# Heart Rate Variability by Dynamical Patterns in Windows of Holter Electrocardiograms: A Method to Discern Left Ventricular Hypertrophy in Heart Transplant Patients Shortly after the Transplant

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## Abstract

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## 1. Introduction

## 2. Materialsand Methods

#### 2.1. The Dynamical Landscape Method of ECG Processing

- 1.
- Extraction of R-event time moments from QRS complexes in the acquired ECG recording and their annotation as normal or abnormal;
- 2.
- Preprocessing annotated series of R-event time moments to a signal with normal-to-normal RR intervals, i.e., to a signal with lengths of time intervals between two consecutive heart contractions annotated as normal; in case the resulting RR interval was to short ($RR<250$ ms) or too long ($RR>3000$ ms), the RR interval was replaced by the median of the surrounding 7 RR intervals, i.e., 3 preceding, 3 following, and by itself;
- 3.
- Estimates of HRV on RR intervals by the chosen HRV measures.

#### 2.2. Complexity Measures Used for HRV Assessment

- —
- probability of inflection points: $PIP=p\left(ad\right)+p\left(da\right)$;
- —
- probability of alternation segments: $PAS=p\left(ada\right)+p\left(dad\right)$;
- —
- probability of short segments: $PSS=1-p\left(aaa\right)-p\left(ddd\right)$.

#### 2.3. Visualization of Complexity of RR Increments

- –
- probability matrix $\mathbf{P}$ with elements$$P(i,j)=p(i,j)\phantom{\rule{1.em}{0ex}}for\phantom{\rule{1.em}{0ex}}i,j\in {S}_{{\Delta}_{0}}$$Thus ${\sum}_{i,j}P(i,j)=1$.
- –
- transition matrix
**T**where an element $T(i,j)$ is the probability that increment ${\Delta}_{j}$ occurs given increment ${\Delta}_{i}$ happened:$$T(i,j)=p\left(j\right|i)=\frac{p(i,j)}{p\left(i\right)}\mathrm{in}\mathrm{the}\mathrm{case}p\left(i\right)>0,\phantom{\rule{1.em}{0ex}}0\mathrm{otherwise}$$Thus ${\sum}_{j}T(i,j)=1$, and ${\sum}_{i}T(i,j)=p\left(j\right)$ - –
- entropic matrices:$\mathbf{E}$ matrix of Shannon entropy $ShE\_2$ with elements:$$E(i,j)=-p(i,j)lnp(i,j)\mathrm{in}\mathrm{the}\mathrm{case}p(i,j)>0,\phantom{\rule{1.em}{0ex}}0\mathrm{otherwise}.$$$\mathbf{S}\_\mathbf{T}$ matrix of entropy of transition rates with elements:$$S\_T(i,j)=-p(i,j)ln\frac{p(i,j)}{p\left(i\right)}\mathrm{in}\mathrm{the}\mathrm{case}p(i,j)>0,\phantom{\rule{1.em}{0ex}}0\mathrm{otherwise}.$$$\mathbf{TTE}$ tensor of self-transfer entropy $sTE$ with elements$$TTE(i,j)=-\sum _{m}p(h,i,j)ln\frac{p(h,i,j)}{p(i,j)}$$$$\mathrm{in}\mathrm{the}\mathrm{case}\mathrm{any}p(h,i,j)0,\phantom{\rule{1.em}{0ex}}0\mathrm{otherwise}.$$

**P**are arranged with increasing $\Delta $s then the matrix can be visualized as the 3D Poincaré plot where each $P(i,j)$ describes the probability that an event $(i,j)=\left({\Delta}_{i}{\Delta}_{j}\right)$ occurs in the signal of RR increments. A similar representation used to visualize the transition matrix $\mathbf{T}$ and entropic matrices $\mathbf{E}$ provides the general information of event availability while the system executes the event in question.

#### 2.4. Study Population

- –
- LVM, calculated according to the linear `cube’ method formula of Devereux and Reichek;
- –
- LVMI (LVM index): the ratio of LVM with respect to the body surface area (BSA) to normalize heart mass measurement in subjects with different body sizes;
- –
- RWT (relative wall thickness): to report the relationship between the wall thickness and ventricle size.

