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Effect of Meditation on Heart Rate Variability

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The dynamics of the autonomic nervous system, a prime factor for variation of heart rate is modulated by lifestyle factors like meditation and breathing exercises. The effect of meditation (dhyana)practiced by disciples of Ramakrishna Mission(RKM) on the heart rate variability is examined. The heart rate (HR)of a group of disciples of RKM is obtained from ECG signal recorded over a short time duration. Lagged Poincare plot of the heart rate(HR), the method of the principal component analysis, and the autocorrelation of HR fluctuations are used to analyze the HR. The variation of Poincare parameters (SD1),(SD2) and their ratio (SD12), with a lagged number, are non-linear and reveal a significant change with meditation. In particular, the magnitude of the slope and the curvature of(SD12) with lagged number increases after meditation. The meditation reduces the heart rate and increases the stroke volume. A strong correlation between slope and curvature of (SD12) is noted from the correlation matrix of multi-dimensional data set resulting from the Poincar\'e plot. The principal components (PC) of data resulting from pre-and post-meditation are well separated in PC-space. The entropy associated with R-wave fluctuations for all meditators is reduced after meditation. The auto-correlation of HR fluctuations exhibits a highly correlated pattern after meditation. The study suggests that meditation improves the heart rate dynamics and the 'calmness' of mind.
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Effect of Meditation on Heart Rate Variability
Sobhendu Kumar Ghatak
Department of Physics, Vidyamandir, Belur, 700123, India
Abstract
The dynamics of the autonomic nervous system,a prime factor for variation of heart rate is modu-
lated by life style factors like meditation and breathing excercise.The effect of meditation (’dhayan ’)
practiced by disciples of Ramakrishana Mission(RKM) on the heart rate variability is examined. The
heart rate (HR)of a group of disciples of RKM is obtained from ECG signal recorded over short time
duration. Lagged Poincar´e plot of the heart rate(HR),the method of the principal component analy-
sis and the autocorrelation of HR fluctuation are used to analyze the HR.The variation of Poincar´e
parameters (SD1),(SD2) and their ratio (S D12), with lagged number are non-linear,and reveal a
significant change after meditation. In particular,The magnitude of the slope and the curvature of
(SD12) with lagged number increases after meditation.The meditation reduces the heart rate and
increases the stroke volume.A strong correlation between slope and curvature of (SD12) is noted from
the correlation matrix of multi-dimensional data set resulting from the Poincar´e plot.The principal
components (PC) of data resulting from pre- and post- meditation are well separated in PC-space.The
entropy associated with R-wave fluctuations for all meditators is reduced after meditation.The auto-
correlation of HR fluctuation exhibits highly correlated pattern after meditation.The study suggests
that the meditation improves the heart rate dynamics and the ’calmness’ of mind.
Keywords: Heart Rate Variability;Poincar´e analysis;Principal Components;Meditation.
e-mail for correspondence :skghatak@phy.iitkgp.ac.in
1
arXiv:2107.08644v1 [physics.med-ph] 19 Jul 2021
1Introduction
Heart rate variability (HRV),a measure of fluctuations of heart rate (HR) obtained from
the measurement of two consecutive R-R interval in ECG signals is of importance in as-
sessing health of living being [1] -[6].The autonomous nervous system(ANS)is prime factor
for modulating HR,and thereby any change in ANS is reflected in HRV.The measurement
of heart rate variability(HRV) which is non-invasive,sensitive,faster and reproducible is
successfully utilized to find the influence of any factor that alter cardiovascular autonomic
function.A number of indices of HRV obtained from the detailed analysis seem to estab-
lish notable relationship between ANS and various diseases [2][3].The sympathetic and
parasympathetic branches of ANS affects cardiac rhythm in non-additive fashion and any
change in these branches results corresponding changes of the parameters of HRV.
The HRV is quantified from HR data using linear measures in the time and frequency
domain.The data acquired for long time provides better measure in frequency domain.
However,long time ECG recording is inconvenient for subjects staying in a given position
and also time consuming.The spectral analysis in frequency assumes stationarity of signal
and sudden changes in HR results alteration of power spectrum which often difficult to
interpret.The power spectrum of HR signal provides the power in high frequency (HF)
band (0.15–0.4 Hz) representing mostly of parasympathetic response and low frequency
(LF) band (0.04 0.15 Hz) resulting from combined influence of the sympathetic and
that (albeit small)the parasympathetic responses.The ratio of power LF/HF is often con-
sidered as a measure of sympathovagal balance [1].Simpler method to assess complex
non-linear behavior in the study of physiological signals is Poincar´e plot [2], [13],[14] .
