Institute of Physics and Engineering in Medicine Physiol. Meas. 36 (2015) 1075–1091

Physiological Measurement doi:10.1088/0967-3334/36/6/1075

Influence of heart motion on cardiac output estimation by means of electrical impedance tomography: a case study Martin Proença1,5, Fabian Braun1,5, Michael Rapin1,6, Josep Solà1, Andy Adler2, Bartłomiej Grychtol3, Stephan H Bohm4, Mathieu Lemay1 and Jean-Philippe Thiran5,7 1

  Systems Division, Swiss Center for Electronics and Microtechnology (CSEM), Neuchâtel, Switzerland 2   Systems and Computer Engineering, Carleton University, Ottawa, Canada 3   Fraunhofer Project Group for Automation in Medicine and Biotechnology, Mannheim, Germany 4   Swisstom AG, Schulstrasse 1, 7302 Landquart, Switzerland 5   Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland 6   Department of Health Sciences and Technology (D-HEST), Swiss Federal Institute of Technology (ETHZ), Zürich, Switzerland 7   Department of Radiology, University Hospital Center (CHUV) and University of Lausanne (UNIL), Lausanne, Switzerland E-mail: [email protected] Received 30 November 2014, revised 2 February 2015 Accepted for publication 16 February 2015 Published 26 May 2015 Abstract

Electrical impedance tomography (EIT) is a non-invasive imaging technique that can measure cardiac-related intra-thoracic impedance changes. EITbased cardiac output estimation relies on the assumption that the amplitude of the impedance change in the ventricular region is representative of stroke volume (SV). However, other factors such as heart motion can significantly affect this ventricular impedance change. In the present case study, a magnetic resonance imaging-based dynamic bio-impedance model fitting the morphology of a single male subject was built. Simulations were performed to evaluate the contribution of heart motion and its influence on EIT-based SV estimation. Myocardial deformation was found to be the main contributor to the ventricular impedance change (56%). However, motioninduced impedance changes showed a strong correlation (r = 0.978) with left ventricular volume. We explained this by the quasi-incompressibility of blood and myocardium. As a result, EIT achieved excellent accuracy 0967-3334/15/061075+17$33.00  © 2015 Institute of Physics and Engineering in Medicine  Printed in the UK

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in estimating a wide range of simulated SV values (error distribution of 0.57 ± 2.19 ml (1.02 ± 2.62%) and correlation of r = 0.996 after a twopoint calibration was applied to convert impedance values to millilitres). As the model was based on one single subject, the strong correlation found between motion-induced changes and ventricular volume remains to be verified in larger datasets. Keywords: electrical impedance tomography, EIT, stroke volume, cardiac output, non-invasive, continuous monitoring (Some figures may appear in colour only in the online journal) 1. Introduction Cardiac output (CO) is a key physiological parameter for risk stratification in critically ill and hemodynamically unstable patients (Shoemaker et al 1999). In intensive care units (ICU), CO is routinely monitored via the pulmonary artery catheter thermodilution method, which relies on the injection of a known mass of cold saline in the right heart. CO is computed from the area under the temperature curve measured at a point downstream (Levick 2010, Marik 2013). Although this procedure is sometimes associated with severe complications and nonnegligible mortality rates (Connors et al 1996, Dalen and Bone 1996), it remains the gold standard technique for CO monitoring in ICU, as no alternative method has yet been accepted as a reliable clinical surrogate (Hett and Jonas 2004). 1.1.  Non-invasive CO monitoring

Various non-invasive approaches for estimating CO have been proposed over the last decades, most of which rely on the joint estimation of stroke volume (SV) and heart rate (HR), as CO = SV × HR. Ultrasound cardiography and other imaging modalities such as MRI rely on geometric measurements of the cardiac chambers for determining SV. Doppler echocardiography measures the cross-sectional area of the aorta and the velocity of blood—from which the so-called stroke distance is derived—to calculate SV as area times stroke distance (Levick 2010). Even though quite accurate, these imaging modalities, which require the supervision of skilled personnel, are time-consuming, technically demanding and not adapted for continuous monitoring (Northridge et al 1990, Marik 2013). Another CO monitoring technique is the non-invasive pulse contour analysis, a model-based approach for deriving the aortic flow waveform from peripheral measurements (typically obtained through the vascular unloading technique, tonometry or photoplethysmography). The main limitation of this technique lies in its dependency on time-varying physiological quantities such as arterial compliance (Levick 2010). Another modality, impedance cardiography (ICG), is easy to use and allows continuous monitoring (Kubicek et al 1966). However, it has not gained widespread acceptance in clinical practice because of its contested accuracy and the lack of understanding of the phenomena being measured (Wang and Gottlieb 2006). In their review, Shephard et al (1994) described the eight ideal characteristics for CO monitoring techniques: accuracy, reproducibility, fast response time, operator independency, ease of use, absence of morbidity, measurement continuousness and cost effectiveness. To this day, no existing CO monitoring technique has been able to meet all of these requirements. 1076

