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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 R−Rinterval (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

M−1XTX(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

∆RRi∆RRi−m(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[(RRi−RRM)(RRi+m−RRM)] 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

SD1SD20

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 χ2'10−6. 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

x10⁻²

‐3.5

‐2.5

‐1.5

‐0.5

SD1c

x10⁻³

0

5

10

15

20

25

SD12s

x10⁻²

‐32

‐24

‐16

‐8

0

SD12c

x10⁻²

0

0.5

1

1.5

2

SD2s

x10⁻²

‐2

‐1.5

‐1

‐0.5

0

SD2c

x10⁻³

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

‐1

‐0.6

‐0.2

0.2

0.6

1

123456789

1SD1 2SD2 3SD12 4SD1s 5SD1c

6SD2s 7SD2c 8SD12s 9SD12c

‐1

‐0.6

‐0.2

0.2

0.6

1

123456789

1SD1 2SD2 3SD12 4SD1s 5SD1c

6SD2s 7SD2c 8SD12s 9SD12c

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

CorrelationbetweenvariableandPc‐ 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.

Correlationvariable‐Pc

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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