The Poincar´e plot,that reflects non-linear aspect of cardio-dynamics,depicts graphically
HR fluctuation and it is scattered plot where each RR interval is plotted against its next
interval. The plot uses unfiltered data and simpler to study dynamics of heart rate vari-
2
ability.The scattered plot of RR intervals forms a cluster and the visual inspection of the
shapes of the cluster in the Poincar´e plot is a guide to assess the quality of recorded ECG
signals and identification of premature and ectopic beats [15],[16].The studies based on
short-term HRV with epochs as short as 300 beat to beat interval(around 5 minutes of
ECG recording) in time domain suggest that the measures are better reproducible than
frequency domain measures [3].The measures are different in two domains but are not
mutually independent due to strong correlation between the parameters.As a result any
additional information useful for better discrimination of subjects with cardiovascular
deregulation are limited [17].Therefore,the search for new parameters,which are able to
provide additional information embedded in the HRV signals is pertinet.In the plot, it is
implicitly assumed that two successive R-R intervals are well correlated.This assumption
lends itself to further generalization to lagged Poincar´e plots by plotting RRi+magainst
RRiwhere mrepresents the distance (in number of beats) between beats.Due to nonlin-
ear nature of heart dynamics, a nonlinear analysis of HRV would provide more details
of the dynamic process [2], [18],[19],[25],[27].The Lagged Poincar´e method,an extension
of conventional Poincar´e one has been found to be a better quantitative tool [20] and is
substantiated from some studies on Chronic Renal failure (CRF) [21],Congestive Heart
Failure (CHF)[22], diabetic subjects [23],[25] and rotatory audio stimulation [26].Different
methodology for non-linear analysis of HRV are being examined [19]. The methods like
3-D return mapping [28], wavelet analysis [6],Detrended fluctuation analysis (DFA)[29],
[30], [31] have been applied to extract different aspects of variability of heart rate.The
principal components analysis of Poincar´e parameters with hypertension,diabetic and con-
trol group have pointed importance of cardiovascular dynamics [27].
The meditation,a practice that augments mind-body relationship often used in life-style-
medicine[35].There are different types of meditation ,e.g Mindfulness,Healthfulness Vipasayana
and Dhayan.The effect on the heart rate variability due to meditation procedure has
3
been studied in time domain [36][37][38][39] with different. In this work,the heart rate
variability of twenty disciples of Ramkrishna Mission who practice Dhayan regularly,are
studied in time domain from ECG signal recorded before and after performance of medi-
tation.The HR variability is mainly analyzed using measures obtained from HR analysis
in time domain.The results of the lagged behaviour of the Poincar´e parameters,the Prin-
cipal component analysis (PCA),the entropy associated with Rwave and the correlation
of HR fluctuation are presented.The study is aimed to explore and assess health benefit
of meditation(Dhayan).
2Method
The disciples (swami)from Ramkrishna Mission,Belur twenty in numbers agreed to vol-
unteer for this endeavour. They are regular meditator and with good health. Each of
them was explained about the object of study,and non-invasive aspect of ECG.The writ-
ten consent from each participant was taken. Except two senior disciples, the age of other
disciples are in the range of 24 to 36 years.The ECG data were recorded in supine position
for 6 minutes before and after Meditation(dhayan)at mission campus.The sampling rate
of ECG signal with II-lead configuration 500Hz. The RR interval were extracted from
the ECG data with the help of ORIGIN software.The peaks other than regular one were
discarded in the analysis.
2.1 Poincar´e Plot
A scatter plot of duplets of successive RRinterval (RR) is the Poincar´e plot. Further
generalization of Poincar´e plots is obtained by plotting m-lagged plots where m represents
the distance(in number of beats) between the duplet beats, that is, the’lag’ of the second
beat from the first one [1],[3],[18],[13],[20]. Three parameters namely (SD1),(SD2) and
SD12 = SD1/SD2 quantify the character of the plot.The parameter (SD1) is the measure
4
of the standard deviation of instantaneous variability of beat-to-beat interval and (SD2)
is that of the continuous long-term RR interval variability.The relative measure SD12 =
SD1/SD2 provides non-linear aspects RR interval.Any activity that stimulates ANS such
as meditation causes the change in peak value of R.Such effects can be examined with the
help of similar plot successive peak value(Rpk) and a significant change has been found
in this study.