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1.2.  EIT-based CO estimation

EIT measures and reconstructs the spatial distribution of intra-thoracic impedance changes. At present, its most promising field of application is the monitoring and optimization of ventilation at the bedside (Adler et al 2012). Over the last decades, cardiovascular applications have received increasing attention as the low-cost, safe, easy-to-use, operator-independent and continuous nature of EIT is an undeniable advantage over alternative imaging modalities, particularly in the context of CO monitoring. Provided that the accuracy and reproducibility of EIT for CO estimation can be demonstrated in large-scale trials, it would be the first modality to comply with all aforementioned requirements (Shephard et al 1994) for CO monitoring techniques. 1.2.1. Previous work.  The determination of SV—and thus CO, as HR is easy to obtain— by means of EIT was first reported by Vonk-Noordegraaf et al (2000). Through multivariate regression, an indirect correlation between SV and the ventricular impedance change was found. Zlochiver et al (2006) proposed a parametric approach where the axes of an ellipsis representing the left ventricle were iteratively optimized from the analysis of the impedances measured. High correlation with the reference was found despite some limitations: the use of ICG as reference and the dependency of their approach on anatomical and conductivity a priori assumptions. A similar approach was used by Rashid et al (2010) who expressed the boundary of the left ventricle as truncated Fourier series coefficients and used a first-order kinematic model as state evolution model. A recent publication (Pikkemaat et al 2014) showed the feasibility of assessing SV from a cardiac impedance change derived from principal component analysis. High correlation was found after application of a subject-wise calibration to convert the impedance values to millilitres. Due to unresolved issues in their results (unexpected scaling effects), the authors highlighted the need for further investigations before considering the transfer of their technique to clinical practice. These three studies differ in their approach for computing an SV-related quantity. Their signals of interest are different and are implicitely based on different (anatomical or physiological) assumptions regarding the cardiac-related impedance change in the ventricular region. The exact origin of this change appears to be still unclear and subject to interpretation. 1.2.2.  Origin of cardiac-related changes in the ventricular region.  EIT and bio-impedance in general, is an appealing tool for flow-related parameter estimation. However, as in ICG, the exact origin of cardiac-related impedance changes in EIT remains unclear. Many potential cardio-synchronous sources of impedance change (such as atrial, ventricular and pulmonary blood volume changes, heart motion, arterial distensibility and pulsatility, or blood flowinduced conductivity changes) act in concert within the thorax. Yet, the correct interpretation of impedance-derived parameters requires a fundamental understanding of the physiological origin of the signals being measured. Several model-based studies have tackled this issue for ICG (Patterson 1985, Kim et al 1988, Wang and Patterson 1995, Patterson 2010, Ulbrich et al 2014), without reaching consensus, as discussed by Patterson (2010), who even concluded that the aorta is highly unlikely to be a major contributor to the ICG waveform. Much remains to be done in EIT, particularly in the documentation of the origin of the cardiac-related impedance change in the ventricular region ΔZ. This point must be thouroughly investigated before exploring the potential of EIT for SV estimation. In particular, heart motion is hypothesized to play a significant role in the genesis of ΔZ, in addition to blood volume-related changes. Indeed, as myocardial deformation occurs, interactions between heart muscle and low conductivity tissues (mostly adipose and lung) at 1077

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Contribution of heart motion to ∆Z (section 2.5.1)

Dynamic MR data (section 2.2.1)

Cardiac scenario (sections 2.1 & 2.2.2)

Dynamic bioimpedance model (section 2.2.4)

EIT simulations (section 2.3)

Impedance change ∆Z in the ventricular region (section 2.4)

Closeness of fit of ∆Z with LVV (section 2.5.2) Tracking of SV changes with ∆Z MAX (section 2.5.3)

Simulated SV (section 2.2.3)

Figure 1. Overview of the simulation and analysis process (light blue boxes and arrows). The black boxes and arrows describe inputs or parameters of the dynamic model.

the periphery of the heart generate cardio-synchronous impedance changes that directly contribute to the genesis of ΔZ, but are not caused by variations in blood volume. Isolating these motion-induced changes from those caused by variations in blood volume is virtually impossible, as strong mechanical (e.g. myocardial deformation and ventricular volume change) and physiological (e.g. cardiac inotropy and SV) interdependencies link both of these two factors (Klabunde 2011). Simulations on a dynamic model to quantify the contribution of each of them to the genesis of ΔZ are therefore suggested. The goal of this study is thus twofold: (1) to provide a better understanding of the origins of the cardiac-related impedance change ΔZ in the ventricular region, in particular by quantifying and characterizing the influence of heart motion; and (2) to evaluate the validity of using ΔZ as an estimator of left ventricular volume (LVV) and thus for SV estimation. To that end, simulations on a dynamic model are considered. Section 2 will describe the model creation and EIT simulation details. The simulation results will be presented in section 3 and discussed in details in section 4. Finally, section 5 will conclude the present study. 2. Methods Figure 1 shows an overview of the simulation and analysis process used in this study. In short, a dynamic bio-impedance model is created from segmented MR images and can simulate different SV values. The model is used to perform EIT simulations (generation of data and reconstruction of image sequences). The cardiac-related impedance change in the ventricular region ΔZ is analyzed to investigate the influence of heart motion in its genesis and to evaluate the possibility of tracking changes in SV in EIT. The contribution (inexistent, partial or total) of heart motion to the genesis of ΔZ can be controlled in the model through the choice of one of its parameters, the cardiac scenario. 2.1.  Cardiac scenarios