- NG:
- when RWT < 0.42 and LVMI <115 g/m${}^{2}$ in the case of a man and LVMI < 95 g/m${}^{2}$ in the case of a woman;
- CR:
- when RWT ≥ 0.42 and LVMI <115 g/m${}^{2}$ in the case of a man and LVMI < 95 g/m${}^{2}$ in the case of a woman;
- H:
- when LVMI ≥115 g/m${}^{2}$ in the case of a man and LVMI ≥ 95 g/m${}^{2}$ in the case of a woman, independently of RWT value.

#### 2.5. ECG Signals Processing

#### 2.6. HRV Measures Estimates

#### 2.7. HRV Analysis of Segmented Signals

- (I)
- HRV of an individual segment: segments corresponding to the lowest and the greatest value of HR were extracted, and then HRV analysis was performed for each of these special segments only;
- (II)
- complexity in HRV measure values for a given window size: the variability among the HRV series was investigated by the standard deviation of HRV series and by SampEn to assess whether two similar consecutive L points from a series remain similar if we add the next $(L+1)$th point to each subsequence. The estimates of SampEn were performed assuming $L=2$ and $r=0.2\ast std$

#### 2.8. Statistical Analysis of Data

## 3. Results

#### 3.1. HRV of Whole Signals

- (1)
- Probability of the no-change event p(zero) is the greatest for the CR group.
- (2)
- Patterns consisting of two–three elements of alternating a and d, i.e., the probabilities: p(ad), p(da), p(ada), p(dad), and corresponding entropies: e(ad), e(da), e(ada), e(dad), are less prevalent in the series of the CR group than in the other groups.
- (3)
- Above observations are in agreement with the lowest values of the probability of points-of-inflection PIP = p(ad) + p(da). The entropic measures: ShE_L, L=1,2,3, S_T and sTE attain the lowest values for signals from the CR group.
- (4)
- The short-term variability measures: pNN20, pNN50, RMSSD display group properties similar to p(da).
- (5)
- The highest values of the studied pattern measures were attained for signals of the NG group. The frequency domain measures, the long-range variability measure, such as SDNN, and the short-range time-domain measures pNN20, and pNN50 took the highest values for signals of H group.
- (6)
- In all groups, the medians of S_T were lower than ShE_1 and sTE were significantly greater than 0, which means that the dynamics of changes in RR increments is richer than in a simple Markov chain. The greatest memory effects were revealed in the signals from the NG group, the smallest in the signals from the CR group.

#### 3.2. Visualization of HRV by Matrices of Dynamical Dependence

#### 3.3. Segmented Signal HRV Analysis

## 4. Discussion and Summary

- The probability distribution $\mathbf{P}$ of HTX patients was strongly steep, and sharply peaked at pattern $\left(00\right)$m where the basic transitions involving accelerations and/or decelerations of magnitude $\le 16$ covered more than 90%.
- Accelerations and decelerations were likely to occur alternately, which affected RR intervals (i.e., to change the mean value in a pendulum-type motion rather than as a stochastic walk). Alternating patterns were observed 100 times more frequently than monotonic patterns. This pendulum-type motion was damped in HTX patients.
- Similar to the healthy coevals, the strongest memory effects in patients after HTX were associated with transitions opposite to damped alternating dynamics.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**The contour plots of probability (in the logarithmic scale) to meet an event: ${\Delta}_{i}$ followed by ${\Delta}_{j}$, obtained from signals of RR intervals pooled in groups NG, H, and CR. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

**Figure A2.**The contour plots of probability of the transition ${\Delta}_{i}\to {\Delta}_{j}$ while being in ${\Delta}_{i}$, obtained from signals of RR increments pooled in groups NG, H, and CR. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

**Figure A3.**The contour plots of the Shannon entropy matrix $ShE\_2$ for probability distribution to meet an event: ${\Delta}_{i}$ followed by ${\Delta}_{j}$. Results were obtained from signals of RR intervals pooled in groups NG, H, and CR. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