2.2 Principal Components Analysis
Principal component analysis (PCA) is a statistical procedure by which a large set of
correlated variables can be transformed to a smaller number of independent new set of
variable without throwing out essence of original data set[32].The new set of variables are
referred as the principal components (PCs).They are linear combination of original one
with weights that form orthogonal basis vectors.The diagonalisation of the covariant ma-
trix of data set gives these basis vectors-e.g. eigenvectors and eigenvalues with decreasing
value.The Each PC’s are linear combination of data weighted with the eigenvectors and
carries new information about the data set. The first few components of PC normally
provide most of the variability of data set. In this study, two sets of data are considered for
the PCA analysis.First set contains the parameters obtained from extended Poincar´e plot
[32],[33].The variables namely SD1,SD2,SD12 for lag m= 1 and the maximum value
of the slope and the curvature of these variables with lag mare considered assuming
that these parameters specify important features of the HRV [26],[27]. The parameters
are in different units and are normalized using the norm of respective parameter of the
group.The normalized and mean subtracted data sets are presented as matrix XM,N where
Mrows and Ncolumns refer to number of subjects and parameters respectively.Second
set of data contains five time-domain parameters namely -HR ,its fluctuation S T D,the
magnitude of R-wave Rpk, its ST D and the entropy Sobtained from the fluctuation of
Rpk values.
5
The covariance matrix Cof normalized data was then obtained as
C=1
M1XTX(1)
The eigenvalues and the eigenvectors of matrix Care obtained for each group using
MATLAB programme.Out of Neigenvalues it turns out that the first n(according to their
magnitudes)values can account most of the data and the corresponding neigenvectors are
considered as basis vectors for calculation of principal components.The eigenvector is given
by
ΨN,n =
ϕ1,1ϕ1,2· · · ϕ1,n
ϕ2,1ϕ2,2· · · ϕ2,n
.
.
..
.
.....
.
.
ϕN,1ϕN,2· · · ϕN,n
(2)
The principal components P C can then be calculated from the matrix equation
P Cn,M = ΨTXT(3)
where P C is the matrix of nxM.The eigenvector is the measure of the weight of data
in determining the principal components and so P Cn,M is nprincipal component of M
subject. The elements of covariant matrix represent the amplitude of correlation between
the Poincar´e parameters.
2.3 Correlation Function
It is observed that there are significant changes in heart rate and the peak value of R-
wave,and the nature of changes are examined through correlation of both heart rhythm
and R-peak before and after meditation.The time-series of the increments of (RRi) was
constructed and the correlation of deviation of successive beat interval was calculated.
6
The autocorrelation function Corr RR was obtained from the equation
Corr RR(m) = 1
σ
N
X
i
RRiRRim(4)
where σis the normalizing factor (Corr RR(0) with zero lag m) and ∆RRi=RRi+1
RRiis the deviation between two consecutive beat interval. Similarly, the correlation
function Corr Rpk of amplitude of peak value of Rwave was obtained replacing RR
by Rpk in above equation.
3Results and Discussions
3.1 The Poincar´e Parameters
A representative scattered Poincar´e plot of RR interval and peak value of Rsignal Rpk
for a subject is shown in Fig.1. The left part of figure is for RRi-RRi+1 and that on
the right for Rpki-Rpki+1 ,and the corresponding data points, marked by red-dot and
green-dot, are for pre- and post- meditation.
0.6
0.8
1
1.2
1.4
0.6 0.8 1 1.2 1.4
Rpki+1
Rpki
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
RRi+1
RRi
Figure 1: The Poincar´e plot of RRiand RRi+1 (a), and similar plot of amplitude Rpk of Rwave (b)
before (Red-dot) and after (Green-dot) meditation.The blue and yellow diamond are respective mean
values.Both results are for a young monk.
The depiction shows the RRiinterval after meditation becomes longer and so heart rate
7
is reduced. The mean values of RR intervals before (blue-diamond) and after (yellow-
diamond) meditation are well separated.The plot of the magnitude Rpk of R-peak in-
creases due to meditation and more importantly, the scattering of data is much reduced
(Fig.1).As Rpk is associated with pumping action, and so it indicates a better ventricular
activity of heart after meditation.This general trend was observed for all subjects though
amount of scattering and shift of mean values differ from person to person.
