El Capítulo 4 se centra en la aplicación de modelos de ajuste lineal, cuadrático y cúbico para cuantificar ∆[K+] a partir de los marcadores de distorsión temporal obtenidos con πCA. Por lo tanto, en el Capítulo 5 se propone un paso de ponderación en el cálculo de los marcadores de distorsión del tiempo.
Motivation of the thesis
The kidneys
Structure and main functions of kidneys
Renal failure
CKD is defined by a glomerular filtration rate of less than 60 mL/min/1.73 m2, albuminuria of at least 30 mg per 24 hours, or any other indicator of kidney damage persisting for more than 3 months [42]. ESRD is defined as an irreversible decline in a person's kidney function that is severe enough to be fatal in the absence of HD or transplantation [44,45].
Hemodialysis
The heart
Electrical activity of the heart
Phases of the cardiac action potential
CKD affects between 8% and 16% of the population worldwide and is often unrecognized by patients and physicians [38–41]. The transient net outward current that causes a small downward AP deflection is primarily due to the movement of potassium (K+) ions carried by the transient outward potassium currentIto1.
The electrocardiogram
The lead system
V3 and V4 face the anterior wall of the left ventricle, while V5 and V6 face the lateral wall of the left ventricle [53]. The orthogonal conduction system reflects the electrical activity of the heart in the right-left axis (lead X), the head-to-feet axis (lead Y), and the anterior-posterior axis (lead Z) [81].
ECG patterns
In non-diseased hearts, the polarity of the QRS complex and TW tend to be concordant [53]. The ST segment is the time during which the ventricles are completely depolarized and contracting and is measured from the S wave (J point) to the beginning of TW Figure 1.7.
Dyskalemia and ECG changes
Review of the state of the art
Associations between serum electrolyte concentrations and changes in cardiac elec-
Blood potassium concentration estimation from the ECG
Automatic, neural network and deep-learning techniques
As explained in Section 1.3.2, the cardiac cycle begins with firing of the SAN in the right atrium. One of the first attempts to estimate blood potassium levels by ECG was made by Frohnertet al.
Objective and outline of the thesis
The chapter concludes by presenting and comparing the performance in the three scenarios of the proposed πCA with respect to PCA, and then discussing the improvements in clinical terms obtained by using πCA-based time-warping markers. Nonlinear T-Wave Time Warping Based Sensing Model for Noninvasive Personalized Blood Potassium Monitoring in Hemodialysis Patients: A Pilot Study”.
Collaborations and research stay
As explained in section 1.4.3, changes in ECG patterns are known to be directly related to [K+]. The time warp analysis, described in Section 2.3.4, was proposed for quantifying changes in the overall TW morphology.
Materials: DEKOALE dataset
General information
Blood sample analysis
ECG measurements
Methods
- ECG preprocessing
- ECG waveform detection and delineation
- Spatial lead reduction by principal component analysis
- Time warping analysis
- Unsigned time warping parameter
- Signed time warping parameters
- Mean warped TW
- Potassium concentration variations ∆ [ K + ]
- Statistical analysis
An example of an ECG with demarcation marks for the QRS complex and TW is shown in Figure 2.2b. Spatial dispersion of ventricular repolarization is a property of the human heart and is responsible for the formation of TW on the ECG [173]. Since TW on ECG reflects the spatiotemporal dispersion of ventricular myocyte repolarization times [178], several metrics are associated with TW morphology (such as amplitude [173], width [179], non-dipolar components [180], notches or asymmetries, and duration ( as QT dispersion [184] and Tapex–Tend has been proposed to quantify repolarization heterogeneity.
Isolating the strictly nonlinear variability information could provide additional insight into the different sources that generate T-wave morphology.
