How should the Stroke Volume Variation be calculated? Insights from a mathematical model.

Vandenbosch T, Wyffels P, De Hert S, Wouters P.
Department of anesthesiology, Ghent University Hospital, Belgium

Background and Goal of Study:
Stroke Volume Variation (SVV) can be calculated in two ways, either as the mean of the calculated SVV’s of each individual respiratory cycle (RC) (I-approach) or as the mean of the pooled Stroke Volumes (SV) of all RC’s (P-approach). Also, the number of RCs included varies between studies1.
As heart rate/mechanical ventilation rate ratio (HR/MVR) is known to influence the predictive value of SVV, the methodology used to calculate SSV may affect the number2.
This simulation study investigates the impact of these different variables on the precision of the calculated SVV, and this across a wide range of HR/MVR.
Materials and Methods:
A mathematical model was build based on the assumption that venous inflow follows a sinusoidal curve. Variation was arbitrarily set at 20%. This curve was then partitioned into equal segments. The length of the segments depended on the HR/MVR. SV’s were simulated by the integral of the curve over these individual segments. Each calculation was repeated 100 times, using a different phase lag between the beginning of the RC and the beginning of the first SV. For each HR/MVR ratio between 1 and 8, the medians of the calculated SVV’s were compared according to the number of included RC’s (1 to 5) and to the I- and P-approach. 
Results and discussion:
With only one RC, there is a systematic underestimation of the SVV, which is most pronounced at lower HR/MVR. Tolerating a 10% error margin, a minimum HR/MVR of 5.6 is needed for a reliable calculation of SVV. (See Figure)  
With the P-approach, including more RC’s, an upward shift of the curve and a leftward shift of the 10% error threshold were observed. When using the I-approach these effects were absent.
Conclusions:
According to this simulation the P-approach gives a more accurate estimation of the SVV, with an optimal number of 4 RC’s. Further simulations, using different variations within the grey zone (15%) and the classically considered responder zone (<10%), and implementation of the concept in clinical studies are needed to confirm these effects and apply the principles in clinical practice.
References:
1 Michard Anesthesiology 2005,2 De Backer Anesthesiology 2009

How should the stroke volume variation be calculated? Insights from a mathematical model