The Poincar´e indices help to analyze real-time analysis of short duration of ECG
signal. The values of (SD1) and (SD2) were calculated for lag= mfrom the relations
SD1(m) = (Φ(m)Φ(0))1/2and SD2(m) = (Φ(m) +Φ(0))1/2, where the auto-covariance
function Φ(m) is given by Φ(m) = E[(RRiRRM)(RRi+mRRM)] and RRMis the
mean of RRi[24],[25],[?]. We first analyze the results of indices for m= 1.
0
0.02
0.04
0.06
0.08
SD1SD20
0.1
0.2
0.3
0.4
SD12
Figure 2: The box plot of group mean value of (SD1),(SD2) and SD12 before (Red)and after (Green)
meditation for lag m= 1.All changes are statistically significant at level (p < 0.05).
The group mean values of SD1,SD2 and SD12 for m= 1 are presented in Fig.2.Both
short-term (SD1) and long-term (SD2) variance of HR are higher but the ratio (SD12)
is lowered after meditation.The analysis of an extended Poincareˆe plot points out impor-
tance of SD12 and opens up for new measure of HRV.The mean values of SD1,SD2 and
SD12 for different values of mare obtained from RR interval of individual subject before
and after meditation.
The mean values of the parameters for all participants are an increasing function of lag
8
variable m. The growth rate of these parameters are highest close to m= 1 and decreases
with m. This non-linear variation can be characterized by the slope and the curvature of
plot.It is found both the slope and the curvature decrease with m.For large value of m
the curvature becomes negligible as SD12 approaches to its saturation.To estimate the
slope and the curvature we used the Pad´e approximation [25].A simple form for the Pad´e
approximation is chosen for analysis of non-linear variation of these parameters
Y=a+bm
1 + cm (5)
where Yis either SD1,SD2 or SD12 and is represented by the ratio of linear polynomial
of mwith three adjustable parameters a,band c.
0 5 10 15 20
0
0.1
0.2
SD1
0 5 10 15 20
0
0.1
0.2
SD2
0 5 10 15 20
0.4
0.6
0.8
Lag m
SD12
0 2 4 6 8 10 12 14 16 18 20
0
0.1
0.2
SD1
0 2 4 6 8 10 12 14 16 18 20
0
0.1
0.2
SD2
0 2 4 6 8 10 12 14 16 18 20
0.2
0.4
0.6
Lag m
SD12
Figure 3: Plot of the group mean values of SD1(upper),SD2(middle) and SD12(lower)and fitted
curve(line).The left-figure is for Pre- and right-one for Post- meditation period data. Fitted line is
obtained with R2'99.98 percent for all
The data for each participant are fitted using non-linear fit with MATLAB pro-
gramme.The parameters are obtained from the best fitted curve with R2'99.98 per-
cent,and χ2'106. A representative figure with data and the fitted curve is displayed in
Fig.(3) .The slope and curvature of fitted curve had their large magnitude near m= 1.
The maximum values of the slopes SD12sand the curvature SD12cof SD12 m
plot for individual subject within each group are considered.The results of group mean
9
1
1.5
2
SD1S
x10²
3.5
2.5
1.5
0.5
SD1c
x10³
0
5
10
15
20
25
SD12s
x10²
32
24
16
8
0
SD12c
x10²
0
0.5
1
1.5
2
SD2s
x10²
2
1.5
1
0.5
0
SD2c
x10³
Figure 4: The columns represent the group mean value of maximum of the slope and the curvature of
respective plots of SD1 ,SD2 and SD12.The maximum value of these parameters appears close to lag
m= 1. The red and green refers to situation before and after meditation. Note the scale difference
are summarized in Fig.4.The magnitudes of both slopes and curvature are found to be
higher after meditation.The lower magnitude of the curvature of SD12 was associated
with the deviation of normal cardiovascular function of patient [22].It is expected that
this curvature tends to zero for non-innervated heart and is large for heart of healthy
person whose heart beats are less constrained.