Throughout the whole study, three different cardiac scenarios are considered and describe different degrees of heart motion influence. Two of them (scenarios B—for blood—and M—for motion—) are physiologically unrealistic. In B, only blood volume changes are occurring in the heart, but no heart motion is present, i.e. there is no mechanical interaction of the myocardium with its surrouding tissues. Scenario M is the opposite of B: only heart motion is present. There are no blood volume changes in the heart. Finally, scenario R is the real-case scenario and is physiologically realistic. In R, both blood volume changes and heart motion are present. 1078

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0.0 (a)

140

EDVREF

120

LVVREF (ml)

Conductivity (S/m)

0.7

SVREF

100 80 60 40

ESVREF 0

5

10

15

Frame number k

(b)

Figure 2. (a) Example of a segmented frame of the dynamic model. (b) Reference

MRI-derived left ventricular volume LVVREF. The reference end-diastolic, end-systolic and stroke volumes are EDVREF = 128 ml, ESVREF = 51.7 ml and SVREF = 76.3 ml.

Scenarios B and M will allow us to isolate and thus quantify the individual effects that blood volume changes and heart motion have on ΔZ. The real-case scenario R will allow us to evaluate the performance of EIT for SV estimation in physiologically realistic conditions, i.e. when the ventricular impedance change is a mixture of blood volume- and motion-related changes. The way these three scenarios are implemented will be detailed in section 2.2.2. 2.2.  Dynamic bio-impedance model creation 2.2.1.  MR data acquisition and segmentation.  The healthy subject enrolled in this experi-

ment was an 83 kg, 183 cm, 50 year-old male with an underbust girth of 100 cm. MR images were acquired with a 3 T Philips Achieva instrument. ECG-gated scans were performed during apnea in an oblique plane along the long axis of the heart. A full cardiac cycle was imaged with a time resolution of 43 ms, resulting in a total of 20 2D image slices. The spatial resolution in the mediolateral and anterioposterior directions was 0.94 mm/pixel and slice thickness 8 mm. The cardiac cavities (atria and ventricles), the outer boundary of the myocardium and the aorta were segmented manually in each of the 20 MRI frames representing the cardiac cycle. Lungs, fat, skeletal muscle, spine and thorax contour were segmented manually in the first frame only. The aortic wall thickness was assumed to be 12% of the segmented aortic radii (Nichols et al 2011) and the pericardium uniformly 2 mm thick (Wang et al 2003). The resulting segmentation can be seen in figure 2(a) (for one frame of the cardiac cycle). In addition, the segmented area and length of the left ventricle in each frame were used to compute the reference left ventricular volume LVVREF via the single-plane area-length method (Underwood et al 1988) (see figure 2(b)). 2.2.2.  Simulation of scenarios B, M and R.  Simulating the three scenarios described earlier in section 2.1 can be done by modifying adequately the segmentation of the inner boundary of the myocardium (i.e. the boundary of the cardiac chambers), as well as its outer boundary. This process is illustrated in figure 3. In short:

• In scenario B (where the impedance change in the ventricular region is caused by changes in blood volume only), the same segmentation of the myocardial outer boundary is used 1079

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Scenario M

Scenario R

End-systole

End-diastole

Scenario B

Figure 3.  Zoom on the segmentation of the ventricular region for each scenario at end-

diastole (ED) and end-systole (ES). The inner and outer boundaries of the myocardium at ED are shown in light blue for both ED and ES.

for all 20 frames of the cardiac cycle instead of using the true segmentation. This suppresses impedance changes related to heart motion. • In scenario M (where the impedance change in the ventricular region is caused by heart motion only), the same segmentation of the myocardial inner boundary is used for all 20 frames of the cardiac cycle instead of using the true segmentation. This suppresses impedance changes related to blood volume variations. • In scenario R, no modification is made to the segmentation, as scenario R depicts the real-case scenario. Our segmentation can therefore be adapted depending on which cardiac scenario is to be simulated. However, just as our 20 MR images, the segmentation covers one cardiac cycle and therefore one corresponding SV value only (SVREF). Investigating the possibility of tracking SV changes with EIT requires the possibility of artificially changing this SV value and to use it as an input parameter to the model, along with the chosen cardiac scenario (figure 1). This can be done through appropriate modification of the heart segmentation, as described in the next section. 2.2.3.  Simulation of SV changes.  Simulating a different SV value can be achieved by morph-

