Providing therapies tailored to each patient is the vision of precision medicine, enabled by the increasing ability to capture extensive data about individual patients. In this position paper, we argue that the second enabling pillar towards this vision is the increasing power of computers and algorithms to learn, reason, and build the ‘digital twin’ of a patient. Computational models are boosting the capacity to draw diagnosis and prognosis, and future treatments will be tailored not only to current health status and data, but also to an accurate projection of the pathways to restore health by model predictions. The early steps of the digital twin in the area of cardiovascular medicine are reviewed in this article, together with a discussion of the challenges and opportunities ahead. We emphasize the synergies between mechanistic and statistical models in accelerating cardiovascular research and enabling the vision of precision medicine.

Objective: Chronic kidney disease affects more than 10% of the world population. Changes in serum ion concentrations increase the risk for ventricular arrhythmias and sudden cardiac death, particularly in end-stage renal disease (ESRD) patients. We characterized how T wave amplitude, duration and morphology descriptors change with variations in serum levels of potassium and calcium and in heart rate, both in ESRD patients and in simulated ventricular fibers. Methods: Electrocardiogram (ECG) recordings from twenty ESRD patients undergoing hemodialysis (HD) and pseudo-ECGs (pECGs) calculated from twenty-two simulated ventricular fibers at varying transmural heterogeneity levels were processed to quantify T wave width ( ${\rm T_{w}}$ ), T wave slope-to-amplitude ratio ( ${\rm T_{S/A}}$ ) and four indices of T wave morphological variability based on time warping ( ${\rm d_{w}, d_{w}^{NL},d_{a}\ and\ d_{a}^{NL}}$ ). Serum potassium and calcium levels and heart rate were measured along HD. Results: ${\rm d_{w}^{NL}}$ was the marker most strongly correlated with serum potassium, ${\rm d_{w}}$ with calcium and ${\rm d_{a}}$ with heart rate, after correction for covariates. Median values of partial correlation coefficients were 0.75, -0.74 and -0.90, respectively. For all analyzed T wave descriptors, high inter-patient variability was observed in the pattern of such relationships. This variability, accentuated during the first HD time points, was reproduced in the simulations and shown to be influenced by differences in transmural heterogeneity. Conclusion: Changes in serum potassium and calcium levels and in heart rate have markable effects on T wave descriptors, particularly those quantifying morphological variability. Significance: ECG markers have the potential to be used for monitoring serum ion concentrations in ESRD patients.

Objective: Non-invasive estimation of serum potassium, $\left[{\mathrm{K}}^{+}\right]$, and calcium, $\left[{\mathrm{Ca}}^{2+}\right]$, can help to prevent life-threatening ventricular arrhythmias in patients with advanced renal disease, but current methods for estimation of electrolyte levels have limitations. We aimed to develop new markers based on the morphology of the QRS complex of the electrocardiogram (ECG). Methods: ECG recordings from 29 patients undergoing hemodialysis (HD) were processed. Mean warped QRS complexes were computed in two-minute windows at the start of an HD session, at the end of each HD hour and 48 h after it. We quantified QRS width, amplitude and the proposed QRS morphology-based markers that were computed by warping techniques. Reference $\left[{\mathrm{K}}^{+}\right]$ and $\left[{\mathrm{Ca}}^{2+}\right]$ were determined from blood samples acquired at the time points where the markers were estimated. Linear regression models were used to estimate electrolyte levels from the QRS markers individually and in combination with T wave morphology markers. Leave-one-out cross-validation was used to assess the performance of the estimators. Results: All markers, except for QRS width, strongly correlated with $\left[{\mathrm{K}}^{+}\right]$ (median Pearson correlation coefficients, r, ranging from 0.81 to 0.87) and with $\left[{\mathrm{Ca}}^{2+}\right]$ (r ranging from 0.61 to 0.76). QRS morphology markers showed very low sensitivity to heart rate (HR). Actual and estimated serum electrolyte levels differed, on average, by less than 0.035 mM (relative error of 0.018) for $\left[{\mathrm{K}}^{+}\right]$ and 0.010 mM (relative error of 0.004) for $\left[{\mathrm{Ca}}^{2+}\right]$ when patient-specific multivariable estimators combining QRS and T wave markers were used. Conclusion: QRS morphological markers allow non-invasive estimation of $\left[{\mathrm{K}}^{+}\right]$ and $\left[{\mathrm{Ca}}^{2+}\right]$ with low sensitivity to HR. The estimation performance is improved when multivariable models, including T wave markers, are considered. Significance: Markers based on the QRS complex of the ECG could contribute to non-invasive monitoring of serum electrolyte levels and arrhythmia risk prediction in patients with renal disease.

