Threshold sensitivity in time domain BRS estimation: Minimum beat-to-beat changes and minimum correlation

Abstract

In the sequences technique, baroreflex sensitivity (BRS) is estimated as the slope between SBP and RR values in baroreflex sequences (BS). For BS identification, thresholds are applied to SBP and RR series and no recommendation on the appropriate values is given in the literature. Changes in their values can modify the number of BSs and the BRS estimate, making difficult to compare results from different studies, if not impossible. In this work, optimum thresholds values for the identification of baroreflex related events are given. The results in the EuroBaVar dataset indicate that BRS analysis can be improved if no minimum SBP and RR beat-to-beat changes are imposed and the minimum SBP-RR correlation is 0.8. This combination duplicates the number of beats (located in more and longer segments) with global SBP-RR correlation close to 0.8, without introducing substantial changes in BRS estimates distribution. Also, it makes possible to estimate the BRS when BSs are not identified.

Full text

Page 1

Threshold Sensitivity in Time Domain BRS Estimation:
Minimum Beat-to-Beat Changes and Minimum Correlation
S Gouveia1,2, AP Rocha1,2, P Laguna3, P Lago1
1Dep de Matem´ atica Aplicada, Faculdade de Ciˆ encias, Universidade do Porto, Portugal
2Centro de Matem´ atica da Universidade do Porto, Portugal
3Comm Tech Group, Aragon Institute of Eng Research / CIBER-BBN, Univ of Zaragoza, Spain
Abstract
In the sequences technique, baroreflex sensitivity (BRS)
is estimated as the slope between SBP and RR values in
baroreflex sequences (BS). For BS identification, thresh-
olds are applied to SBP and RR series and no recommen-
dation on the appropriate values is given in the literature.
Changes in their values can modify the number of BSs and
the BRS estimate, making difficult to compare results from
different studies, if not impossible.
In this work, optimum thresholds values for the
identification of baroreflex related events are given. The
results in the EuroBaVar dataset indicate that BRS anal-
ysis can be improved if no minimum SBP and RR beat-
to-beat changes are imposed and the minimum SBP–RR
correlation is 0.8. This combination duplicates the num-
ber of beats (located in more and longer segments) with
global SBP–RR correlation close to 0.8, without intro-
ducing substantial changes in BRS estimates distribution.
Also, it makes possible to estimate the BRS when BSs are
not identified.
1. Introduction
The sequences technique is the most used time domain
methodforarterialbaroreflexsensitivity(BRS)estimation.
It is based in the joint analysis of SBP and RR beat-to-
beat spontaneous variability, being the BRS estimated as
the slope between SBP and RR values in baroreflex se-
quences (BS) [1]. For BS identification it is usual to im-
pose several numerical thresholds on SBP and RR series.
Such thresholds are usually set to increase the reliability of
BS being a baroreflex related segment and, therefore, in-
crease the assurance that the BRS estimate is measuring a
real baroreflex effect. However their use may also reduce
the ability of providing an individual estimate, particularly
if the thresholds values are very restrictive and/or the ana-
lyzedsubjecthaspoorBRSfunction(casesassociatedwith
few or nonexistent BSs and lower BRS values).
The sequences technique was originally described in
cats [1] and has been widely applied unchanged in hu-
mans, without the evidence that the thresholds values used
in cats are adequate in human BRS studies. Moreover, no
consensual opinion about those values is found in the lit-
erature [2, 3]. A slight modification in the thresholds val-
ues can change the number of BSs and the BRS estimate.
Therefore, literature results on BRS may not be compara-
ble in practice and the need to establish reference values
is evident. In this work, the effect of changing the thresh-
olds values for baroreflex related segments identification
is studied towards the goal of establish reference values.
2.Time domain BRS estimation
TimedomainBRSanalysisisbasedonBSsidentification
following the BRS estimation as the slope between the cor-
responding SBP and RR values.
A valid BSk, k = 1,2,···,K is a SBP–RR seg-
ment with Nk≥Nminbeats length that satisfies minimum
SBP and RR beat-to-beat changes in the same direction
(∆SBP
k≥∆SBP
minand ∆RR
k≥∆RR
min) and a minimum SBP–RR
correlation value (rk≥rmin). Table 1 resumes the values
imposed in this work for the identification of a valid BS.
Table 1. Thresholds values for BS identification.
Thresholds (Units) BS
Nmin(beats)3
∆SBP
min(mmHg)1
∆RR
min(ms)5
rmin(no units)0.8
The choice of ∆SBP
estimated slope to values above the ratio ∆RR
subjects with BRS values > 10 ms/mmHg, the generally
accepted threshold of ∆SBP
min=1 mmHg will lead, in aver-
age, to RR values higher than 10 ms, exceeding the ∆RR
minand ∆RR
minvalues can restrict the
min/∆SBP
min. In
min
ISSN 0276−6574
557
Computers in Cardiology 2007;34:557−560.