3.2 Principal Component Analysis of Poincar´e Parameters
The parameters SD1,SD2,SD12 and their growth with lag mnamely-the maximum val-
ues of the slopes and the curvature before and after meditation describe most aspects of
the Poincar´e plot.The principal component analysis of these data is used to envisage the
10
relative importance of these 9 parameters. The covariant matrix has been constructed
with the normalized values following Eq.(1) and the matrix element represents the corre-
lation coefficients. The correlation matrix of Poincar´eparameters derived from normalized
Figure 5: Plot of the correlation amplitudes which are elements of covariant matrix of before (PRE) and
after (POST) meditation.The x-axis number represents the SD-parameters,marked (1 9) as indicated
below the figure and y-axis the magnitude of components of correlation matrix
data of Pre- and Post- are displayed in Fig.11.The slope and the curvature of a particular
Poincar´e parameter are highly correlated and negative value of the correlation coefficient
is due to opposite sign of the slope and the curvature.The parameters SD1,SD2 are
strongly correlated.On the other hand,SD12 is less dependent on other parameters.The
slope and the curvature of SD12 are strongly correlated.The magnitude of the correlation
aspects are augmented due to meditation.For example,the correlation coefficient between
slope and curvature of SD12 is increased from 0.85 to 0.93.Such correlation between slope
and curvature of SD1 is reduced in meditative state whereas that of SD2 shows opposite
trend.
There are nine eigenvalues of the correlation matrix. The eigenvalue decreases rapidly
with eigenvalue number indicating that only few are relevant (Fig.6).The weight(dotted
line) of eigenvalue indicates relative importance of eigenvalue in determining principle
components.The value 100 refers to complete data retrieval.It is evident that only first
four eigenvalues account 99 and 97 percents of Poincar´e parameters of Pre- and Post-
11
0
20
40
60
80
100
123456789
EigenvalueNo.
Figure 6: Plot of Eigenvalue(column)and weight(dotted line) of each eigenvalue with Eigenvalue num-
ber.For presenting in same scale eigenvalues are multiplied by thousand.Red and green correspond to
before and after meditation.
situation.
The principal components corresponding to four significant eigenvalues of individual
person for Pre- and Post- meditation are obtained using eq.(3).We analyse the result with
respect to the first principal component P C 1 that corresponds to highest eigenvalue.The
variation of other components (either single or combination) vis-vis first one are then
expected to elucidate importance of spectrum of PCA.The trend of other components
like second P C2, third P C 3 and the sum P C2 + P C 3 visa-vis P C1 is displayed in Fig.7
(a),(b) and (d)respectively.The Fig.7(c) depicts the variation of P C3 with P C 2.First
thing to note is the concentration of the data into different region in phase space of the
principal components.The data before and after meditation are well separated (Fig.7).
For each participant there are significant changes of P C indicating that HRV are altered
in meditative state.
The correlation strength between P C and nine derived variables are calculated along
with pvalues. The correlation coefficient with p < 0.005 are tabulated given in Ta-
12
0.4
0.3
0.2
0.1
0
0.1
00.2 0.4 0.6 0.8 1
PC2
PC1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0 0.2 0.4 0.6 0.8 1
PC3
PC1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.4 0.3 0.2 0.1 0 0.1
PC3
PC2
ab
cd
1.1
0.7
0.3
0.1
0.5
0 0.2 0.4 0.6 0.8 1
PC2+PC3
PC1
Figure 7: Plot of values of PC follows from normalized 9 Poincar´e parameters. Figs. a,b,d are results of
P C2,P C 3 and P C 2 + P C3 against P C 1 whereas c for the variation of P C 3 with P C2.The data marked
with Red and Green are respectively before and after meditation.
PRE PC1 PC2 PC3
SD1 0.79 0 0.7235
SD2 0 0 0
SD12 0.68 00
SD1s 0.79 0.69
SD1c 0.76 0.69 0
SD2s 0 0 0
SD2c 0 0 0
SD12s 0.88 0.96 0.85
SD12c 0.98 0.87 0.99
PST PC1 PC2 PC3
SD1 0.72 0.78 0
SD2 0 0 0
SD12 0 0 0
SD1s 0.81 0.81 0.73
SD1c 0 0 0
SD2s 0 0 0
SD2c 0 0 0
SD12s 0.96 0.91 0.95
SD12c 0.99 0.98 0.99
CorrelationbetweenvariableandPc‐ Poincare
Table 1: The correlation amplitudes among P C and the 9 derived variables listed in rows.
ble.1.The zero values refer to case where pvalues are larger than above limit.The only
6 variables contribute to P C 1.The short-time RR interval fluctuation and its time eval-
13
uation are found to be more important than long-time one and their ratio.However,the
growth of SD12 measured by maximum value of the slope and the curvature played
dominant role in all three P C and their contributions are augmented after meditation.
