mice (y = 82.5 · x  351.7, r2 = 0.998). PRSW of the senescent mouse was much less than that of the young mouse, which suggests that senescent mouse had a decreased contractile function.

Efficiency of LV Work

The LV efficiency [ratio of external work to pressure-volume (EW/PVA)] and SWI of young mice were significantly greater than those of the senescent mice (P < 0.05). The E_a was not different between the two age groups; however, the ratio of arterial elastance to ventricular elastance (E_a/E_es) was increased by threefold in the senescent compared with the adult young mice (P < 0.01) (Table 2).

Calibration of Volume

When the conductances of the surrounding tissues in the two groups were compared, there was no significant difference between the senescent mice (0.82 ± 0.07 V¹) and the young mice (0.78 ± 0.09 V¹).

After the calibration with VCF and V_p, the ventricular V_ed was 15.04 ± 0.86 µl for the adult young mice and 15.35 ± 1.10 µl for the senescent mice. Furthermore, the direct volumetric V_ed measurements from the saline displacement and the polymer cast model were 15.5 ± 0.55 µl and 15.07 ± 0.95 µl, respectively. There were no significant differences among the V_ed results measured by these three methods (P = 0.936) (Table 3). The SV of the young mice measured by the CCS (9.99 ± 0.24 µl) was found to be equivalent to the SV measured by the aortic flow probe (9.96 ± 0.97 µl; P = 0.96) (Table 3). In summary, an  of 1.003 was used for volume computations based on the Doppler flow measurements and validated by the volumetric determinations.

View this table: [in this window] [in a new window]   Table 3.   Volume and SV of left ventricle by different methods

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES APPENDIX

Senescent Heart Function

Our study defined significant in vivo functional differences between the senescent mouse heart compared with the young adult heart. In agreement with other studies reporting other species, we found that the contractile state of the murine senescent heart was significantly decreased. Our study incorporated multiple measurements that were both load dependent and load independent. Load-independent measurements of ventricular contractile state consistently demonstrated decreased function in the senescent mice; however, the diastolic function was slightly different between the two groups. These findings suggest that the senescent contractile dysfunction is related to innate cardiac factors other than response to peripheral vascular resistances, since the E_a was not different between the age groups. Furthermore, the energetic indexes of the senescent mouse heart were shown to be much less efficient than the younger adult heart. In summary, the load-independent parameters PRSW and ESPVR demonstrated an age-related decrease in contractile function of the LV.

Comparative Hemodynamics

The LV functional parameters of the young mice were consistent with those reported by others (12, 14, 35, 36). These reports have described similar changes in aging rats (23 mo old), including decreased dP/dt_max, CI, and peak pressure of LV (9, 41). Furthermore, these reports also suggest that the LV diastolic function was minimally different between the two rat age groups (41), which is comparable with our results. In summary, we report that the murine senescent LV contractile function was significantly less than that in the younger adult, which is consistent with results reported in other species.

E_es and ESPVR

E_es was computed from the slope of the ESPVR, as illustrated in Fig. 2, A and B. Within a physiologically normal range of LV pressures, E_es is relatively independent of preload and afterload and is a reliable index of LV contractility (27, 42, 47). Our data show that the E_es of old mice was significantly decreased (by threefold) compared with that of young mice, implying that the LV contractility of the senescent mice was significantly less than that of the young. In summary, the decreased E_es in the senescent mice is consistent with the decrease of other LV systolic functions, such as EF, SI, P_es, and dP/dt_max.

PRSW

The attributes favoring the use of the PRSW relationship are as follows: 1) the PRSW is a modification of Frank-Starling law, 2) PRSW is less influenced by noise or ventricular geometry, and 3) PRSW is linear. PRSW is also preload independent and afterload insensitive over the physiological range (13, 33). Because of this feature, PRSW is more statistically robust than E_es (23). From our analysis, the derivation of PRSW, as the SW was plotted with V_ed, yielded an r² of 0.99, P < 0.001 (Fig. 3). The last important point is that PRSW is independent of the calibration of  and V_p (see APPENDIX). This is a very important issue related to the application of the conductance catheter in the murine model. The methods for determination of the calibration factor  are not as precise in the mouse as in larger species. Consequently, the PRSW is an excellent means to characterize LV contractile function because it does not rely on precision of  factors compared with ESPVR.

In normal hearts, including hearts of animals and humans, the PRSW varies from 75 to 90 mmHg (23). Our data were within that range; that is, the PRSW of normal young mice was 83.5 ± 5.7 mmHg, which is also consistent to that reported by Georgakopoulos et al. (12), which was 82.1 ± 5.6 mmHg. The PRSW of senescent mice was much less than that of the normal young mice, which confirms that the LV contractile function of the senescent mice was much less than that of the young mice. Therefore, the conclusions from parameters of preload-dependent hemodynamics are consistent with preload-independent E_es and PRSW.

E_a and Ventricular E_es

E_a directly affects the systolic function of the heart. E_a is equal to the ratio of the end-systolic pressure and the SV and is considered the most reliable index of LV afterload. Our study demonstrated that there was no difference in E_a between the young adult and senescent mice. That is, the peripheral vascular resistance was not different between 6-mo-old and 16-mo-old mice.

In contrast to the E_a data, the ventricular-to-vascular coupling ratio (E_a/E_es) was significantly increased in senescent mice compared with the young mice. Theoretically, the maximal stroke work of LV occurs when E_a/E_es = 1 and the optimal cardiac efficiency is maintained when E_a/E_es = 0.5 (23, 33). In normal human hearts, E_a/E_es is ~0.5 (12), and, in patients with depressed LV function, the ratio has been reported to be >1. It is understood that the increase in E_a/E_es from 0.5 is associated with a decrease in mechanical efficiency (23). Therefore, our results demonstrated that the E_a was equal between the groups; however, the LV function of senescent mice had a decreased mechanical efficiency compared with the hearts of young mice. These observations are supported by our measurement of contractile efficiency.