Noninvasive screening of hypo- and hyperkalemia can prevent fatal arrhythmia in end-stage renal disease (ESRD) patients, but current methods for monitoring of serum potassium (K⁺) have important limitations. We investigated changes in nonlinear dynamics and morphology of the T wave in the electrocardiogram (ECG) of ESRD patients during hemodialysis (HD), assessing their relationship with K⁺ and designing a K⁺ estimator. ECG recordings from twenty-nine ESRD patients undergoing HD were processed. T waves in 2-min windows were extracted at each hour during an HD session as well as at 48 h after HD start. T wave nonlinear dynamics were characterized by two indices related to the maximum Lyapunov exponent (λ^t, λ^wt) and a divergence-related index (η). Morphological variability in the T wave was evaluated by three time warping-based indices (d_w, reflecting morphological variability in the time domain, and d_a and d_a^NL, in the amplitude domain). K⁺was measured from blood samples extracted during and after HD. Stage-specific and patient-specific K⁺ estimators were built based on the quantified indices and leave-one-out cross-validation was performed separately for each of the estimators. The analyzed indices showed high inter-individual variability in their relationship with K⁺. Nevertheless, all of them had higher values at the HD start and 48 h after it, corresponding to the highest K⁺. The indices η and d_w were the most strongly correlated with K⁺ (median Pearson correlation coefficient of 0.78 and 0.83, respectively) and were used in univariable and multivariable linear K⁺ estimators. Agreement between actual and estimated K⁺ was confirmed, with averaged errors over patients and time points being 0.000 ± 0.875 mM and 0.046 ± 0.690 mM for stage-specific and patient-specific multivariable K⁺ estimators, respectively. ECG descriptors of T wave nonlinear dynamics and morphological variability allow noninvasive monitoring of K⁺ in ESRD patients. ECG markers have the potential to be used for hypo- and hyperkalemia screening in ESRD patients.

Objective: Chronic kidney disease patients have a decreased ability to maintain normal electrolyte concentrations in their blood, which increases the risk for ventricular arrhythmias and sudden cardiac death. Non-invasive monitoring of serum potassium and calcium concentration, [K⁺] and [Ca²⁺], can help to prevent arrhythmias in these patients. Electrocardiogram (ECG) markers that significantly correlate with [K⁺] and [Ca²⁺] have been proposed, but these relations are highly variable between patients. We hypothesized that inter-individual differences in cell type distribution across the ventricular wall can help to explain this variability.Methods: A population of human heart-torso models were built with different proportions of endocardial, midmyocardial and epicardial cells. Propagation of ventricular electrical activity was described by a reaction-diffusion model, with modified Ten Tusscher-Panfilov dynamics. [K⁺] and [Ca²⁺] were varied individually and in combination. Twelve-lead ECGs were simulated and the width, amplitude and morphological variability of T waves and QRS complexes were quantified. Results were compared to measurements from 29 end-stage renal disease (ESRD) patients undergoing hemodialysis (HD).Results: Both simulations and patients data showed that most of the analyzed T wave and QRS complex markers correlated strongly with [K⁺] (absolute median Pearson correlation coefficients, r, ranging from 0.68 to 0.98) and [Ca²⁺] (ranging from 0.70 to 0.98). The same sign and similar magnitude of median r was observed in the simulations and the patients. Different cell type distributions in the ventricular wall led to variability in ECG markers that was accentuated at high [K⁺] and low [Ca²⁺], in agreement with the larger variability between patients measured at the onset of HD. The simulated ECG variability explained part of the measured inter-patient variability.Conclusion: Changes in ECG markers were similarly related to [K⁺] and [Ca²⁺] variations in our models and in the ESRD patients. The high inter-patient ECG variability may be explained by variations in cell type distribution across the ventricular wall, with high sensitivity to variations in the proportion of epicardial cells.Significance: Differences in ventricular wall composition help to explain inter-patient variability in ECG response to [K⁺] and [Ca²⁺]. This finding can be used to improve serum electrolyte monitoring in ESRD patients.