3.3 Principal Component Analysis of time domain parameters
The parameters that exhibit changes due to meditation are the heart rate HR,amplitude
Rpk of Rwave and their standard deviations S T D and the entropy ENT obtained from
fluctuation of Rpk.
0
0.4
0.8
1.2
1 2 3 4 5 6 7 8 9 1011121314151617181920
Rpk
0
1
2
3
4
1 2 3 4 5 6 7 8 9 1011121314151617181920
ENT
Subjects
Figure 8: Columnar plot of amplitude of peak Rpk of R(upper) and entropy derived from Rpk (lower)
before and after meditation.Red and green columns are respectively before and after meditation.Subjects
are numbered 1 20 following name alphabetically
14
The results of Rpk and ENT of each subjects are shown in Fig 8.The Rpk is increased
and EN T goes down for each participant.This indicates improvement of vascular activity
of heart in meditative state.Although the percent of change of both parameters varies
the trend of change remains same. The summary of mean results of heart rate HR,
40
50
60
70
80
PRE PST
HR
0.3
0.4
0.5
0.6
0.7
PRE PST
Rpk
2.5
2.7
2.9
3.1
3.3
3.5
PRE PST
ENT
Figure 9: Plot of the heart rate H R, the peak value Rpk of Rwave and the entropy derived from Rpk
data of the group. Red and green columns are respectively Pre- and Post- meditation.
the peak value Rpk of Rwave and the entropy derived from Rpk data are displayed in
Fig.9.The data is statistically significant with p < 0.05.Due to meditation the heart rate
slows down,the ejection goes up.The reduced fluctuation of R-peak results lower entropy
after meditation.
The weight of eigenvalue demonstrates that the first three eigenvalues take care of
more than 97 percent of data Fig.(10 a).The first principle component is more important
compared to P C2 and P C3.The association of these P C ’s resulted from Pre- and Post-
meditation are very different Fig.(10 b,c,d).They are well separated in respective phase
space and trends are different.
The correlation between P C’s and five parameters are noted in Table.2.The non-zero
numbers are with p < 0.001 and zero when pvalues are much larger than above limit.The
analysis shows that the peak of Rwave and its fluctuation and the associated entropy
may play an important role in assessing the cardiovascular activity.Also it is to be noted
that the correlation between these three parameters with P C1 changes in Post- medi-
tative state.Although HR is reduced but plays very little role in determining P C.The
15
0.3
0.1
0.1
0.3
0.5
0.7
0 0.4 0.8 1.2 1.6
PC3
PC1
0.8
0.4
0
0.4
0.8
1.2
0 0.4 0.8 1.2 1.6
PC2
PC1
b
0.3
0.1
0.1
0.3
0.5
0.7
0.6 0.2 0.2 0.6 1 1.4
PC3
PC2
d
0
20
40
60
80
100
12345
Weight
Eigenvalue
a
c
Figure 10: The eigenvalues ( bar) and respective weight(line) are in plot (a). The association of first
principal components P C1 with P C 2 (b) and P C 3 (c) and that of PC 2 with P C 3 (d) are presented in
the plot.The red and green colours refers to pre- and post meditative state.
CorrelationvariablePc
PST PC1 PC2 PC3
RR 0. 00
SdRR 0 0 0.
RPk 0.95 0.98 0.88
SdRPk 0.77 00
Ent 0.8 0 0
PRE PC1 PC2 PC3
RR 0. 00
SdRR 0 0 0.67
RPk 0.72 0.99 0
SdRPk 0.75 00
Ent 0.5600.82
Table 2: The correlation amplitudes among P C and the time-domain variables.
entropy resulting from the fluctuation of heart rate is also considered and change due to
meditation are found to be less prominent.