Page 2

range found in the literature (from 0 up to 6 ms). In poor
BRS cases, there is a much smaller increase in RR for a
given increase in SBP and the estimated slope is expected
to be lower (sometimes < 0.5 ms/mmHg). If ∆RR
is higher than the true slope, these thresholds will reject all
segments and the BRS can not be quantified. It is also pos-
sible that the thresholds identify spurious segments which
will lead to higher BRS estimates. These BSs with high
slopes are unusual in subjects with low BRS and may not
correspond to real baroreflex effects.
The rmin threshold value is set to specify for which
value the SBP–RR correlation is considered as significant.
If rminis high it is expected to find less and shorter BSs.
On the contrary, if rminis low a higher number of beats is
found at the expense of a higher SBP–RR joint variability.
After BS identification, the BRS can be estimated us-
ing the local, global or total approach, as detailed else-
where [1, 4]. Figure 1 presents an illustrative example of
the application of the methods. In the local approach (or
Sequences technique), a slope is estimated for each BS and
the mean of the slopes is the overall estimator BL,O[1]. In
the global approach, a global slope BG,Ois estimated by
OLS minimization from the SBP and RR values in the set
of all BSs, after local mean detrending (respectively, dSBP
and dRR) [4]. In the total approach, a global slope BG,Tis
estimated by TLS minimization from the SBP and RR val-
ues in the set of all BSs, after local mean detrending and
outlier BS removal (respectively, dSBP,αand dRR,α) [4].
min/∆SBP
min
120130140 150
n (beat number)
160 170 180190 200
xsbp(n)
xrr(n)
(a)
−10 −5
dsbp(mmHg)
05 10
−50
−25
0
25
50
drr(sec)
(b)
−10 −50510
−50
−25
0
25
50
drr,α(sec)
dsbp,α(mmHg)
(c)
Figure 1. Illustrative example of time domain BRS esti-
mation using the first 512 beats of the “A001LB” file from
EuroBavar dataset [2]. (a) Excerpt of xSBP(n) and xRR(n)
displaying with bullets the identified BS. Dispersion di-
agrams superimposing lines with slopes estimated by (b)
local/global (dashed/full) and (c) total approach.
3.Results
The effect of changing the thresholds values in BS
identification is illustrated with the 46 records of the Eu-
roBaVar dataset [2]. In this study, the variables in table 2
were evaluated in the first 512 beats of each record consid-
ering 1 beat lag, i.e., each SBP value is paired with the sub-
sequent RR interval. The variable r quantifies the global
SBP–RR correlation, ie, the correlation between the dSBP
and dRRvariables. High values of r indicate high similar-
ity between the slopes of all identified segments (station-
arity on baroreflex sensitivity strength) while low values
indicate BRS variation over time.
Table 2. BRS analysis variables (VAR) for each record.
VARUnitsDescriptionRange
N
beats# beats [0, 512]
K
segments# segments[0, 128]
r
no units
dSBP– dRRcorrelation[0, 1]
ˆBL,O
ˆBG,O
ˆBG,T
ms/mmHg
local BRS estimate[0, 30]
ms/mmHg
global BRS estimate[0, 30]
ms/mmHg
total BRS estimate[0, 30]
Figure 2 presents the distribution of the variables in Ta-
ble 2 as a function of ∆SBP
minand ∆RR
in column (a), when rmin=0.8 is imposed N<200 and
K<50. The similar pattern of colors in N and K distri-
butions indicate that the segments median length N/K is
fairly constant, lower than 4 beats per segment (ratio of N
and K maximum values). Probably due to the fact that N
and N/K are small, r is higher than 0.8. Regarding the
BRS estimates, lower ∆SBP
minand higher ∆RR
to higherˆB values whereas higher ∆SBP
values lead to lowerˆB. TheˆBL,Ovalues are higher than the
ˆBG,Ovalues and correlated (evidenced by a darker similar
pattern of colors). For ∆SBP
minor ∆RR
ˆBG,Tmedian values present more variability due to the fact
that xSBPand xRRin the identified segments present lower
correlation. As illustrated in Figures 2(b), for ∆SBP
∆RR
same either with or without rmin. The identified segments
are the same, meaning that the corresponding xSBPand xRR
values present correlation exceeding rmin=0.8. For lower
∆SBP
minand ∆RR
min, N increases and K decreases so that
N/K increases. The value of r decreases almost to 0,
because rminis not imposed and also because ∆SBP
∆RR
minare so low that almost all xSBPand xRRvalues are ac-
cepted. TheˆB values tend to 0, indicating once more no
linear relation between the identified xSBP–xRRvalues. In
this situation, rminthreshold is essential to achieve accept-
able r values, in order to the linear model to be adequate.
min. As illustrated
minvalues lead
minand lower ∆RR
min
minaround zero, the
min>0 or
min>0, the distribution of N, K, r andˆB medians is the
minand
558