Results
Discussion
- Comparison between d u w and d w
- The HR correction of the d w improve the correlation with ∆ [ K + ]
- d a marker shows poor correlation with ∆ [ K + ]
- The non-linear time warping markers reflect [ K + ] fluctuations
- Relationship between HR and [ K + ]
- Performance evaluation of the proposed time warping indexes respect to T w and T S/A 31
- Limitations
Panels (b) and (c) provide an overview of the time evolution of these descriptors along the ECG acquisition from the onset of HD onwards. It should also be noted that the small differences between ρandr calculated for dˆw,c and dw may be due to the low heart rate variations observed during HD, but larger heart rate variations and consequently a larger correction effect are expected in ambulatory monitoring. Furthermore, this finding lends validity to the dˆw,c proposal presented in this work, which predicts no correlation between HR and [K+]-related changes in TW morphology.
In a previous study [154] a comparison of Tw,TS/A,dw,dNLw,daanddNLa, based on an electrophysiological simulation of ECG in hyperkalemia was performed and tested in a subgroup of ESRD patients undergoing therapy HD.
Conclusions
In chapter 2, TW morphology markers, obtained by applying time-warping analysis, were proposed for non-invasive [K+] variation monitoring in ESRD patients undergoing HD, and their performance was assessed using two previously proposed TW- based markers: the width of the TW [134], the TW slope-amplitude ratio [141]. In other words, PCA may be unable to distinguish between noise and the useful [K+]-driven TW morphological variations, compromising the potential clinical significance of time-warping-based markers. An alternative LSR technique to PCA is periodic component analysis (πCA), which transforms the multi-lead ECG signal by maximizing the periodic components on the TL.
In this chapter, πCA was performed to increase TW one-beat periodicity under the hypothesis that it would outperform PCA by minimizing the contribution of noise and other non-cardiac no-beat periodic sources before deriving time-distortion based markers to monitor [K+ ] variations.
Materials
BPC dataset
Methods
- ECG preprocessing and single lead analysis
- Lead space reduction techniques
- Computation of πCA transformation matrix
- TW morphology markers
- ECG simulation
- LSR performance quantification and statistical analysis
The ΨPCA matrix defining the PCA transformation was obtained from the eigenvectors of the 8 × 8 lead-to-lead ECG autocorrelation matrix calculated using samples in TW as described in Section 2.3.3, within the appropriate learning window (see Table 3.2). To maximize them=1-beat periodicity of the signal, the desired πCA transformation must minimize the following residual periodicity measure [163]:. For each of the three types of noise, 100 different Vhi realizations were extracted and added to the same pure ECG (previously described).
Therefore, to correlate realistically, the first step was to estimate the spatial correlation of real ECG noise.
Results
DEKOALE dataset
BPC dataset
DEKOALE and BPC dataset results comparison
ECG simulation
Discussion
- Preliminary considerations
- DEKOALE dataset
- BPC dataset
- Comparing results from DEKOALE and BPC datasets
- ECG simulation
- Clinical Significance
- Limitations
Marker values were grouped according to body position: supine (S), right (R) and left (L) and by the LSR technique: πCB (full purple box), πCT (full blue box) and PC (full green box). Additionally, πCT-based indices are slightly more correlated with ∆[K+] (higher and lower mean deviation as in the case of dNLw). Moreover, it appears that πCT averages less than πCB in most of the proposed markers.
This suggests that πCT should be the TL of choice for daily monitoring of ESRD patients undergoing HD therapy.
Conclusion
In Chapter 3, two LSR techniques, πCA and PCA, were tested as a step prior to TW temporal curvature analysis to extract markers that can monitor [K+] variations. As a result of this analysis, dw and ˆdw,c were the markers showing the highest median Pearson correlation with ∆[K+]. Direct assessment of the marker as a surrogate [K+] by Pearson correlation analysis implies the assumption of a linear relationship between them.
Therefore, the analysis in this chapter was performed under the hypothesis that the use of patient-specific polynomial models based on TW time-warping-derived markers can provide a better quantitative assessment of ∆[K+].