Contractile Efficiency

The PVA is the area circumscribed by ESPVR, EDPVR, and the systolic portion of the pressure-volume loop (Fig. 4). PVA is an index of myocardial O₂ consumption and is a powerful tool in evaluating the coupling of LV mechanical performance to energy use (49). The cardiac energy efficiency can be defined by the EW-to-PVA ratio (Fig. 4) and represents the amount of energy that can be transformed into external work. Our results demonstrated a significant difference (P < 0.009) between young and senescent mice related to the efficiency of the EW-to-PVA ratio. The young mouse hearts transformed 90.6% of the total energy into external work, whereas the senescent LV transformed 75.9% of total energy into external work. In summary, the decrease in cardiac efficiency (EW/PVA) is consistent with the increase in E_a/E_es without changes in the systemic E_a of the senescent mice.

View larger version (31K): [in this window] [in a new window]   Fig. 4.   Definition of pressure-volume loop parameters.

Mechanisms of Cardiac Senescence

There are two potential mechanisms of senescent cardiac dysfunction. Cardiac senescence has been characterized by functional lowering of myocardial strength and contraction speed, prolongation of the relaxation phase, and stiffening of the muscle cells, mural connective tissue, and heart valves (6, 9, 48). The integrated calcium influx increases markedly but the rate of uptake of cytoplasmic calcium decreases with each heart beat in the senescent heart (2, 6, 52). This could be a compensatory mechanism to the senescent contractile dysfunction (2, 52) and could account for the reported decreased magnitude of maximal velocity of relaxation (6, 48). However, our data are not consistent with a calcium mechanism due to a lack of differences of the measured  values between the two age groups.

However, in senescent mice, the serum concentrations of interleukin (IL)-4, IL-6, tumor necrosis factor-, interferon-, and IL-1 are increased compared with young mice (21, 31, 32). These proinflammatory cytokines can induce myocytes to express inducible nitric oxide synthase (iNOS) (5, 19, 45), which is not normally expressed in this tissue (39). We have compared the young with senescent LV using immunohistochemistry and demonstrated significantly enhanced expression of iNOS in the senescent tissues (data not shown). This observation is consistent with that reported in other myocardiopathies (10, 17). Therefore, a second possible mechanism of senescent LV dysfunction may be mediated through high concentrations of NO that cause a negative inotropic effect through the cGMP pathway (15, 16, 38, 45) and depressed cardiac efficiency through the peroxynitrite pathway (40, 44). In summary, a coupling between immune dysregulation related to the aging process and cardiac dysfunction provides a possible means of explaining our observed results in the senescent mouse.

Study Limitations

There are some limitations to this technique. The single-frequency conductance catheter used by us may underestimate the LV volume (51). Second, the plastic block model may confine the electrical field produced by the source electrodes. Therefore, it does not exactly model the electrical fields formed in mouse thoracic cavity tissues. However, the volumes of the cylinders were constructed to the volumes acquired as raw conductance signals (V_cc) and not the LV volumes [V(t)] specifically. Furthermore, the restriction of the electrical field may have more of an influence on V_p rather than on V(t) due to the geometry of the field.

Both load-dependent parameters (EF, SW, SWI, SI, CI, P_es, and dP/dt_max) and load-independent parameters (E_es and PRSW) revealed marked decreases in contractile function of the senescent mouse heart without differences in the E_a compared with the young adult heart. The mechanical efficiency of LV was also significantly decreased with decreased EW/PVA and increased E_a/E_es. These age-related functional differences between the two age groups appeared to be due to innate cardiac factors rather than compensatory responses related to systemic vascular properties.

	APPENDIX

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES APPENDIX

The PRSW relationship is plotted by SW vs. V_ed, and is linear. The slope of this line is named PRSW (13). Therefore
where V_{ed 1} and SW₁ and V_{ed 2} and SW₂ are any two selected points (point 1 and point 2) on the line of PRSW relationship in the x-y axis.
where MEP is LV mean ejection pressure and EDP is LV end-diastolic pressure (13).

If we let P = MEP  EDP, and since SV = V_ed  V_es, then
The volume measured by the conductance catheter was calculated by the following equation
where L is the distance across sensor electrodes,  is the conductivity of the blood,  is an experimental slope coefficient for V_(t)  G_(t) correlationship, and V_p is a volume signal error due to the conductance of the tissue surrounding LV (24). Thus



Therefore, according the equation above, PRSW is just related to pressure (MEP and EDP) and the value of the raw conductance signals, which is uncalibrated by  and V_p. As a result, PRSW is independent of the calibration of  and V_p (and its unit is mmHg).

	ACKNOWLEDGEMENTS

We thank Drs. David Kass and Marc Feldman for collaborative support with the application of the conductance system in this murine study. We thank Julie Beischel for editing assistance with the manuscript. Also, we thank Ryan Kelly and Mary Rose for technical support.

	FOOTNOTES

This study was supported by National Heart, Lung, and Blood Institute Grant HL-59794-01.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

Address for reprint requests and other correspondence: D. F. Larson, Department of Surgery, University of Arizona, Tucson, AZ 85724 (E-mail: dflarson{at}u.arizona.edu).

Received 20 April 1999; accepted in final form 25 June 1999.

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TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES APPENDIX

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