ing the segmentation of the heart at end-diastole and end-systole to different end-diastolic and end-systolic volumes, respectively. This process is detailed hereunder. It is worth mentioning that this only needs to be done for two frames of the cardiac cycle, namely frame 0 (enddiastolic frame) and frame 7 (end-systolic frame), as this is when ΔZ reaches its minimal and maximal value, respectively; as later detailed in section 2.5.3, only the peak-to-peak amplitude of ΔZ, namely ΔZMAX, is needed for SV estimation. • For each 2D point located on the inner boundary (defining the cardiac chambers) or the outer boundary of the segmented myocardium at frame 0 (i.e. end-diastolic frame), its corresponding point is manually identified at frame 7 (end-systolic frame). 1080

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• Aggregating all these 2D boundary points into matrices at frame 0 and 7 leads to X[0] and X[7], respectively. • We then obtain a displacement matrix Y = X[7] − X[0]. • Introducing the pair of parameters {κ, λ} (both being equal to 1 for the moment), we can write X[0] = X[7] − κY and X[7] = X[0] + λY. • Simulating different SV values can then be done by morphing the segmentation X[0] to a different EDV value using X[0] = X[7] − κY with κ ≠ 1 and/or by morphing the segmentation X[7] to a different ESV value using X[7] = X[0] + λY with λ ≠ 1. Simulating an SV value (different from SVREF) is thus done by applying as is the procedure described above when the chosen cardiac scenario is scenario R (real-case scenario). When the scenario is B, the procedure is applied only for the inner boundary of the myocardium. In M, it is applied only for its outer boundary. A given segmentation is thus characterized by two parameters: the SV value and the cardiac scenario it simulates. The next section describes how—for a given segmentation—a bio-impedance model can be created. As the parameterization of the model is entirely based on the segmentation, a given model will also be characterized by the SV value and the cardiac scenario it simulates. 2.2.4.  Model generation.  An 2.5D (2D extruded) fine mesh fitting the subject’s segmented thorax contour is generated using NETGEN (Schöberl 1997) and the dedicated function (Grychtol et al 2012) of the EIDORS toolbox (Adler and Lionheart 2006) (figure 4(a)). A total of ∼4.6 · 105 tetrahedral elements with an average edge length of 5.1 mm are obtained. For a given segmentation, at each kth frame8, each finite element of the mesh is assigned an electrical conductivity value of the organ or tissue its centre belongs to (by considering an extrusion of the segmentation to 3D) in the time laps of the current frame (figure 4(b)). The biological values of electrical conductivity used in this model are listed in table 1 (Hasgall et al 2014). Cardiac-related impedance changes in the lungs are simulated by varying their conductivity value according to the curve depicted in figure 5(a), reproduced from Vonk-Noordegraaf et al (1998), set to a baseline (end-diastolic) conductivity value of 1.07 · 10−1 S m−1 (Hasgall et al 2014) and scaled in order to produce a maximal conductivity change of 10% (Brown et al 1992). The conductivity value of the aorta depends on the shear rate profile (Visser 1989). From the MRI-based blood flow curve and aorta radii measured in a healthy subject9, the conductivity curve is computed using Visser’s model, set to a baseline (end-diastolic) conductivity value of 7.03 · 10−1 S m−1 (Hasgall et al 2014) and scaled in order to produce a maximal conductivity change of 15% (Raaijmakers et al 1996), as depicted in figure 5(b). Following this procedure, for each given segmentation (i.e. for each SV value and each scenario), a corresponding model was created. EIT data were then simulated for each model, as detailed in the next section. 2.3.  EIT simulations 2.3.1.  EIT data generation: the forward problem.  EIT relies on the application of small alter-

nating electrical currents and peripheral voltage measurements v to estimate the intra-thoracic conductivity distribution σ. In the present study, for a given model, EIT voltages v are obtained using EIDORS with 32-electrode stimulation and measurement patterns where each injecting 8  For the true reference SV value (obtained from the MR data), the whole cardiac cycle (20 frames) is simulated. For the other SV values (obtained by morphing the original segmentation), only the frames 0 and 7 are simulated, as explained earlier in section 2.2.3. 9  Not the same subject as the one on which the bio-impedance model is based, as no such dynamic MR images were acquired for the latter.

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(a)

(b)

Figure 4. Mesh of the 2.5D dynamic bio-impedance model before (a) and after (b) assigning a conductivity value to each of its finite element. Table 1.  Tissue conductivities at 100 kHz (Hasgall et al 2014).

