Search tips
Search criteria 


Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Am Soc Echocardiogr. Author manuscript; available in PMC 2010 April 1.
Published in final edited form as:
PMCID: PMC2673721

Impact of Acute Moderate Elevation in Left Ventricular Afterload on Diastolic Transmitral Flow Efficiency: Analysis by Vortex Formation Time



Formation of a vortex alongside a diastolic jet signifies an efficient blood transport mechanism. Vortex formation time (VFT) is an index of optimal conditions for vortex formation. We hypothesized that left ventricular (LV) afterload impairs diastolic transmitral flow efficiency and, therefore, shifts the VFT value out of its optimal range.


In 9 open-chest pigs, we elevated LV afterload by externally constricting the ascending aorta and increasing systolic blood pressure to 130% of baseline value for 3 minutes.


Systolic LV function decreased, diastolic filling velocity increased only during the late (atrial) phase from 0.46 ± 0.06 to 0.63 ± 0.19 m/s (P = 0.0231), and end-diastolic LV volume and heart rate remained unchanged. VFT decreased from 4.09 ± 0.27 to 2.78 ± 1.03 (P = 0.0046).


An acute, moderate elevation in LV afterload worsens conditions for diastolic vortex formation, suggesting impaired blood transport efficiency.

Keywords: blood flow velocity, vortex formation, diastolic filling

Left ventricular (LV) diastolic filling and mechanical function are important indicators of overall cardiac health status [1-4] and aid in early diagnosis of cardiovascular disease [1, 5]. Clinical evaluation of diastolic filling with Doppler ultrasound is, however, angle-dependent and limited both in detecting flow alterations in early stages of cardiac disease [6] and spatial characterization of intraventricular flow patterns.

We have shown by echocardiographic particle imaging velocimetry [7], or echo PIV [8] - and other investigators demonstrated by magnetic resonance imaging [9] - that transmitral flow can produce an intraventricular rotational body of fluid referred to as a vortex ring [10-12], which supports a more efficient fluid transport compared to a straight jet alone [13, 14]. Gharib et al. [15] derived a dimensionless index for quantitatively characterizing the optimal conditions for vortex formation from the duration of flow through an orifice with known diameter and, thus, referred to the index as vortex formation time (VFT), and proposed that the process of vortex ring formation during diastole could serve as an indicator of cardiac health.

Acute changes in afterload, such as those induced by a sudden increase in blood pressure due to activation of the adrenergic system during stress [16] or paroxysmal hypertension [17], can negatively impact diastolic filling [18]. We hypothesized that an acute moderate increase in LV afterload, accomplished by mechanical aortic constriction, would alter transmitral blood transport efficiency and, therefore, the VFT value as compared to the baseline condition.


Animal Preparation

The study was approved by the Mayo Clinic Institutional Animal Care and Use Committee. Pigs weighing 40 to 45 kg were fasted overnight, sedated with Telazol (5 mg/kg), Xylazine (2 mg/kg), and Buprenex (0.005 mg/kg), intubated, and anesthetized by isoflurane inhalation. Heart rate, cardiac rhythm, and arterial oximetry were continuously monitored. Blood pressure was monitored by manometer-tipped catheters (Millar Instruments, Inc, Houston, TX) placed under ultrasound guidance [19] into the LV, aorta (upstream to the constricted segment described below), and LA. Following midsternotomy, the heart was suspended on a pericardial cradle.

Experimental Intervention

An experimental increase in LV afterload was induced by briefly (approximately 3-minute) constricting a short segment of ascending aorta by umbilical tape (Ethicon, Piscataway, NJ) placed as a tourniquet. The corresponding level of vascular resistance (VR) was estimated as [20]:


where BPm (mmHg) is mean blood pressure, CO (L/min) denotes cardiac output, and the constant 80 is a conversion factor so that VR is measured in dyn·s·cm-5 [21].

Hemodynamic Measurements

Basic hemodynamic measurements are summarized in Table 1. LV end-diastolic pressure (LVEDP) was determined at the peak of the R-wave on the synchronous ECG tracing. Besides peak positive and peak negative dP/dt (ie, +dP/dt and -dP/dt, respectively), the time constant of LV pressure decay during the isovolumic relaxation period (ie, Tau) was ascertained by using a zero-asymptote model [22].