Materials and Methods
- Study population
- ECG preprocessing and single lead analysis
- Spatial lead reduction by periodic component analysis
- Warping-Based TW morphology markers
- Blood potassium concentration variations
- Marker fitting models for ∆ [ K + ] estimation
- Statistical analysis
Panel (a) shows an example of an ECG (the independent leads I, II, V1 to V6 are depicted) obtained from one of the patients in the DEKAOLE dataset (see section 2.2). In panel (c), the transformedπCT1 signal with both QRS complexes and TW is detected and delineated as detailed in section 2.3.2. Finally, in panel (f) is an example of fitting model for ˆ∆fd,m[K+] estimation, evaluated as in section 4.2.6.
For each patient and marker, the parameters of the three models were estimated using two different approaches: (i).
Results
Discussion
- Correlation coefficients reveal over-fitting in m = a approach
- Quadratic model shows the smallest estimation error
- Technical considerations
- Clinical significance
- Limitations
Similarities in the distribution of real∆[K+] and ˆ∆fd,m[K+] for each marker and regression model can be observed in Figure 4.3, a result, this, confirmed by Spearman's correlation coefficient (ρ) between measured and estimated variations in [ K+] as reported in Table 4.1. However, an improvement can be seen when comparing the Pearson's correlation coefficient (r) evaluated in the three models, IQR being reduced ind=dw and m = a by 0.06 and 0.08 when comparing the quadratic and cubic models respectively in terms of linear model. The median error goes from 0.30 in the linear model to 0.22 and 0.21 in the quadratic and cubic models, respectively.
However, the results from Chapter 3 showed low marker dynamics late post-HD treatment, as shown in Figure 3.3.
Conclusions
The use of TW morphological indices, calculated from time warping analysis, to monitor and quantify [K+] variations in ESRD patients undergoing HS was validated in previous Chapters 2 and 3. In particular, boat pigeon (Section 2.3.5) and dw (section 2.3). 6), have demonstrated high correlation with ∆[K+], and duw was found to be highly correlated with the spread of ventricular repolarization [166]. Notably, the TW morphology recovery index (TMR), obtained from duw, was found to be specifically associated with sudden cardiac death (SCD) patients [222] in 651 chronic heart failure (CHF) patients when tested in MUSIC (MUerte Súbita en Insuficiencia Cardiaca) study [223].
Automatic location of TW boundaries (i.e., start and end position) is a necessary step in the calculation of both markers, so reliable delineation of TW boundaries is very important for TW-based morphological marker assessment for SCD risk stratification [225]. ].
Materials
DEKAOLE dataset
MUSIC dataset
Methods
- Real ECG preprocessing and lead space reduction techniques
- Time warping markers
- Weighting functions computation
- Simulation of TW boundaries shift
- Simulated variability in an electrophysiological model
- DEKOALE Dataset
- MUSIC dataset
Panels (g)-(l) in Figure 5.2 show the resulting TWs after simulating movements only in the To position, panels (m)-(r) show the resulting TWs only after the Te displacement, while panels (s)-(x ) are TW after the displacement To and Te at the same time. To evaluate the effects of the proposed WFs on the reported ability of dw and duw to track [K+] variations, as assessed in Chapter 2, the correlation between serum ∆[K+] and duw,Γ and dw,Γ was reassessed. Construction of the RR histogram: The histogram of the RR intervals for all beats in the 24-hour Holter ECG was obtained by considering bins with a width of 10 ms (Figure 5.3a).
Calculation of MWTW: The MWTW TW in the RRmin and RRmax bins were calculated (Figure 5.3b and Figure 5.3c, respectively) as described in Section 2.3.4.