**Figure A4.**The contour plots of the entropy of transition rate matrix $\mathbf{S}\_\mathbf{T}$ quantifying Markovian dynamics for an event, i.e., ${\Delta}_{i}$ followed by ${\Delta}_{j}$. Results were obtained from signals of RR intervals pooled in groups NG, H, and CR. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

**Figure A5.**The contour plots of matrix $\mathbf{TTE}$ quantifying the memory effects in probability to observe a sequence of events, i.e., ${\Delta}_{i}$ followed by ${\Delta}_{j}$. Results were obtained from signals of RR intervals pooled in groups NG, H, and CR. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

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**Figure 1.**Plots of subsequent 20,000 HR points of a typical signal recorded from HTX patient (

**top**row), and resulting values of meanHR, RMSSD, and pNN20 obtained in consecutive segments of RR intervals. The segment size is: (

**left**column) $s=20$, (

**right**column) $s=450$ RR intervals.

**Figure 2.**The contour plots of probability (in logarithmic scale) to meet an event: ${\Delta}_{i}$ followed by ${\Delta}_{j}$, obtained from signals of RR intervals pooled in groups of healthy persons and HTX patients. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

**Figure 3.**The contour plots of the Shannon entropy matrix $\mathbf{E}$ for probability distribution to meet an event: ${\Delta}_{i}$ followed by ${\Delta}_{j}$. Results were obtained from signals of RR intervals pooled in groups of healthy persons and HTX patients. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

**Figure 4.**The contour plots of probability of the transition ${\Delta}_{i}\to {\Delta}_{j}$ while being in ${\Delta}_{i}$, obtained from signals of RR intervals pooled in groups of healthy persons and HTX patients. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

**Figure 5.**The contour plots of the entropy of transition rates matrix $\mathbf{S}\_\mathbf{T}$ quantifying Markovian dynamics for an event: ${\Delta}_{i}$ followed by ${\Delta}_{j}$. obtained from signals of RR intervals pooled in groups of healthy persons and HTX patients. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

**Figure 6.**The contour plots of matrix $\mathbf{sTE}$ quantifying the memory effects in probability to observe a sequence of events: ${\Delta}_{i}$ followed by ${\Delta}_{j}$. Results were obtained from signals of RR intervals pooled in groups of healthy persons and HTX patients. $\Delta $ means the magnitude in ms of a deceleration, $\Delta >0$, or acceleration, $\Delta <0$.

**Figure 7.**Kruskal–Wallis test results for HRV measures estimated from windows with the highest SDNN (

**left**) and dependence of the group medians for e(dad), p(da), e(da), pNN20, and RMSSD, consecutively, on segment size (

**right**).

**Left**: names of HRV measures against the segment size, red asterisk indicates segment size for which a statistically significant difference was found, green asterisk indicates a result supported by more than 70% in the bootstrap test. Only measures that discerned groups at least once are listed.

**Right**: The five most statistically confirmed measures of HRV differentiating the studied groups are shown. A black cross indicates the size of a window for which a statistically significant difference was found. A green cross indicates a result supported by the bootstrap test (70%).

**Figure 8.**Kruskal–Wallis test results for HRV measures estimated from windows with the smallest SDNN (

**left**) and dependence of the group medians for p(da), LF and VLF, consecutively, on segment size (

**right**). Plots present the group medians which differentiated the studied groups in at least five segments. See the caption in Figure 7 for other details of the used notation.

**Figure 9.**Kruskal–Wallis test results for HRV measures estimated from windows with the highest HR (

**left**) and dependence of the group medians for e(ad), e(da), e(dad), ShE_1 and sTE, consecutively, on segment size (

**right**). The five most statistically confirmed measures of HRV differentiating the studied groups are shown. See the caption in Figure 7 for other details of the used notation.

**Figure 10.**Kruskal–Wallis test results for HRV measures estimated from windows with the smallest HR (

**left**) and dependence of the group medians for VLF, p(a), and p(zero), consecutively, on segment size (

**right**). Only the measures that differentiated the studied groups in at least five segments are presented. See the caption in Figure 7 for details of the used notation.