Table 1
Hemodynamic Parameters

LV afterload was quantitated in relative (%) values using the following formula: [(peak systolic blood pressure at increased afterload)/(peak systolic blood pressure at baseline)]× 100. The afterload severity in our setting was then determined using the following scale: (low afterload) < 125% ≤ (moderate afterload) ≤ 140% < (high afterload) [23].

Data Acquisition with 2D and Flow Doppler Echocardiography

Echocardiographic images were acquired using a Vivid 7 system (GE Healthcare, Milwaukee, WI) and a hand-held 3.5 MHz transducer placed epicardially for scanning through a bulk of acoustically-coupling gel. Apical 4-chamber, 3-chamber, and 2-chamber and short-axis basal, mid-level, and apical scans of the LV were recorded for subsequent offline analyses. Measurements included peak transmitral flow velocities at mitral tip during early (E-wave) and atrial (A-wave) phases of LV filling, LV end-diastolic volume (EDV) [24], end-systolic volume (ESV), stroke volume (SV), and ejection fraction (EF) [20].

VFT Definition

Gharib and colleagues [15] mathematically derived the VFT formula based on LV function, mitral orifice diameter, and diastolic filling flow velocities, ie, utilizing easily obtainable physiological and echocardiographical measures, as follows:


where β is the fraction of SV contributed from the atrial component of LV filling and is calculated from Doppler spectra of the E- and A-waves. The symbol α is a dimensionless index of LV geometry defined as α=EDV13D, where EDV is measured in cm3 (or mL) and D is the mitral valve diameter in cm. D has been obtained by averaging the largest mitral orifice diameters measured during early diastolic filling in the 2, 3, and 4-chamber apical views. Although in this study we used the VFT formula derived by Gharib et al. to be able to assess the effect of each of its component variables on the results, the definition can be simplified, by incorporating the α term into the previous equation and considering that EF = SV/EDV, as follows:


Data Analysis

Data are expressed as mean ± standard deviation (SD). Hemodynamic, 2D, and Doppler echocardiographic measurements, as well as VFT values were obtained at baseline and during intervention and compared by using a 2-tailed paired t-test. The relation between the increase in VR and decrease in VFT was also assessed by linear regression analysis. A P value less than 0.05 was considered statistically significant.


Eleven pigs were entered into the study; severe hypotension in one animal and first-degree atrioventricular block in another animal affected baseline hemodynamic conditions, and those 2 were therefore excluded. Complete measurements were obtained from all 9 of the remaining animals.

Systemic Hemodynamic Analysis

At baseline, the hemodynamic data were within the usual ranges (Table 1). Experimentally increased afterload, signified by elevation of systolic and mean blood pressures, was accompanied by a decrease in CO and an increase in the calculated VR. By careful adjustment of the compressive aortic tourniquet, a relative LV pressure load of 130% was approximated in each animal and resulted in the consistent moderate afterload severity within the testing group.

Diastolic blood pressure and heart rate remained without significant changes. LVEDP and +dP/dt did not change with the moderate increase in afterload. On the contrary, the absolute value of -dP/dt decreased, although Tau was not changed significantly.

Echocardiographic Analysis

Peak mitral flow velocities during the early (E-wave) filling phase did not change, but velocities at the atrial (A-wave) phase increased significantly (Table 2). Consequently, the E/A ratio showed a decreasing trend. EDV did not change but ESV had an increasing trend and impact, resulting in a significant reduction in SV and EF.

Table 2
Echocardiographic Parameters

Vortex Formation Analysis

The mean values of D and α, when compared between baseline and moderately elevated afterload, remained nearly identical (Table 3). β and VFT significantly decreased during the intervention. There was a trend of an inverse linear correlation between the percent change of VFT compared with that of VR (Figure 1).

Figure 1
Relation between percent change of vascular resistance (VR) and percent change of vortex formation time (VFT).
Table 3
Vortex Formation Parameters


The main finding of our experimental study is that even a brief, moderate elevation in LV afterload negatively affects transmitral flow efficiency as expressed by a shift of VFT values out of their optimal range.