Results
Simulation of TW boundaries shift
Simulated variability in electrophysiological model
DEKOALE dataset
MUSIC dataset
Discussion
- Simulation of TW boundaries shift
- Simulated variability in an electrophysiological model
- DEKOALE dataset
- MUSIC dataset
- Considerations on the use of the WFs
- Clinical significance
- Limitations
As shown in Figure 5.4, the R values (representing the relative error caused by these misalignments) were significantly lower for duw,T induw,D relative to duw, and similarly for dw,T and dw,D relative to on the other hand, C. The obtained results proved the preservation of the linear relationship between duw,Γ and dw,Γ and changes in the dispersion of repolarization at the cellular level, which varied only by a proportional factor, as shown in Figures 5.5 panels (b), (c) and panels ( e), (f). The results of the Mann-Whitney test (Figure 5.7) showed that TMRuΓ and TMRΓ are specific markers of SCD with no association with PFD risk, regardless of the WF used.
This may be due to the avoidance of opposite-sign objects with similar absolute value, which may have been erroneously considered regular values when using TMRuΓ (Figure 5.7a).
Conclusions
- Time dynamics of time warping based markers are able to follow blood potassium
- Periodic component analysis increases the robustness of time warping based markers
- Quadratic regression models for noninvasive quantification of blood potassium
- Weighting stage improves the robustness to TW delineation errors
The main objective of this thesis was to develop a new approach to estimate [K+] variations in CKD patients undergoing HS, based on the analysis of the overall TW morphology. This objective has been addressed by using morphological indices extracted through TW time-shift analysis, a method that allows the comparison of two different TW shapes and the quantification of their differences. This thesis started by evaluating whether the proposed time-distortion-based markers, calculated either in PCA-based spatially transformed wiring or SL approach, could improve routine [K+] monitoring in ESRD patients undergoing HS.
This confirmed our hypothesis that quantification of the entire TW morphology, not only local features, provides additional information reflecting the effects of [K+] variations on TW, allowing more reliable monitoring of ESRD patients undergoing HD.
Clinical significance
Conclusion
Future works
Vohra, “The enduring role of the electrocardiogram as a diagnostic tool in cardiology,” Journal of the American College of Cardiology, vol. Jaber, “Worldwide incidence of AKI: A meta-analysis,” Clinical Journal of the American Society of Nephrology, vol. Levey, “Prevalence of chronic kidney disease in the United States,” Journal of the American Medical Association, vol.
Friedman, "Novel bloodless potassium determination using a signal-processed single-lead ECG," Journal of the American Heart Association, vol. Willems, “Which QT correction formulas to use for QT monitoring?” Journal of the American Heart Association, vol. Laguna, “T-wave morphology restitution predicts sudden cardiac death in patients with chronic heart failure,” Journal of the American Heart Association , vol.
Internal anatomy of the left kidney
Schematic representation of a hemodialysis machine connected to a patient
Electrical conducting system of the heart
Inward, depolarising and outward, repolarizing currents that underlie the atrial and ven-
Frontal and horizontal leads
Vectorcardiographic loop and its projection onto the three orthogonal planes
Example of ECG waves from the lead II
Diagram of the DEKOALE study protocol
Representative diagram of the preprocessing and transformation used to obtain PCs from
Calculation of the non-linear warping and amplitude markers: d NL w and d NL a
Example of the heart-rate-corrected d w
Distribution of blood potassium variations and PCA-based time warping markers during
PCA-based time warping markers and RR interval time trends
Example of linear fitting computation for marker dynamics evaluation in post HD
Distribution of blood potassium variations and PCA-based time warping markers in
Relative error distributions for under the presence of additive bw, em and ma noises at
Flow chart showing the main steps from ECG acquisition to the evaluation of personalised
Estimation error distributions across patients for each hour h i and when pooling all samples
Examples of cubic regression models computation for a given patient by imposing different
Example of evolution of linear and nonlinear time and amplitude simulated variations and
Quantification of TMR index in MUSIC dataset
Distribution of R Γ for each shift test, maker and WF
Evaluation of WF performance by electro-physiological cardiac model
TMR distributions for SCD, PFD and non-CE in MUSIC dataset
Kaplan-Meier survival curves for the two groups defined after dichotomise patients in