16
3.4 Correlation of Fluctuation of Beat Interval and Ramplitude
The correlation functions (Corr RR) and (Corr Rpk) as a function of lag mfor two
meditators were obtained using Eq.4.
a
b
c
d
Figure 11: Plots are for the correlation functions C orr RR of RR interval fluctuation and Corr Rpk
of Rpk amplitude fluctuation for different values of lag m.Plots (a,b) are for youngest and (c,d) for eldest
member in the group.Red and green lines represent data before and after meditation and dotted ones are
for shuffled data.
The subjects were chosen considering their experience in the meditative practice.In the
group they were respectively oldest,practising for many years and youngest,in the process
17
of mastering the meditation.In order to examine extent of the correlation the data on RR
intervals and Rpk were randomised by shuffling successively 5 times.Further shuffling did
not change the character of the correlation of the shuffled data. It is clear from Fig.11 that
both the heart rate and the amplitude of Rwave significantly more correlated after(Green
line)meditation compared to starting state(Red one).The correlation of the shuffled data
are all alike and exhibit random character with near-zero correlation for finite m.The small
fluctuation around zero is related to error.The correlation of RR fluctuation decays with
mwith superimposed oscillatory character and remains finite for appreciable number of
RR.The oscillation aspect of correlation is more prominent for Rpk. Though the number
of distinct oscillation are found to be different for different pupil but it always exists.
18
4Discussions and Conclusions
The influence of (Dhayana) a form of meditation regularly practiced by monk of Ramkr-
ishna Mission on the HRV are studied using short duration of the ECG. The effects of
meditation on the HRV are assessed from the behavioural changes of the Poincar´e pa-
rameters obtained from the Poincar´e plot of the RR interval.The analysis of the Poincar´e
parameters and their dynamics clearly reveal beneficial aspect of meditation. The al-
teration of the cardiovascular regulation are reflected in the difference in distribution of
parameters. It has been recognized that any given RR interval influences nearly eight
consecutive of heart beats that follow, and this notion triggers the analysis of lagged
plot [22],[21].The lagged Poincar´e plot is found to be more effective in finding out the
differences in HRV [25],[27] on the state of ANS. The parameter SD1,the short-time
fluctuation. As SD1 correlates with short term variability of heart rate and is mainly de-
termined by parasympathetic response,the higher value of SD1 after meditation indicates
augmentation of parasympathetic response. Autonomic imbalance(increased sympathetic
and decreased parasympathetic tone)is known to be associated with increased cardiovas-
cular morbidity and mortality.On the other hand both components of ANS contribute
to the SD2 (long term variability) that is more in post meditative state. The Poincar´e
parameters are increasing function of lagged value m.For large value of m,SD12 tends
to unity as the correlation among beats in time nearly vanishes.Important characteristics
of growth of these indices turn out to be slope and curvature for low value of m. Out of
these six derived quantities the slope and -in particular curvature of SD12 in pre - and
post- meditation differ significantly. The increase in absolute values of both slope and cur-
vature of the SD12 after meditation indicates change of ANS activity that is beneficial
to health.The principal component analysis of the variables provides more information
embedded in the lagged Poincar´e plots.The first four PC associated with four significant
eigenvalues of the covariant matrix of data restore most of the variability of data.The
19
trajectory of PC when plotted with appropriate combination of PC clearly separates Pre-
and Post- meditation.It also turns out that the PC which is weighted sum of original
variables is dominated by the dynamics of non-linear Poincar´e parameter SD12.The cor-
relation of beat interval fluctuation shows that the heart beats are far from random in
character.Oscillatory character of the correlation function is more prominent with younger
participant. The study with larger set of meditator are needed for understanding of the
oscillatory aspect of the correlation.
In conclusion, the comparative strength of the Poincar´e indices and their growth with
lag index and thereafter the principal component analysis might be useful to assess the
health benefit of meditation practice. As the analysis of ECG data clearly demonstrate
alteration of ANS activity for better cardiovascular activity and ’calmness’ of mind,it
calls for study with larger meditator group to understand the meditative state. Addition-
ally,similar study of depressed subjects can be utilized to assess extent of improvement
with meditation.
Acknowledgement
The authors is grateful to the disciple of Ramkrishna Mission,Belur,W.B for volunteer-
ing.The encouragement, assistance and permitting me to serve Vidyamandir,Belur from
Swami Divyananda Maharaj are gratefully acknowledged.I am thankful for consultation
and help from cardiologist Dr.Subhra Aditya.
Declaration of Interest
The author declared no biomedical financial interest or potential conflicts of interest.
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