Tissue

Conductivity (S m−1)

Tissue

Conductivity (S m−1)

Blood Blood (aorta) Skeletal muscle Aortic wall Myocardium

7.03 · 10−1 See figure 5(b) 3.62 · 10−1 3.19 · 10−1 2.15 · 10−1

Lungs Spinal cord Fat Vertebrae

See figure 5(a) 8.08 · 10−2 2.44 · 10−2 2.08 · 10−2

0.85

Aorta conductivity (S/m)

Lung conductivity (S/m)

0.12

0.115

0.11

0.105

0

5

10

15

0.8 0.75 0.7 0.65

Frame number k

(a)

0

5

10

15

Frame number k

(b)

Figure 5. (a) Lung conductivity change and (b) aorta conductivity change over the

whole cardiac cycle (see section 2.2.4 for details).

or measuring pair of electrodes is separated by four non-injecting or non-measuring electrodes, respectively (Gaggero 2011). The default EIDORS first-order forward solver is used to generate the voltages v. 2.3.2. EIT image reconstruction: the inverse problem.  EIT is a severely ill-conditioned

inverse problem and the diffusive nature of electrical current propagation only adds to the complexity. Obtaining absolute impedance values in EIT is of great difficulty, but fortunately not necessary for most EIT-based biomedical applications, for which functional information 1082

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(a)

(b)

(c)

(d)

(e)

Figure 6.  Automatic segmentation of the ventricular region of interest (see section 2.4 for details).

is of more interest. The variation of impedance around a reference baseline value is thus sufficient (Holder 2010). For this reason, difference EIT is typically used and the problem is linearized. Instead of directly considering the voltage measurements v and the conductivity distribution σ, difference EIT makes use of difference data y = v − vr, where vr is a reference set of voltages typically obtained by averaging the measurements of the first frames of an EIT recording. It corresponds to the so-called background conductivity distribution σr, used to define the difference conductivity distribution x = σ − σr. As a result, linearized EIT reconstruction can be represented by a reconstruction matrix R, which translates difference measurements y into an estimate of the difference conductivity image as ˆ x = Ry. The computation of the reconstruction matrix depends on the chosen reconstruction method. The GREIT algorithm distinguishes itself by explicitly deriving the reconstruction matrix from a set of figures  of merit such as amplitude response and position error (Adler et al 2009). In this study, the GREIT algorithm was used with the recommended parameters. Difference data were obtained by using the first frame (representing end-diastole) as reference data set, resulting in sequences of 40 × 60 pixel images after image reconstruction. Some examples of reconstructed images are provided in figure 7. For SV estimation with EIT, the cardiac-related impedance change in the ventricular region ΔZ must be extracted from these EIT image sequences. This is done automatically, as detailed in the next section. 2.4.  Automatic extraction of ΔZ in EIT image sequences

Automatically obtaining ΔZ from an EIT image sequence first requires the automatic extraction of a ventricular region of interest (ROI). The ROI is computed in scenario R (real-case scenario). This process is illustrated in figure 6. A sign image is computed as the sign of the average value of each pixel over the cardiac cycle (figure 6(a)). As the reference EIT frame corresponds to end-diastole, a positive sign indicates that—on average—impedance increases over the course of the cardiac cycle. A cardiac power image is then computed as the pixel-wise variance of the impedance change across time (figure 6(b)) and is segmented using the watershed algorithm (Meyer 1994) as proposed by Ferrario et al (2012) (figure 6(c)). The segmented region containing the positive-sign pixel with maximal cardiac power is defined as the ventricular ROI (figure 6(d)). For visual comparison, a segmented frame (the same as in figure 2(a)) is displayed in figure 6(e). The total impedance change in the ventricular region ΔZ[k] at each kth frame is then computed by summing the impedance change of all pixels within the ROI. 2.5.  Analysis protocol

The simulated EIT data are then analyzed to (1) quantify (in terms of amplitude) and (2) characterize (in terms of signal morphology) the influence of heart motion on ΔZ (sections 1083

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Simulated condition 4

Simulated condition 7

Scenario R

Scenario M

Scenario B

Simulated condition 1

Figure 7.  End-systolic reconstructed EIT frame in various conditions (see table  2): the baseline condition (1) and the two conditions (4 and 7) showing the most extreme SVSIM values. The red and blue colours respectively depict an increase and a decrease in impedance with respect to the reference (end-diastolic) frame. The colour scale is the same for all images.

2.5.1 and 2.5.2) and (3) to evaluate the validity and accuracy of EIT for SV estimation (section 2.5.3). 2.5.1.  Analysis 1.  This analysis aims at quantifying the influence (i.e. the contribution in terms of amplitude) of heart motion on the genesis of ΔZ. To do so, EIT images are reconstructed for all scenarios using the same SV value (SVREF, the SV value obtained from the MR images, see figure 2(b)). The peak-to-peak amplitude of ΔZ, i.e. ΔZMAX, is then compared between all scenarios, in particular scenarios B and M. The contribution of heart motion to the global M) B) M) cardiac-related change in the ventricular region is estimated as ΔZ(MAX /(ΔZ(MAX + ΔZ(MAX ) (the superscripts refer to the corresponding scenario). 2.5.2. Analysis 2.  Using ΔZMAX for SV estimation implicitly requires ΔZ to be representa-