**Figure 11.**Kruskal–Wallis test results for std of the whole HRV series (

**left**) and dependence of the group medians of the std of series p(a), p(ad), PIP, p(a), p(zero) and e(da), consecutively, on segment size (

**right**). Only the measures that differentiated the studied groups in at least five segments are presented. See the caption in Figure 7 for details of the used notation.

**Figure 12.**Kruskal–Wallis test results for SampEn of the whole HRV series (

**left**) and dependence of the group medians of the SampEn of series for VLF, p(a), and p(zero), consecutively, on segment size (

**right**). The five most statistically confirmed measures of HRV differentiating the studied groups are shown. See the caption in Figure 7 for details of the used notation.

**Table 1.**Demographic and echo characteristics of patients. Data are expressed as the mean ± std error or as the number (percentage).

Characteristic | NG | CR | H | Difference between Groups |
---|---|---|---|---|

number of patients | 12 (29%) | 22 (52%) | 8 (19%) | |

age at transplantation, | 43 ± 14 | 49 ± 11 | 48 ± 11 | NS |

male gender, n | 10 (83%) | 20 (91%) | 8 (88%) | |

BMI | 26± 4 | 26 ± 6 | 27 ± 5 | NS |

BSA | 1.9 ± 0.1 | 2.0 ± 0.2 | 2.0 ± 0.2 | NS |

LVMI (g/m${}^{2}$) | 82 ± 10 | 92 ± 14 | 122 ± 9 | (NG,H) (CR,H) |

LVM (g) | 156 ± 25 | 184 ± 28 | 245 ± 33 | all pairs are different |

RWT | 0.39 ± 0.03 | 0.53 ± 0.07 | 0.50 ± 0.07 | (NG,H) (NG,CR) |

EF % | 64 ± 3 | 64 ± 4 | 67 ± 10 | NS |

LV SV (mL) | 66 ± 7 | 60 ± 11 | 76 ± 16 | NS |

standard measures: | long–term time domain | meanRR, meanHR, |

based on a series of | SDNN, stdHR | |

{$RR\left(t\right)$} | ||

frequency | PS, VLF, LF, HF | |

short-term time domain | RMSSD, pNN50, pNN20 | |

increment pattern measures: | probability of patterns | p(zero), p(a), p(d), |

based on series of increments | p(aa), p(ad), p(da), p(dd), | |

between consecutive RR intervals: | p(aaa), p(ada), p(dad), p(ddd) | |

{$\Delta RR\left(t\right)$ } | ||

a is an acceleration if $\Delta RR\left(t\right)\le -8$ ms | fragmentation measures | PIP = p(ad)+p(da) |

d is a deceleration if $\Delta RR\left(t\right)\ge 8$ ms. | PAS = p(ada) + p(dad) | |

Otherwise an increment is zero | PSS = 1 – [p(aaa) +p(ddd)] | |

entropic measures: | ||

–Shannon entropy of L-length patterns | ShE_L for L=1,2,3 | |

–dynamics by entropy patterns, | S_T = ShE_1 - ShE_2, | |

sTE = ShE_2 - ShE_3 – S_T | ||

–partial entropy of patterns | e(aa), e(ad), e(da), e(dd), | |

e(aaa), e(ada), e(dad), e(ddd) |

**Table 3.**Medians and their first and third quartiles estimated for the groups of healthy individuals, and NG, CR, H for HRV measures listed in Table 2, together with the p-value from the Kruskal–Wallis test for differences between HTX groups. In brackets() the bootstrap support value is provided if observed.

HRV | Healthy | HTX Groups | Kruskal–Wallis | ||
---|---|---|---|---|---|

Index | Coveals | NG | CR | H | Test p for HTX |

meanRR | 958 [870, 1067] | 697 [679, 819] | 688 [635, 791] | 714 [683, 757] | p = 0.587 |

meanHR | 62.85 [56.95, 69.80] | 86.23 [73.35, 88.39] | 87.62 [75.88, 94.72] | 84.16 [79.36, 88.04] | p = 0.542 |

SDNN | 87.10 [72.18, 102.30] | 22.17 [20.10, 31.66] | 28.44 [20.77, 35.89] | 31.15 [25.65, 35.17] | p = 0.415 |

stdHR | 6.577 [5.849, 7.253] | 2.853 [1.953, 3.330] | 3.807 [2.322, 4.162] | 3.266 [3.193, 4.185] | p = 0.128 |