Another finding of our study is that the mean VFT values at baseline and during moderately increased LV afterload are within and out of the normal range, respectively, of VFT values that are found both in natural and experimental jet propulsion systems [13]. That is, our results further support the notion that VFT index is a setting- and species-independent measure [15, 25].

Assessment of LV Systolic and Diastolic Function during Elevated Afterload

Elevated afterload can influence LV systolic function by blunting contractile reserve, increasing cardiac energy required to provide blood flow, and raising myocardial oxygen consumption for a given SV [26]. LV diastolic function can become abnormal due to impaired relaxation in the ventricle with elevated systolic pressure [18]. In our setting, the elevated resistance to LV ejection (reflected by a significant increase in the VR parameter) was controlled by maintaining the systolic blood pressure at approximately 130% of its baseline value (Table 1), which yielded a moderate elevation in afterload. The hemodynamic impact of such an intervention was expressed in systole by a drop in SV accompanied by decreases in EF and CO, and by elevation in ESV. In diastole, the impact of moderately increased afterload on relaxation was demonstrated by an E/A ratio less than 1, resulting primarily from a significant increase in A-wave velocity (Table 2). The E-wave velocity did not change, which can occur despite impairment in LV relaxation if left atrial pressure has increased [27] or if early relaxation is controlled by an early transmitral pressure gradient, primarily driven by diastolic untwisting [7, 28, 29].

Consistent with results by others [23], the rate of LV pressure increase [30], was not affected by the moderate elevation in afterload. However, the magnitude of the rate of LV pressure fall (ie, the magnitude of -dP/dt), significantly decreased and such findings can be explained as follows [23]: At low afterload, the onset of LV pressure fall is delayed and the rate of LV pressure fall is, therefore, accelerated (ie, the -dP/dt magnitude increases). However, with moderate or high afterload, the onset of LV pressure fall occurs earlier, and the -dP/dt magnitude decreases.

Tau, when calculated by a zero-asymptote model, has been shown to correlate with -dP/dt for Tau ranging from 50 to 130 ms [31]. However, with a consistent and only moderate elevation in afterload, the values of Tau obtained at baseline and during the intervention accumulated around the lower values of that range, without showing a significant increase (Table 1).

A range of VFT from 3.3 to 4.5 characterizes optimal hemodynamic conditions for vortex ring formation. Outside this range, a vortex ring may be limited in its growth or duration [25, 32].

Gharib and colleagues [15] initially employed the simplified formula, time-velocity integral divided by the diameter of the mitral annulus, in their analysis of vortex formation in healthy subjects and in patients with dilated cardiomyopathy. While LV dysfunction in dilated cardiomyopathy caused a shift of VFT values clearly out of the optimal range, we speculate that the use of the mitral valve annulus is not a good generally usable measure, because mitral annular diameter would not reflect the actual exit orifice in mitral stenosis and other clinical cases with altered valvular geometry and orifice.

Hemodynamic Implications of Vortex Ring Formation

The diastolic vortex ring acts as a kinetic energy reservoir that facilitates propulsion of blood in systole [33], contributes to blood redirection into the outflow tract and aorta [34, 35], and helps in preventing blood stagnation within the LV apex [35]. In addition, the vortex ring is supposed to exert a force that contributes to timely closure of the mitral valve [36]. Premature disintegration of the vortex and dissipation of the stored energy eliminates the beneficial effects of vortex formation and may necessitate an increase in the physical work generated by the cardiac muscle, thus augmenting the consumption of the oxygen, and in turn reducing efficiency of the heart pump [33].

Changes in VFT and its Component Parameters with Moderately Increased Afterload

The acute moderate increase in afterload not only impairs LV systolic and diastolic function, but our study shows that this condition also negatively impacts vortex ring formation. The latter finding is signified by the mean VFT value below the optimal range. The moderately elevated afterload in our study results in grade 1 diastolic dysfunction defined by a low early (E-wave) component and an increased late (A-wave) component of diastolic filling. The augmented atrial contraction could be an adaptive functional mechanism activated in response to elevated LV afterload. However, as we show, this mechanism, in turn, impairs formation of a diastolic vortex suggesting reduced hemodynamic efficiency during LV filling [27].

