**4. Simulations**

The development of mathematical and physical models of a haemodynamics is of great importance for the cardiovascular research [32]. The model is a simplified approximation of the real system, which incorporates most of the features. By using simulations, it is possible to predict the performance of the instrumentation, optimise and minimise the design and cost.

Noninvasive sensing instruments for bioimpedance measurement on the radial artery are highly sensitive to noise, and small errors on the measured data could turn into large mistakes in the final results [33]. In order to optimise the signal acquisition of the approach and to understand the impact of arterial pulse propagation to the results, it is reasonable to use modelling and simulation. In addition, we can determine the highest sensitivity of bioimpedance sensing on the radial artery.

## **4.1 Simulation of sensitivity distribution for EBI measurement**

Sensitivity field is a frequently discussed topic in the impedance measurements. The transfer impedance (Ζ) can be approximated as the ration measured between the pick-up (PU) couple voltage (E) and the injected current (I) between the current-carrying (CC) couple [34].

$$\mathbf{Z} = \frac{\mathbf{E}}{I} \tag{2}$$

As biological tissue is inhomogeneous, the total measured impedance (Ζ) is the sum of all local resistivity (ρ) values of all small sub-volumes in the sample and can be written as following [35]:

$$\mathbf{Z} = \iiint \rho \cdot \frac{I\_{\rm CC} \cdot I\_{\rm PU}}{I\_{\rm CC} \cdot I\_{\rm PU}} d\mathbf{} \tag{3}$$

The sensitivity (S) of an impedance measurement is the scalar value representing the CC current density lines *JCC* projection on the PU current density lines *JPU* [35].

$$\mathbf{S} = \frac{Jcc \cdot Jpc}{I\_{CC} \cdot I\_{PU}} \tag{4}$$

S is a positive value if measured impedance Z increases and negative if measured impedance Z decreases [35]. The sensitivity field S can be expressed by the following equation [36]:

$$\mathbf{S} = \mathbf{f}\_{\text{reic}}^{'} \cdot \mathbf{f}\_{\text{cc}}^{'} \tag{5}$$

**23**

**Figure 14.**

**5. Transfer function**

*Noninvasive Acquisition of the Aortic Blood Pressure Waveform*

*Simulated current density lines on the wrist (reprinted from [33]).*

and it describes how effectively different regions are contributing to the measured signal (**Figure 13**) [33]. In **Figure 14**, the configurations A and C have regions of both positive and negative sensitivities, but B (electrodes circularly) detects that the radial artery have only positive (or negative) sensitivity [34]. The maximum sensitivity is concentrated close to the surface of the forearm, near the artery.

*Examples of calculated sensitivity maps obtained for different electrode configurations. Four electrodes are placed on the wrist in distal (a and c) and circular (b) configuration. Scaling of the colour map is kept the same within each simulation. The sensitivity is shown in the colour map: Positive values are indicated with red* 

*colour, and negative values are indicated with blue colour (reprinted from [33]).*

The electrical bioimpedance-based method for central aortic pressure waveform reconstruction allows long-term monitoring of the CAP and obtaining of haemody-

namic parameters like the augmentation index (AI) [41] (see **Figure 15**).

*DOI: http://dx.doi.org/10.5772/intechopen.86065*

**Figure 13.**

where *Jcc* ′ is current density and *Jreci* ′ Jreci ′ reciprocal density.

The sensitivity field in EBI measurements depends on several parameters like electrode number and geometry, orientation, configuration and spacing between electrode couples. Several configuration strategies have been published and researched for EIT applications. Some of these are neighbouring method [37], cross method [38], opposite method [33], adaptive method [39] and focused impedance measurement (FIM) [40].