PS | 3.384 [3.033, 3.755] | 2.432 [2.114, 2.916] | 2.558 [2.373, 2.671] | 2.569 [2.358, 2.750] | p = 0.938 |

VLF | 1.392 [1.308, 1.507] | 1.112 [0.929, 1.167] | 1.180 [1.054, 1.323] | 1.110 [1.066, 1.200] | p = 0.338 |

LF | 1.000 [0.862, 1.281] | 0.265 [0.224, 0.366] | 0.297 [0.244, 0.369] | 0.302 [0.257, 0.399] | p = 0.603 |

HF | 0.868 [0.668, 1.051] | 1.005 [0.708, 1.235] | 0.958 [0.786, 1.192] | 1.035 [0.855, 1.326] | p = 0.859 |

RMSSD | 32.12 [22.85, 46.87] | 9.879 [7.308, 11.29] | 7.189 [6.593, 9.669] | 9.575 [7.012, 12.24] | p = 0.328 |

pNN50 | 6.215 [2.435, 18.76] | 0.025 [0.004, 0.059] | 0.015 [0.005, 0.025] | 0.040 [0.020, 0.185] | p = 0.099 (0.05) |

pNN20 | 39.68 [29.89, 55.69] | 3.815 [2.001, 5.566] | 0.583 [0.184, 3.109] | 3.908 [0.320, 4.885] | p = 0.244 |

p(zero) | 0.145 [0.101, 0.181] | 0.358 [0.317, 0.456] | 0.448 [0.405, 0.469] | 0.430 [0.352, 0.489] | p = 0.289 |

p(a) | 0.441 [0.415, 0.465] | 0.325 [0.274, 0.353] | 0.273 [0.265, 0.296] | 0.294 [0.257, 0.318] | p = 0.174 |

p(d) | 0.423 [0.398, 0.446] | 0.307 [0.272, 0.340] | 0.276 [0.264, 0.301] | 0.276 [0.257, 0.323] | p = 0.415 |

PSS | 0.883 [0.853, 0.919] | 1.000 [0.996, 1.000] | 1.000 [0.998, 1.000] | 0.999 [0.997, 1.000] | p = 0.862 |

p(aa) | 0.183 [0.165, 0.207] | 0.028 [0.007, 0.049] | 0.017 [0.009, 0.029] | 0.021 [0.009, 0.038] | p = 0.915 |

e(aa) | 1.019 [0.859, 1.175] | 0.137 [0.038, 0.232] | 0.077 [0.045, 0.118] | 0.097 [0.043, 0.169] | p = 0.857 |

p(aaa) | 0.058 [0.039, 0.078] | 0.000 [0.000, 0.003] | 0.000 [0.000, 0.001] | 0.001 [0.000, 0.001] | p = 0.625 |

e(aaa) | 0.461 [0.312, 0.621] | 0.003 [0.001, 0.020] | 0.002 [0.000, 0.008] | 0.005 [0.000, 0.008] | p = 0.672 |

p(dd) | 0.176 [0.152, 0.195] | 0.021 [0.005, 0.038] | 0.016 [0.009, 0.028] | 0.012 [0.008, 0.035] | p = 0.992 |

e(dd) | 1.006 [0.871, 1.127] | 0.109 [0.027, 0.187] | 0.069 [0.046, 0.118] | 0.064 [0.039, 0.157] | p = 0.999 |

p(ddd) | 0.058 [0.039, 0.069] | 0.000 [0.000, 0.001] | 0.000 [0.000, 0.001] | 0.000 [0.000, 0.002] | p = 0.996 |

e(ddd) | 0.477 [0.302, 0.574] | 0.002 [0.000, 0.007] | 0.001 [0.000, 0.007] | 0.001 [0.000, 0.013] | p = 0.993 |

PAS | 0.125 [0.082, 0.189] | 0.165 [0.132, 0.207] | 0.156 [0.136, 0.165] | 0.161 [0.146, 0.170] | p = 0.704 |