The parameter α has not significantly changed in response to increased afterload in our acute setting. It can be anticipated, however, that in chronically increased afterload with impact on LV geometry, the value of α would change significantly.

We found a linear trend between percent increase in vascular resistance and percent decrease in VFT (Figure 1). If confirmed by further studies, the utility of this relation could be in grading the severity of LV pressure loading and its impact on diastolic filling efficiency.

Study Limitations

We obtained values of the β parameter from maximum mitral tip-to-tip diameter recordings and from peaks of E- and A-wave Doppler spectra rather than by utilizing time integrals. These simplifications have not impacted the consistency of our results with VFT analyses by others [15, 25].

We used an open-chest pig setting, which was necessary for controlling the acutely induced afterload elevation by the aortic tourniquet, but could have theoretically affected cardiac filling due to cancellation of negative intrathoracic pressure during inspiration. However, the baseline hemodynamic data as well as VFT values were well within the normal ranges and all paired comparisons were done at the same experimental setting.

Finally, we were unable to determine from the current study whether the VFT formula would work in conditions with abnormal direction of flow during diastole such as aortic regurgitation.

Clinical Perspectives

The VFT parameter contributes to a conceptually novel interpretation of cardiac function. While ventricular EF, regional strain, and transmitral flow velocities are only a few of many examples of association of quantitative functional measurements to certain aspects of tissue or blood motion, VFT is a multifactorial parameter characterizing whether the ultimate goal of LV functional performance - blood transport - is achieved efficiently. Moreover, VFT may supersede conventional parameters of cardiac function in that it is a dimensionless index defined on a universal timescale [25] and, thus, VFT measurements can be interpreted without considering patient-specific effects. For example, no correction of VFT with respect to body surface is needed or, unlike with E-wave and A-wave analyses, there is no “pseudonormalization” of VFT with progressive diastolic dysfunction [15, 37].

In patients with diastolic dysfunction related to cardiac dyssynchrony [38], quantitative evaluation of cardiac efficiency by VFT before and after resynchronization could be a useful indication of the clinical severity and success of therapy, respectively.

Studies relating vortex ring formation to the functionality of native and prosthetic mitral valves [39-41] suggest that VFT could have a role in functional evaluations of the valves and in optimization of prosthetic valve design.


An experimental acute moderate increase in ventricular afterload impairs hemodynamic conditions for vortex ring formation alongside the diastolic filling jet and, thus, for efficient transmitral blood transport. Implementation of the VFT parameter as a noninvasively measurable, fundamental fluid dynamic index of the presence or absence of efficient intracardiac blood transport could contribute to clinical evaluations as a measure of cardiac health that is disease stage- and patient effects-independent.


We thank Theresa Lombari for veterinary assistance, Danielle R. Wright for secretarial help, Krystal S. Tsosie, our Summer Undergraduate Research Fellowship participant, for technical help, and Stephen Cha for statistical analyses. We thank GE Healthcare for providing the Vivid 7 ultrasound system.

This study was supported by the National Institutes of Health Grant HL68573 (M.B.) and by the Arizona State University and Mayo Clinic Seed Grant (J.J.H., M.M., M.B.)


Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Disclosure: Dr. Belohlavek's research is funded in part by GE Healthcare.


