A Method to Calculate Tissue Impedance Through a Standard Bipolar Pacing Lead

Abstract

The transthoracic impedance (T) and its variations may be estimated through the measurement of the electrical impedance between the can and the right ventricular coil of a defibrillation lead. This method may allow the monitoring of fluid overload before a heart failure attack. Aim of this study was to validate in vitro a method to calculate T in case of a standard bipolar pacing lead, by performing 3 measurements: standard unipolar impedance from the tip (Zuni-tip); unipolar impedance from the ring (Zuni-ring); standard bipolar impedance (Zbip). The formula we used is derived from the standard equivalent circuit of a pacing system:

$$\hbox{T} = (\hbox{Zuni-tip}-\hbox{Zbip}+\hbox{Zuni-ring})/2$$

T represents the tissue impedance between the can and the electrodes of the lead. To validate the method we used a saline solution and 3 different pacing leads manufactured by Vitatron (Vitatron BV, Arnhem, The Netherlands): Impulse II (high impedance lead), Crystalline ActFix (screw-in lead), Brilliant S⁺ (VDD single-lead). The measured values of the saline solution impedance were compared to the values calculated through the formula.

Results

The calculated impedance of the solution, evaluated through the proposed formula, is reliable independently of the electrode used and highly correlated to the corresponding measured values (R > 0.9).

Conclusion

Tissue impedance may be calculated from standard unipolar and bipolar impedance measurements with a standard bipolar pacing lead.

Appendix

$$ {\bf Zbip}={\bf Ztip} + {\bf Zring} + {\bf Rbip} $$

(1)

$$ {\bf Zuni\hbox{-}ring}={\bf T} + {\bf (Rbip}- {\bf Runi)} + {\bf Zring} $$

(2)

$$ {\bf Zuni\hbox{-}tip}={\bf T} + {\bf Runi} + {\bf Ztip} $$

(3)

We can write the same equations in the following way:

$$ \hbox{Ztip}=\hbox{Zbip}-\hbox{Zring}-\hbox{Rbip} $$

(1)

$$ \hbox{Zring}=\hbox{Zuni-ring}-\hbox{T}-(\hbox{Rbip}-\hbox{Runi}) $$

(2)

$$ \hbox{T}=\hbox{Zuni-tip}-\hbox{Runi}-\hbox{Ztip} $$

(3)

Now we can include equation (1) into equation (3):

$$\hbox{T} = \hbox{Zuni-tip}-\hbox{Runi}-\hbox{Zbip} + \hbox{Zring} + \hbox{Rbip} $$

(3)

Now we include equation (2) into equation (3):

$$ \hbox{T} = \hbox{Zuni-tip}+\hbox{Rbip}-\hbox{Runi}-\hbox{Zbip} + \hbox{Zuni-ring}-\hbox{T}-\hbox{Rbip}+\hbox{Runi}\Rightarrow \qquad (3)\quad 2\hbox{T} = \hbox{Zuni-tip}-\hbox{Zbip} +\hbox{Zuni-ring} $$

we can now obtain the value of T as a function of the measurable parameters:

$$ {\bf T} = {\bf (Zuni\hbox{-}tip}-{\bf Zbip} +{\bf Zuni\hbox{-}ring)/2} $$

(6)

Regarding Ztip and Zring the method is similar:

$$ \begin{array}{lll} \hbox{Zring}&=&\hbox{Zuni-ring-} (\hbox{Zuni-tip}-\hbox{Zbip} + \hbox{Zuni-ring})/2 - (\hbox{Rbip} - \hbox{Runi})\\ \quad\Rightarrow&&2\hbox{Zring} = 2\hbox{Zuni-ring}-\hbox{Zuni-tip}+\hbox{Zbip}-\hbox{Zuni-ring}- 2\hbox{Rbip}+2\hbox{Runi}\\ \quad\Rightarrow&&2\hbox{Zring}=\hbox{Zuni-ring}-\hbox{Zuni-tip}+\hbox{Zbip} -2\hbox{Rbip} + 2\hbox{Runi}\\ \quad\Rightarrow&&{\bf (5) Zring} = {\bf (Zbip}-{\bf Zuni\hbox{-}tip}+{\bf Zuni\hbox{-}ring}-{\bf 2Rbip}+{\bf 2Runi)/2.} \end{array} $$

$$ \begin{array}{lll} \hbox{Ztip}&=&\hbox{Zbip}-(\hbox{Zbip}-\hbox{Zuni-tip}+\hbox{Zuni-ring} - 2\hbox{Rbip} +2\hbox{Runi})/2 - \hbox{Rbip}\\ \quad\Rightarrow&&2\hbox{Ztip} = 2\hbox{Zbip}-\hbox{Zbip} + \hbox{Zuni-tip}-\hbox{Zuni-ring}+2\hbox{Rbip}-2\hbox{Runi}- 2\hbox{Rbip}\\ \quad\Rightarrow&&2\hbox{Ztip} = \hbox{Zbip}+\hbox{Zuni-tip}- \hbox{Zuni-ring}-2\hbox{Runi}\\ \quad\Rightarrow&&{\bf (4) Ztip} = {\bf (Zbip} + {\bf Zuni\hbox{-}tip}- {\bf Zuni\hbox{-}ring}- {\bf 2Runi)/2.} \end{array} $$