Page 3

−10−50510
−50
−25
0
25
50
(a)
∆rr
min
−10−50510
(b)
N (# beats)


0
128
256
384
512
−10−50510
−50
−25
0
25
50
∆rr
min
−10−505 10
K (# segments)


0
32
64
96
128
−10−50510
−50
−25
0
25
50
∆rr
min
−10 −50510
r (correlation)


0
0.25
0.5
0.8
1
−10−50510
−50
−25
0
25
50
∆rr
min
−10−50510
ˆBl,o(local)


0
10
20
30
−10−50510
−50
−25
0
25
50
∆rr
min
−10−50510
ˆBg,o(global)


0
10
20
30
−10−505 10
−50
−25
0
25
50
∆sbp
min
∆rr
min
−10−50510
∆sbp
min
ˆBg,t(total)


0
10
20
30
Figure 2. N, K, r andˆB median values distribution as a
function of ∆SBP
minand ∆RR
min, either (a) setting rmin= 0.8
or (b) removing rmin. Darker indicates higher density.
Figure 3 presents the distribution of the variables in
Table 2 as a function of rmin. As illustrated in figures
3(a), if ∆SBP
min=1 and ∆RR
min=5 all variables are constant for
rmin<0.8. The identified segments are the same, meaning
that the corresponding xSBPand xRRvalues present correla-
tion exceeding 0.8. In median, N is approximately 128 of
all 512 beats and K is close to 32, so that N/K is lower
than 4 beats per segment. The r value is very high proba-
bly due to the small N and N/K values. For rmin>0.8, N
and K decrease so that N/K is kept constant for all rmin
values. The segments that exhibit lower correlation are re-
jected for rmin>0.8, leading to higher r values. As illus-
trated in Figures 3(b), without ∆SBP
N decreases and K increases for increasing rmin, indicat-
ing that the segments tend to be shorter in duration. The
r value is close to rminfor 0.2<rmin<0.8 and around 0.8
for rmin>0.8. The BRS estimatesˆBL,OandˆBG,Oincrease
with increasing rmin. For small values of rmin, segments
presenting lower xSBP–xRRcorrelation/slope are identified.
When rminincreases, these segments are more unlikely
to be identified andˆBG,Otend to be more similar toˆBG,O
obtained when ∆SBP
minand ∆RR
minare imposed. The robust
estimatesˆBG,Tdo not seem to be much affected by rmin,
mainly due to the outlier rejection rule.
minand ∆RR
minthresholds,
The comparison between Figures 3(a) and 3(b), evi-
dencethatwithout∆SBP
minand∆RR
higher, K is higher (for rmin>0.5) and r is always lower.
Regarding the BRS estimates,ˆBL,Ois higher thanˆBG,Oand
ˆBG,Thave similar distribution either in (a) or in (b).
When∆SBP
minand∆RR
minthresholdsareimposed(regarde-
less the rminvalue), there are 4/46 files without identified
segments and, therefore, the BRS can not be estimated.
Without ∆SBP
minand ∆RR
min, these files present segments and
the corresponding BRS analysis results are displayed with
the circles in Figures 3(b). The N and K values decrease
and r increases with increasing rminvalues. These files
present lower N and higher K comparing to the remaining
files. The r values are higher than the remaining, probably
due to the lower N and N/K. Finally, the corresponding
ˆB are lower than the remaining, indicating a poorer BRS
function for these cases.
minthresholdsN isalways
Without enforcing ∆SBP
value of rmin=0.8 (traditionally imposed for BSs
identification) allows to achieve a trade-off between N and
r, as N decreases and r increases for increasing rmin. As
shown in Figures 3(b), rmin=0.8 makes available more
than 50% of all beats presenting a correlation close to
0.8. TheˆBG,OandˆBG,Tvalues have similar distributions
when obtained either imposing or not the ∆SBP
thresholds. The apriori setting of rmin=0.8 leading to r
close to 0.8 indicates stationarity of BRS over time in this
dataset and supports the use of global/total approach for
BRS estimation, which assume implicitly stationarity.
minand ∆RR
minthresholds, the
minand ∆RR
min
559