tive of LVV. Therefore, this analysis aims at evaluating the influence of heart motion on EITbased LVV estimation by comparing ΔZ, transformed to LVVEIT in millilitres, with LVVREF in scenarios B, M and R (simulating the same SVREF value for all three scenarios). This conversion is done using a two-point calibration based on EDVREF and SVREF (see figure 2(b)): LVVEIT = EDVREF − SVREF·ΔZ/ΔZMAX. The closeness of fit between LVVREF and LVVEIT is evaluated in terms of absolute and relative estimation error and using Pearson’s correlation coefficient. The results are compared between scenarios B, M and R. 2.5.3.  Analysis 3.  This analysis aims at evaluating the influence of heart motion on EIT-based SV estimation by comparing the correlation between various simulated SV values and ΔZMAX in scenarios B, M and R. To do so, 11 physiologically realistic stroke volumes10 are simulated and are hereafter referred to as SVSIM (see table 2). Some of these SV values are very close to 10  The interdependent effects of preload, afterload and cardiac inotropy on SV are taken into account (Klabunde 2011).

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Table 2.  Simulated SV values (adapted from Klabunde (2011)).

ID

Description

EDVSIM (ml)

ESVSIM (ml)

SVSIM (ml)

1 2 3 4 5 6 7 8 9 10 11

Baseline Preload (small increase) Preload (moderate increase) Preload (large increase) Preload (small decrease) Preload (moderate decrease) Preload (large decrease) Afterload (increase) Afterload (decrease) Inotropy (increase) Inotropy (decrease)

128.0 144.0 160.0 176.0 114.6 101.3 88.0 138.7 122.7 117.3 144.0

51.7 54.3 56.9 59.5 46.5 41.3 36.2 67.2 41.4 36.2 72.4

76.3 89.7 103.1 116.5 68.1 60.0 51.8 71.5 81.3 81.1 71.6

140

2.5

∆Z (AU)

2 1.5 1 0.5

120

LVV (ml)

B M R

LVVREF

LVVREF

LVVREF

LVVEIT

LVVEIT

LVVEIT

100 80 60

(B)

0 0

5

10

Frame number k

15

40

0

5

10

15

(M) 0

Frame number k

(a)

5

10

Frame number k

15

(R) 0

5

10

15

Frame number k

(b)

Figure 8. (a) Cardiac-related impedance change in the ventricular region ΔZ for all scenarios. (b) For each scenario, ΔZ-based estimate of LVV using a two-point calibration (see sections 3.1 and 3.2 for details).

each other, but are obtained through widely different EDVSIM and ESVSIM values. The correlation between SVSIM and ΔZMAX is evaluated and compared between scenarios B, M and R, as well as the (absolute and relative) error between SVSIM and SVEIT, where SVEIT is obtained by translating ΔZMAX into millilitres using the two-point calibration computed for each scenario during Analysis 2. Examples of reconstructed images for various values of SVSIM are provided in figure 7. 3. Results 3.1.  Contribution of heart motion to the genesis of the ventricular impedance change

The cardiac-related impedance change ΔZ in the ventricular region computed for each scenario via Analysis 1 is depicted in figure 8(a). The peak systolic amplitude ΔZMAX is found to be 0.84, 1.08 and 1.99 AU (arbitrary units) for scenarios B, M and R, respectively. The contribution of heart motion to the global cardiac-related change in the ventricular region is M) B) M) ΔZ(MAX /(ΔZ(MAX + ΔZ(MAX )= 1.08/(0.84 + 1.08) ≃ 56.3 %. 3.2.  Impact of heart motion on EIT-based LVV estimation

The curve of LVVEIT, obtained via Analysis 2 by mapping ΔZ onto LVVREF via a twopoint calibration, is shown in figure  8(b) for each scenario. The error (mean  ±  SD) between LVVEIT and LVVREF is  −6.70  ±  6.44  ml,  −4.85  ±  5.85  ml and  −5.02  ±  4.96  ml 1085

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5

2-point calibration Least square fit

4

10 2

1 5 11 6

9

2

8

r = 0.996 _ p < 10 9

7

-5 -10 5

M

0 5

R

0

1

Scenario

∆ZMAX (AU)

3

B

0

SVSIM - SVEIT (ml)

3

-5 40

60

80

100

1

120

3

2

4

5

6

7

8

9

10

SVSIM (ml)

SVSIM (referred by ID: see Table 2)

(a)

(b)

11

Figure 9. (a) Maximal cardiac-related impedance change in the ventricular region

versus its corresponding simulated SV in scenario R. The numbers inside the data points refer to the ID of each simulated SV value in table  2. (b) Error between the simulated and estimated SV values for scenarios B, M and R.

