This tutorial provides guidelines on volume signals management and Baan’s equation application. As a general rule for any module, recalculation must be done after each step in order to analyze the right volume signal.

### Volume signals connection to PVL10l module

Connection of *n* volume signals to the PVL10l volume input is achieved using *n-1* OPR10a modules (simple arithmetic operation between 2 signals). For example, 4 OPR10a modules are needed to connect all volume signals from a 5-segments catheter (Figure below). By default, OPR10a is suitable for summing up all segment volumes without causing any change in the properties window.

Before using all segments to estimate the ventricular volume, we suggest verifying that: 1) all segments provide a real volume measurement, and 2) segment volumes are synchronized. If these two requirements are not met, the catheter might have to be moved and / or the segment excluded from the ventricular volume calculation.

### Baan’s equation application

#### Parallel volume removal

Two methods exist to remove parallel volume from signal volume:

- One for one-segment catheters only,
- One for one-segment and multi-segment catheters.

##### One-segment volume catheter

After computation, the parallel volume is directly entered as an offset in the calibration window. Zone 1 and 2 standard measures are modified by subtracting parallel volume from current standard measures (Figure 2).

##### One or multi-segments catheter

The parallel volume cannot be applied as an offset in the calibration window for multi-segments catheters. An additional OPR10a module has to be inserted between the last OPR10a module (used to sum up all segment volumes) and the PVL10l module (Figure below).

The parallel volume must then be subtracted by inserting its value as *coefficient b* in the OPR10a properties window (Figure below).

### Field correction factor application

As the electrical field for measuring conductance is not uniform [1], a field correction factor α must be applied to extract the true ventricular volume, following Baan’s equation: V= 1/α x ρL² (G *measured *- G *parallel)*

- V is the ventricular volume

- α is the field correction factor

- ρ is the blood resistivity

- L is the length between the sensing electrodes

- G is the conductance

If α is commonly assumed around 1 for a one-segment catheter (and therefore for small animals), a multi-segments catheter actually requires to estimate this correction factor.

The α field correction factor is assessed, during a ventricular steady-state, as the ratio between the Stroke Volume (SV) estimated with the multi-segment catheter (and therefore PVL10l module) and the SV estimated with another measurement technique (i.e. blood flowmeter, thermodilution…) [2].

SV values in PVL10l module are displayed in the table at the bottom right corner after validation of the steady-state zone (Figure below).

For other measurement techniques, SV is either computed directly or estimated by dividing the cardiac output by the heart rate on the same ventricular steady-state zone.

Following Baan’s equation, the ratio 1/α must be computed and then applied using OPR10a (Figure below).

This ratio can be computed directly using the following equation: 1/α= SV *other */ SV *PVL10l *

- SV
*other*is the stroke volume obtained using the other measurement technique - SV
*PVL10l*is the SV computed by PVL10l module

Then, 1/α must be inserted in the OPR10a module properties window as *coefficient a* (Figure below).

### References

[1] Baan J, Van der Velde ET, de Bruin HG, Smeenk GJ, Koops J, van Dijk AD, Temmerman D, Senden J and Buis B. Continuous measurement of left ventricular volume in animals and humans by conductance catheter. Circulation 1984;70:812-823.

[2] Feldman MD, Erikson JM, Mao YI, Korcarz CE, Lang RM, and Freeman GL. Validation of a mouse conductance system to determine LV volume: comparison to echocardiography and crystals. American Journal of Physiology & Heart Circulation Physiology 2000;279:H1698-H1707.