PIP | 0.373 [0.321, 0.448] | 0.341 [0.328, 0.385] | 0.325 [0.313, 0.333] | 0.330 [0.314, 0.369] | p = 0.084 (0.07) |

p(ad) | 0.188 [0.170, 0.229] | 0.168 [0.154, 0.198] | 0.159 [0.152, 0.169] | 0.165 [0.160, 0.173] | p = 0.418 |

e(ad) | 1.025 [0.848, 1.309] | 0.557 [0.448, 0.709] | 0.427 [0.387, 0.493] | 0.516 [0.392, 0.611] | p = 0.209 |

p(da) | 0.185 [0.154, 0.212] | 0.175 [0.171, 0.203] | 0.162 [0.158, 0.175] | 0.164 [0.157, 0.185] | p = 0.045 (0.72) |

e(da) | 0.938 [0.834, 1.281] | 0.594 [0.462, 0.706] | 0.433 [0.399, 0.593] | 0.528 [0.391, 0.621] | p = 0.225 |

p(ada) | 0.055 [0.040, 0.092] | 0.086 [0.073, 0.105] | 0.080 [0.068, 0.083] | 0.079 [0.074, 0.087] | p = 0.618 |

e(ada) | 0.441 [0.338, 0.682] | 0.355 [0.308, 0.549] | 0.279 [0.252, 0.323] | 0.293 [0.257, 0.409] | p = 0.131 (0.04) |

p(dad) | 0.070 [0.035, 0.100] | 0.077 [0.066, 0.104] | 0.077 [0.069, 0.082] | 0.080 [0.072, 0.086] | p = 0.755 |

e(dad) | 0.534 [0.282, 0.785] | 0.325 [0.280, 0.513] | 0.273 [0.249, 0.326] | 0.307 [0.267, 0.393] | p = 0.229 |

ShE_3 | 7.321 [6.915, 8.250] | 4.049 [3.137, 4.546] | 3.388 [3.079, 4.036] | 3.546 [3.016, 4.361] | p = 0.52 |

ShE_2 | 5.146 [4.792, 5.849] | 2.945 [2.267, 3.123] | 2.374 [2.169, 2.869] | 2.542 [2.147, 3.073] | p = 0.437 |

ShE_1 | 2.663 [2.421, 3.019] | 1.613 [1.280, 1.637] | 1.279 [1.190, 1.525] | 1.404 [1.179, 1.629] | p = 0.27 |

S_T | 2.507 [2.352, 2.844] | 1.339 [0.970, 1.511] | 1.099 [0.988, 1.307] | 1.138 [0.970, 1.438] | p = 0.716 |

sTE | 0.302 [0.204, 0.487] | 0.138 [0.093, 0.205] | 0.097 [0.082, 0.120] | 0.131 [0.108, 0.160] | p = 0.106 (0.02) |

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## Share and Cite

**MDPI and ACS Style**

Makowiec, D.; Wdowczyk, J.; Gruchała, M. Heart Rate Variability by Dynamical Patterns in Windows of Holter Electrocardiograms: A Method to Discern Left Ventricular Hypertrophy in Heart Transplant Patients Shortly after the Transplant. *BioMedInformatics* **2023**, *3*, 220-251.
https://doi.org/10.3390/biomedinformatics3010015

**AMA Style**

Makowiec D, Wdowczyk J, Gruchała M. Heart Rate Variability by Dynamical Patterns in Windows of Holter Electrocardiograms: A Method to Discern Left Ventricular Hypertrophy in Heart Transplant Patients Shortly after the Transplant. *BioMedInformatics*. 2023; 3(1):220-251.
https://doi.org/10.3390/biomedinformatics3010015

**Chicago/Turabian Style**

Makowiec, Danuta, Joanna Wdowczyk, and Marcin Gruchała. 2023. "Heart Rate Variability by Dynamical Patterns in Windows of Holter Electrocardiograms: A Method to Discern Left Ventricular Hypertrophy in Heart Transplant Patients Shortly after the Transplant" *BioMedInformatics* 3, no. 1: 220-251.
https://doi.org/10.3390/biomedinformatics3010015