(−7.79 ± 8.24%, −5.89 ± 9.49% and −6.03 ± 7.83%) for scenarios B, M and R respectively. In the same order, Pearson’s correlation coefficients of 0.973, 0.978 and 0.984 between both curves are obtained. 3.3.  Impact of heart motion on EIT-based SV estimation

The correlation between ΔZMAX and SVSIM (Analysis 3) is shown in figure  9(a) (for scenario R only) along with the two-point calibration obtained via Analysis 2 for this scenario. Figure 9(b) depicts the absolute error on SV estimation for all three scenarios after translating ΔZMAX into SVEIT using the two-point calibration. The error (mean ± SD) between SVEIT and SVSIM is −0.66 ± 3.88 ml, 1.67 ± 2.48 ml and 0.57 ± 2.19 ml (−0.62 ± 4.43%, 2.19 ± 3.38% and 1.02 ± 2.62%) for scenarios B, M and R, respectively. In the same order, Pearson’s correlation coefficients of 0.984, 0.991 and 0.996 between both curves are obtained. 4. Discussion A dynamic bio-impedance model was created for quantifying and characterizing the influence of heart motion on the genesis of the cardiac-related impedance change in the ventricular region. The feasibility of using impedance changes for tracking SV variations was also tested with the same bio-impedance model. 4.1.  Contribution of heart motion to the genesis of ΔZ

From Analysis 1 and in accordance with previous findings in a simplified version of the proposed model (Proença et al 2014a), the impedance change in the ventricular region was found to be dominated by heart motion-induced changes, with a contribution of approximately 56%. This joint contribution of blood volume-related and heart motion-induced changes to the genesis of the global impedance change in the ventricular region can be explained as follows. During ventricular ejection, as illustrated in figure 10, the myocardium in the EIT ventricular 1086

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ED

ES-ED

ES RA

Conductivity

LA

AV plane LV

+

RV

_

MY LC

Figure 10.  Schematic illustration of the impedance change in the heart region between

end-diastole (ED) and end-systole (ES). The rightmost image depicts the difference of both aforementioned images, i.e. what EIT actually aims at reconstructing. The black lines in ES depict the outlines of ED. See section 4.1 for details. LA: left atrium; RA: right atrium; LV: left ventricle; RV: right ventricle; AV plane: atrioventricular plane; MY: myocardium; LC: low conductivity tissue (adipose or lung tissue).

ROI is progressively substituted (spatially speaking) by adipose and/or lung tissue (Grant et al 2011), while blood is substituted by myocardium. These two effects act in concert and increase the global impedance in the ROI. The opposite occurs in the atrial region, where the low conductivity adipose and lung tissues are progressively subtituted by the myocardium and the latter by blood, thus decreasing the global impedance in the atrial region. The ventricular and atrial regions are separated by a zone of negligible impedance change (between the two green dashed lines of the right panel in figure 10). At end-diastole, this zone is occupied by ventricular blood and is progressively substituted by atrial blood as the atrioventricular plane moves towards the apex during ventricular ejection (Carlsson et al 2004). Therefore, no significant impedance change occurs in this region. 4.2.  Impact of heart motion on EIT-based LVV estimation

Analysis 2 aimed at evaluating the influence of heart motion on the closeness of fit between LVVREF and ΔZ converted to millilitres via a two-point calibration. It was found that both blood volume-related changes (scenario B) and—quite unexpectedly—heart motion-induced changes (scenario M) closely fit and strongly correlate with LVVREF (r > 0.97), similar to what preliminary observations in a simplified version of the proposed model suggested (Proença et al 2014b). This strong correlation between heart motion-induced impedance changes and LVVREF can be explained as follows. The myocardium is nearly incompressible (Bistoquet et al 2008). Therefore, in the ventricular region, the deformation of the myocardial inner boundary (i.e. the deformation of the ventricles) must follow that of its outer boundary, as no volume loss can occur. Consequently, as blood is also nearly incompressible (Kenner et al 1977), impedance changes produced by displacements of adipose and lung tissues surrounding the deforming myocardium directly relate to changes of ventricular blood volume. Although this observation holds true in the oblique electrode plane used in this study, where the radial and longitudinal deformations of the myocardium occur along the same axes as those of the left ventricle, it cannot necessarily be generalized to any electrode plane. In particular, using a standard EIT transverse plane for SV measurement would probably induce several limitations, including in-plane myocardial deformations that do not necessarily relate to LVV and weaken the discrimination between the ventricular and atrial impedance changes due to partial volume effect (Vonk-Noordegraaf et al 2000). 1087

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4.3.  Impact of heart motion on EIT-based SV estimation

Analysis 3 aimed at testing the feasibility of tracking changes in SV with EIT by using the maximal amplitude of the cardiac-related impedance change in the ventricular region, i.e. ΔZMAX. A wide range of physiologically realistic SV variations were simulated (SVSIM). A strong correlation (r > 0.98) was found for all scenarios between ΔZMAX and SVSIM. This suggests that EIT can accurately measure SV when myocardial deformation correlates with ventricular volume change. This has shown to be the case in the MR data (and thus the model) used in this study. However, the generalizability of this observation must be confirmed in larger datasets. 4.4.  Reconstruction algorithm independency

