Modified Simpson’s rule for LVEF

Modified Simpson’s rule for LVEF

Modified Simpson's rule for LVEF
Modified Simpson’s rule for LVEF

Modified Simpson’s rule for LVEF (left ventricular ejection fraction) is used not only in echocardiography, but also in cardiac magnetic resonance (CMR) imaging, left ventricular angiography and computed tomography (CT).

Basic assumption in Simpson’s rule is that the shape of the left ventricular cavity is a composite of a cylinder (from base to the level of the mitral valve), a truncated cone from mitral valve level to the level of the papillary muscles and a cone from there to the apex [1].

  1. Volume of the cylinder: Am x L/3
  2. Volume of the truncated cone: {(Am+ Ap)/2} x L/3
  3. Volume of the cone: 1/3 x (Am+ Ap) x L/3

L: Length of the left ventricle from base to apex. Am: Cross sectional area of the cylindrical portion. Ap: Cross sectional area of the base of the conical portion.

Sum of these three volumes will give the left ventricular volume. In modified Simpson’s rule, these three sections are assumed to be of equal height.

In echocardiography, apical four chamber view and two chamber views are obtained in both systole and diastole. The endocardial borders are traced out. The computer algorithm divides the left ventricular cavity into discs, usually 20 in number. Sum of volumes of these discs will give the left ventricular volume. Difference between the diastolic and systolic volumes divided by the diastolic volume will give the LVEF. This is the method recommended by American Society of Echocardiography [2].

Ejection fraction = (EDV – ESV)/EDV

EDV: End diastolic volume; ESV: End systolic volume. The difference between the two gives the stroke volume. Ejection fraction is in fact the stroke volume divided by the end diastolic volume.

In other modalities of imaging also, the same principle is applied. In CMR and CT, the thickness of the slice is taken as the interval between the slices [2]. In invasive left ventriculography, biplane orthogonal cineangiography is required to apply the modified Simpson’s rule [3].


  1. E D Folland, A F Parisi, P F Moynihan, D R Jones, C L Feldman, D E Tow. Assessment of left ventricular ejection fraction and volumes by real-time, two-dimensional echocardiography. A comparison of cineangiographic and radionuclide techniques. Circulation. 1979 Oct;60(4):760-6.
  2. Ateet Kosaraju; Amandeep Goyal; Yulia Grigorova; Amgad N. Makaryus. Left Ventricular Ejection Fraction. StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2020 Jan-.
  3. M R Starling, R A Walsh. Accuracy of biplane axial oblique and oblique cineangiographic left ventricular cast volume determinations using a modification of Simpson’s rule algorithm. Am Heart J. 1985 Dec;110(6):1219-25.