Page 4

4.Conclusions
In this work, the effect of changing the thresholds values
for the identification of baroreflex related segments in SBP
and RR series is studied, with the goal of establish refer-
ence values. The results in the EuroBaVar dataset indicate
that the simultaneous use of ∆SBP
avoided. BRS analysis from the traditional BSs (∆SBP
∆RR
min=5 and rmin=0.8) presents 128 out of 512 beats, lo-
cated typically in 3 beats length segments. Moreover, in
4/46 of the files it is not possible to identify BSs and the
BRS can not be quantified.
Without imposing ∆SBP
minand ∆RR
ber of beats and identified segments is always higher, at
the expense of a slight reduction in the global SBP–RR
correlation. Also, BRS quantification is always possible,
even for the files without BSs. With the unique setting
of rmin=0.8 (traditionally imposed for BSs identification)
the number of identified beats is higher than 256 out of
512 beats, located in longer segments. Also, there are no
substantial changes in the BRS estimates distributions for
global/total approach.
Inshort, timedomainBRSestimationisimproved byre-
moving ∆SBP
minand ∆RR
minthresholds and setting rmin=0.8.
min, ∆RR
minand rmincan be
min=1,
minthresholds, the num-
Acknowledgements
This work was partially supported by CMUP (financed
by FCT Portugal through POCI2010/POCTI/POSI pro-
grammes, with national and CSF funds) and TEC2004-
05263-C02-02 from CICYT/FEDER Spain. S Gouveia ac-
knowledges the grant SFRH/BD/18894/2004 by FCT/ESF.
References
[1] Bertineri G, Rienzo MD, Cavallazzi A. Evaluation of barore-
ceptor reflex by blood pressure monitoring in unanesthetized
cats. Am J Physiol 1988;254:H377–H383.
[2] Laude D et al. Comparison of various techniques used to
estimate spontaneous baroreflex sensitivity. Am J Physiol
Regul Integr Comp Physiol 2004;286(1):R226–R231.
[3] Davies L et al. Effect of altering conditions of the sequence
methodonbaroreflexsensitivity. JHypertens2001;19:1279–
1287.
[4] Gouveia S, Rocha AP, Laguna P, Lago P. Improved time
domain BRS assessment with the use of baroreflex events.
Proc Comput Cardiol 2007;34:to appear.
Address for correspondence:
S´ onia Gouveia
Dep Matem´ atica Aplicada, Faculdade Ciˆ encias Univ Porto
Rua do Campo Alegre, 687; 4169-007, Porto, Portugal.
E-mail address: sagouvei@fc.up.pt.
00.25 0.5 0.81
0
128
256
384
512
(a)
N (# beats)
0 0.25 0.50.81
(b)
0 0.250.50.81
0
32
64
96
128
K (# segments)
00.25 0.50.81
00.250.50.81
0
0.25
0.5
0.8
1
r (correlation)
00.25 0.50.81
00.250.50.81
0
10
20
30
ˆBl,o(local)
00.250.50.81
00.250.50.81
0
10
20
30
ˆBg,o(global)
00.250.50.81
00.250.50.81
0
10
20
30
rmin
ˆBg,t(total)
00.250.50.81
rmin
Figure 3. N, K, r andˆB distribution as a function of rmin
values, either (a) setting ∆SBP
min=1 and ∆RR
moving ∆SBP
minand ∆RR
min. Bars represent quartiles and cir-
cles localize the files without identified segments for (a).
min=5 or (b) re-
560