All experiments performed in this paper were repeated using the Gauss–Newton (GN) algorithm for image reconstruction to verify the algorithm indenpendency of the results. The hyperparameter was fixed from the noise figure, chosen to be the same as for the GREIT algorithm (0.5) (Graham and Adler 2006). Very similar results were obtained. In Analysis 1, the contribution of heart motion to the genesis of ΔZ was found to be 57.5% (56.3% with GREIT). In Analysis 2, the correlation between the GREIT- and GN-based LVVEIT estimates was 0.9992, 0.9983 and 0.9994 for scenarios B, M and R, respectively. In the same order, in Analysis 3, correlation coefficients of 0.9994, 0.9995 and 0.9997 were obtained between both SVEIT estimations. 4.5.  Study limitations

The main limitations of the model used in this study are: • Although the impedance changes in the ventricular region show a physiologically coherent behavior (Vonk-Noordegraaf et al 2000), the model has yet to be validated against real EIT measurements and tested at various noise levels. • The model is 2.5D. Electrical currents are known to propagate in three dimensions. Impedance changes occurring above and below the electrode plane are thus not considered adequately. • The dynamic conductivity behaviours used in the proposed model were obtained from other sources. Also, the static conductivity values were compiled by Hasgall et al (2014) and acquired post mortem, therefore not necessarily reflecting exactly the true conductivity values of living tissues. • All simulations were performed using one single current frequency (100 kHz) and a fixed injection/recording pattern. The influence of using other frequencies or other injection/ recording patterns was out of scope of the present study. • The simulation of the different SV values SVSIM (table 2) using the morphing procedure described in section 2.2.3 is limited by the linearity assumption of the latter. Extrapolating EDVREF and ESVREF to larger, respectively smaller, EDV and ESV values is therefore only valid to a certain extent. • Heart motion is a general term that includes both myocardial deformation (change of shape resulting from cardiac cell contraction/relaxation) and heart displacement (translation of or rotation around the center of mass resulting for instance from pericardial effusion (Maisch et al 2004)). In our healthy subject MR images, little or no heart displacement was observed. Therefore, heart motion in the proposed model was only/mostly simulated as myocardial deformation. As a result, the impact that heart displacement (if observed) 1088

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would have on the correlation between ventricular volume change and motion-induced impedance changes remains unknown. Nevertheless, it can be hypothesized that artefacts would be generated at the interface between the heart and its surrounding tissues. Our model—based on one single subject—can neither confirm nor rule out such artefacts. Future work should focus on the validation of the model with real measurements and its extension to 3D. Furthermore, the simulations performed in this study should be tested under various noise conditions for robustness. Finally, measurements on human volunteers under very controlled conditions (measurements in apnea, accurate oblique electrode belt placement, changes in preload, afterload, etc) should be performed to confirm our observations and validate the potential of EIT for non-invasive SV and CO monitoring. 5. Conclusions Simulations were performed on a dynamic bio-impedance model to investigate the origins of the cardiac-related impedance changes in the ventricular region. It was found that the main contributor to this change is heart motion, by approximately 56%. It was further found that the cardiac-related motion-induced impedance changes in the ventricular region were strongly correlated (r = 0.978) with left ventricular volume. As the study is based on one single subject, the generalizability of this observation remains to be tested, but was verified by our MR data and explained by the quasi-incompressibility of blood and myocardial tissue. Under those circumstances, EIT was found to be able to estimate SV (and thus CO) over a wide range of physiologically realistic values with great accuracy. Acknowledgments This work was made possible by grants from the Swiss National Science Foundation (SNSF, no. 205321_153364/1), the SNSF/Nano-Tera project OBESENSE (20NA21-1430801) and the ESA NPI (no. 4000109393/13/NL/PA). The authors would also like to thank P Krammer (Swisstom AG, Landquart, Switzerland) and M Bührer (Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland) for their help in the acquisition of the MR data. References Adler A and Lionheart W R B 2006 Uses and abuses of EIDORS: an extensible software base for EIT Physiol. Meas. 27 S25–42 Adler A et al 2009 GREIT: a unified approach to 2D linear EIT reconstruction of lung images Physiol. Meas. 30 S35–55 Adler A et al 2012 Whither lung EIT: where are we, where do we want to go and what do we need to get there? Physiol. Meas. 33 679–94 Bistoquet A, Oshinski J and Škrinjar O 2008 Myocardial deformation recovery from cine MRI using a nearly incompressible biventricular model Med. Image Anal. 12 69–85 Brown B H, Sinton A M, Barber D C, Leathard A D and McArdle F J 1992 Simultaneous display of lung ventilation and perfusion on a real-time EIT system Proc. IEEE Annual Int. Conf. of the EMBS pp 1710–1 Carlsson M, Cain P, Holmqvist C, Stahlberg F, Lundback S and Arheden H 2004 Total heart volume variation throughout the cardiac cycle in humans Am. J. Physiol. Heart Circ. Physiol. 287 H243–50 1089

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