#### **4.2 Experimental bioimpedance sensitivity simulation**

A finite element modelling (FEM) was used for simulation of four-electrode impedance measuring on the human forearm with different setups and configurations between electrode couples. The objective of the study was to describe the spatial sensitivity field in order to optimise the bioimpedance measurement acquisition of haemodynamics [34]. Two most common approaches of electrode placement for EBI measurements on the wrist are distal and circular [28] which are also used for simulation. The sensitivity can be represented as a projection of the density lines of current-carrying electrode couple on the voltage pick-up density lines,

*Noninvasive Acquisition of the Aortic Blood Pressure Waveform DOI: http://dx.doi.org/10.5772/intechopen.86065*

**Figure 13.** *Simulated current density lines on the wrist (reprinted from [33]).*

#### **Figure 14.**

*Wearable Devices - The Big Wave of Innovation*

current-carrying (CC) couple [34].

be written as following [35]:

ing equation [36]:

where *Jcc* ′

measurement (FIM) [40].

*Z* = \_\_

*Z* = ∭*ρ* ∙ \_\_\_\_\_\_

*S* = \_\_\_\_\_\_

*S* = *Jreic*

is current density and *Jreci*

**4.2 Experimental bioimpedance sensitivity simulation**

artery.

Noninvasive sensing instruments for bioimpedance measurement on the radial artery are highly sensitive to noise, and small errors on the measured data could turn into large mistakes in the final results [33]. In order to optimise the signal acquisition of the approach and to understand the impact of arterial pulse propagation to the results, it is reasonable to use modelling and simulation. In addition, we can determine the highest sensitivity of bioimpedance sensing on the radial

Sensitivity field is a frequently discussed topic in the impedance measurements. The transfer impedance (Ζ) can be approximated as the ration measured between the pick-up (PU) couple voltage (E) and the injected current (I) between the

*E*

As biological tissue is inhomogeneous, the total measured impedance (Ζ) is the sum of all local resistivity (ρ) values of all small sub-volumes in the sample and can

> *JCC* ∙ *JPU ICC* ∙ *IPU*

The sensitivity (S) of an impedance measurement is the scalar value representing

*JCC* ∙ *JPU ICC* ∙ *IPU*

S is a positive value if measured impedance Z increases and negative if measured impedance Z decreases [35]. The sensitivity field S can be expressed by the follow-

′ ∙ *Jcc*

The sensitivity field in EBI measurements depends on several parameters like electrode number and geometry, orientation, configuration and spacing between electrode couples. Several configuration strategies have been published and

researched for EIT applications. Some of these are neighbouring method [37], cross method [38], opposite method [33], adaptive method [39] and focused impedance

A finite element modelling (FEM) was used for simulation of four-electrode impedance measuring on the human forearm with different setups and configurations between electrode couples. The objective of the study was to describe the spatial sensitivity field in order to optimise the bioimpedance measurement acquisition of haemodynamics [34]. Two most common approaches of electrode placement for EBI measurements on the wrist are distal and circular [28] which are also used for simulation. The sensitivity can be represented as a projection of the density lines of current-carrying electrode couple on the voltage pick-up density lines,

′ reciprocal density.

′ Jreci

the CC current density lines *JCC* projection on the PU current density lines *JPU* [35].

*<sup>I</sup>* (2)

*d* (3)

′ (5)

(4)

**4.1 Simulation of sensitivity distribution for EBI measurement**

**22**

*Examples of calculated sensitivity maps obtained for different electrode configurations. Four electrodes are placed on the wrist in distal (a and c) and circular (b) configuration. Scaling of the colour map is kept the same within each simulation. The sensitivity is shown in the colour map: Positive values are indicated with red colour, and negative values are indicated with blue colour (reprinted from [33]).*

and it describes how effectively different regions are contributing to the measured signal (**Figure 13**) [33]. In **Figure 14**, the configurations A and C have regions of both positive and negative sensitivities, but B (electrodes circularly) detects that the radial artery have only positive (or negative) sensitivity [34]. The maximum sensitivity is concentrated close to the surface of the forearm, near the artery.