1. Ohno M, Cheng CP, Little WC. Mechanism of altered patterns of left ventricular filling during the development of congestive heart failure. Circulation. 1994;89:2241–50. [PubMed]
2. Vasan RS, Larson MG, Benjamin EJ, Evans JC, Reiss CK, Levy D. Congestive heart failure in subjects with normal versus reduced left ventricular ejection fraction: prevalence and mortality in a population-based cohort. J Am Coll Cardiol. 1999;33:1948–55. [PubMed]
3. Yellin EL, Meisner JS. Physiology of diastolic function and transmitral pressure-flow relations. Cardiol Clin. 2000;18:411–33. [PubMed]
4. Zile MR, Brutsaert DL. New concepts in diastolic dysfunction and diastolic heart failure: Part I: diagnosis, prognosis, and measurements of diastolic function. Circulation. 2002;105:1387–93. [PubMed]
5. Hasegawa H, Little WC, Ohno M, Brucks S, Morimoto A, Cheng HJ, et al. Diastolic mitral annular velocity during the development of heart failure. J Am Coll Cardiol. 2003;41:1590–7. [PubMed]
6. Cooke J, Hertzberg J, Boardman M, Shandas R. Characterizing vortex ring behavior during ventricular filling with Doppler echocardiography: an in vitro study. Ann Biomed Eng. 2004;32:245–56. [PubMed]
7. Sengupta PP, Korinek J, Belohlavek M, Narula J, Vannan MA, Jahangir A, et al. Left ventricular structure and function: basic science for cardiac imaging. J Am Coll Cardiol. 2006;48:1988–2001. [PubMed]
8. Kim HB, Hertzberg J, Lanning C, Shandas R. Noninvasive measurement of steady and pulsating velocity profiles and shear rates in arteries using echo PIV: in vitro validation studies. Ann Biomed Eng. 2004;32:1067–76. [PubMed]
9. Kilner PJ, Yang GZ, Wilkes AJ, Mohiaddin RH, Firmin DN, Yacoub MH. Asymmetric redirection of flow through the heart. Nature. 2000;404:759–61. [PubMed]
10. Kheradvar A, Gharib M. Influence of ventricular pressure drop on mitral annulus dynamics through the process of vortex ring formation. Ann Biomed Eng. 2007;35:2050–64. [PubMed]
11. Collier E, Hertzberg J, Shandas R. Regression analysis for vortex ring characteristics during left ventricular filling. Biomed Sci Instrum. 2002;38:307–11. [PubMed]
12. Shandas R, Gharib M, Liepman D, Shiota T, Sahn DJ. Experimental studies to define the geometry of the flow convergence region. Laser Doppler particle tracking and color Doppler imaging. Echocardiography. 1992;9:43–50. [PubMed]
13. Dabiri JO, Gharib M. The role of optimal vortex formation in biological fluid transport. Proc Biol Sci. 2005;272:1557–60. [PMC free article] [PubMed]
14. Krueger PS, Gharib M. The significance of vortex ring formation to the impulse and thrust of a starting jet. Physics of Fluids. 2003;15:1271–81.
15. Gharib M, Rambod E, Kheradvar A, Sahn DJ, Dabiri JO. Optimal vortex formation as an index of cardiac health. Proc Natl Acad Sci USA. 2006;103:6305–8. [PubMed]
16. Opie LH, Paterson DJ. Blood pressure and peripheral circulation. In: Opie LH, editor. Heart Physiology. Lippincott Williams and Wilkins; Philadelphia: 2004. pp. 431–459.
17. Mann SJ. Severe paroxysmal hypertension (pseudopheochromocytoma): understanding the cause and treatment. Arch Intern Med. 1999;159:670–4. [PubMed]
18. Leite-Moreira AF, Correia-Pinto J, Gillebert TC. Afterload induced changes in myocardial relaxation: a mechanism for diastolic dysfunction. Cardiovasc Res. 1999;43:344–53. [PubMed]
19. Anagnostopoulos PC, Pislaru C, Seward JB, Belohlavek M. Epicardial ultrasound guidance of coronary catheter placement in an experimental animal model. J Am Soc Echocardiogr. 2002;15:1387–90. [PubMed]
20. Stefadouros MA, Dougherty MJ, Grossman W, Craige E. Determination of systemic vascular resistance by a noninvasive technic. Circulation. 1973;47:101–7. [PubMed]
21. Lang RM, Borow KM, Neumann A, Janzen D. Systemic vascular resistance: an unreliable index of left ventricular afterload. Circulation. 1986;74:1114–23. [PubMed]
22. Nishimura RA, Schwartz RS, Tajik AJ, Holmes DR., Jr Noninvasive measurement of rate of left ventricular relaxation by Doppler echocardiography. Validation with simultaneous cardiac catheterization. Circulation. 1993;88:146–55. [PubMed]
23. Gillebert TC, Leite-Moreira AF, De Hert SG. Relaxation-systolic pressure relation. A load-independent assessment of left ventricular contractility. Circulation. 1997;95:745–52. [PubMed]
24. Edvardsen T, Urheim S, Skulstad H, Steine K, Ihlen H, Smiseth OA. Quantification of left ventricular systolic function by tissue Doppler echocardiography: added value of measuring pre- and postejection velocities in ischemic myocardium. Circulation. 2002;105:2071–7. [PubMed]
25. Gharib M, Rambod E, Shariff K. A universal timescale for vortex ring formation. J Fluid Mech. 1998;360:121–40.
26. Kawaguchi M, Hay I, Fetics B, Kass DA. Combined ventricular systolic and arterial stiffening in patients with heart failure and preserved ejection fraction: implications for systolic and diastolic reserve limitations. Circulation. 2003;107:714–20. [PubMed]
27. Nishimura RA, Tajik AJ. Evaluation of diastolic filling of left ventricle in health and disease: Doppler echocardiography is the clinician's Rosetta Stone. J Am Coll Cardiol. 1997;30:8–18. [PubMed]
28. Rademakers FE, Buchalter MB, Rogers WJ, Zerhouni EA, Weisfeldt ML, Weiss JL, et al. Dissociation between left ventricular untwisting and filling. Accentuation by catecholamines. Circulation. 1992;85:1572–81. [PubMed]
29. Paetsch I, Foll D, Kaluza A, Luechinger R, Stuber M, Bornstedt A, et al. Magnetic resonance stress tagging in ischemic heart disease. Am J Physiol Heart Circ Physiol. 2005;288:H2708–14. [PubMed]
30. Lieberman R, Padeletti L, Schreuder J, Jackson K, Michelucci A, Colella A, et al. Ventricular pacing lead location alters systemic hemodynamics and left ventricular function in patients with and without reduced ejection fraction. J Am Coll Cardiol. 2006;48:1634–41. [PubMed]
31. De Mey S, Thomas JD, Greenberg NL, Vandervoort PM, Verdonck PR. Assessment of the time constant of relaxation: insights from simulations and hemodynamic measurements. Am J Physiol Heart Circ Physiol. 2001;280:H2936–43. [PubMed]
32. Dabiri JO, Gharib M. Delay of vortex ring pinchoff by an imposed bulk counterflow. Physics of Fluids. 2004;16:128–130.
33. Pedrizzetti G, Domenichini F. Nature optimizes the swirling flow in the human left ventricle. Phys Rev Lett. 2005;95:108101. [PubMed]
34. Sengupta PP, Khandheria BK, Korinek J, Jahangir A, Yoshifuku S, Milosevic I, et al. Left ventricular isovolumic flow sequence during sinus and paced rhythms: new insights from use of high-resolution Doppler and ultrasonic digital particle imaging velocimetry. J Am Coll Cardiol. 2007;49:899–908. [PubMed]
35. Domenichini F, Pedrizzetti G, Baccani B. Three-dimensional filling flow into a model left ventricle. J. Fluid Mech. 2005;539:179–198.
36. Reul H, Talukder N, Muller EW. Fluid mechanics of the natural mitral valve. J Biomech. 1981;14:361–72. [PubMed]
37. Kheradvar A, Assadi R, Jutzy KR, Bansal RC. Transmitral vortex formation: a reliable indicator for pseudonormal diastolic dysfunction. J Am Coll Cardiol. 2008;51(Supplement A):A104.
38. Wang J, Kurrelmeyer KM, Torre-Amione G, Nagueh SF. Systolic and diastolic dyssynchrony in patients with diastolic heart failure and the effect of medical therapy. J Am Coll Cardiol. 2007;49:88–96. [PubMed]
39. Kheradvar A, Gharib M. Influence of Ventricular Pressure Drop on Mitral Annulus Dynamics Through the Process of Vortex Ring Formation. Ann Biomed Eng. 2007 [PubMed]
40. Kheradvar A, Kasalko J, Johnson D, Gharib M. An in vitro study of changing profile heights in mitral bioprostheses and their influence on flow. Asaio J. 2006;52:34–8. [PubMed]
41. Milo S, Rambod E, Gutfinger C, Gharib M. Mitral mechanical heart valves: in vitro studies of their closure, vortex and microbubble formation with possible medical implications. Eur J Cardiothorac Surg. 2003;24:364–70. [PubMed]
42. Torrent-Guasp FF, Whimster WF, Redmann K. A silicone rubber mould of the heart. Technol Health Care. 1997;5:13–20. [PubMed]