Algorithm for the classification of multi-modulating signals on the electrocardiogram This article discusses the algorithm to measure electrocardiogram -LRB- ECG -RRB- and respiration simultaneously and to have the diagnostic potentiality for sleep apnoea from ECG recordings . The algorithm is composed by the combination with the three particular scale transform of aj -LRB- t -RRB- , uj -LRB- t -RRB- , oj -LRB- aj -RRB- and the statistical Fourier transform -LRB- SFT -RRB- . Time and magnitude scale transforms of aj -LRB- t -RRB- , uj -LRB- t -RRB- change the source into the periodic signal and τj = oj -LRB- aj -RRB- confines its harmonics into a few instantaneous components at τj being a common instant on two scales between t and τj . As a result , the multi-modulating source is decomposed by the SFT and is reconstructed into ECG , respiration and the other signals by inverse transform . The algorithm is expected to get the partial ventilation and the heart rate variability from scale transforms among aj -LRB- t -RRB- , aj +1 -LRB- t -RRB- and uj +1 -LRB- t -RRB- joining with each modulation . The algorithm has a high potentiality of the clinical checkup for the diagnosis of sleep apnoea from ECG recordings . Introduction The electrocardiogram -LRB- ECG -RRB- contains well-known PQRST -LRB- U -RRB- pattern . Its morphology has been extensively studied since the technique of recording was introduced in the beginning of the twentieth century . The use of computers for ECG recording enabled studies of dynamic properties of the ECG . In particular , two important characteristics have been revealed : amplitude and frequency modulation . The modulation of the cardiac cycle is extensively studied based on the signal that is generated from intervals between consecutives R-peaks , known as heart rate variability -LRB- HRV -RRB- . Numerous approaches have been proposed and the signal have been decomposed in various ways -- analyzing their spectral properties by frequency and time-frequency methods such as Fourier transform -LSB- 2 -RSB- , autoregressive spectral estimation -LSB- 11 -RSB- , wavelet transform -LSB- 9 , 17 -RSB- , or their scaling properties -LSB- 6 -RSB- . The amplitude characteristics and amplitude modulation received less attention , especially because the notion of the ECG amplitude is ambiguous : the heart as a source of the signal is moving and the signal is collected from the surface of the body that is moving as well . In addition , it is usually recorded as a 2-D projection . However , it has long been recognized that one of the sources of the amplitude modulation -- the respiratory related movement of the thorax can be usefully used to extract the information about the respiration . The influence of respiration on recording cardiac potentials was reported as early as in 1967 ; Flaherty et al. -LSB- 5 -RSB- and Moody et al. -LSB- 13 -RSB- were probably the first to discuss the possibility to derive the respiratory signal from the ECG . Since then several algorithms were proposed to reconstruct respiration by demodulating the ECG signal -LRB- e.g. -LSB- 1 , 4 , 8 , 10 -RSB- -RRB- . The ECG-derived respiration signal either based on changes in heart rate or based on direct effect of respiration on the ECG waveform has been particularly used in studies of obstructive sleep apnoea -LSB- 3 , 16 -RSB- . The problem to reconstruct waveform from the discrete Fourier analysis is that the biological signal has complicated properties ; being non-stationary wave , including random noise and having interactive components . However , though people rarely notice , the essential problem is that there is no way to gather impartial and statistical samples . That is why samples from an unique sampling frequency are biased for spectral analysis even if fine sampling . The purpose of this study is to introduce an algorithm to classify the multi-modulating waveforms on ECG signals . The algorithm is composed by the three particular scale transforms and the statistical Fourier transform -LRB- SFT -RRB- with impartial and statistical samples -LSB- 12 -RSB- . As a result , the multi-modulating source is decomposed by the SFT and is reconstructed into ECG , respiration and the other signals simultaneously by particular transformations . Algorithm The principle of this algorithm is the selection of three particular scale transforms . Two scales convert modulating waveforms into the periodic signal and the other converts the periodic components into a few terms . The role of the SFT is to hold sample information for any transforms . Scale transforms aj -LRB- t -RRB- , uj -LRB- t -RRB- and oj -LRB- t -RRB- on modulating signal Since a source sample at any instant tk has the mutual phase relationship of instantaneous components on the SFT , any scale transform including permutation expresses the same sample as own instantaneous components by each scale -LRB- Appendix 1 -RRB- . Three scale transforms aj -LRB- t -RRB- , uj -LRB- t -RRB- , oj -LRB- t -RRB- are adopted to the periodicity and to the reduction of Fourier components . aj = aj -LRB- t -RRB- is a scale to match time intervals in the standard 's intervals and is called adaptive scale and uj = uj -LRB- τj -RRB- is a scale to match the magnitude spans in the standard 's magnitudes . Those scales convert the source x ′ -LRB- t -RRB- into the standard xj -LRB- t -RRB- as xj -LRB- t -RRB- = x ′ -LRB- aj -RRB- / uj -LRB- aj -RRB- . aj -LRB- t -RRB- and uj -LRB- aj -RRB- , then , are defined as a join of each akj -LRB- t -RRB- and ukj -LRB- akj -RRB- -LRB- k = 1 , ... , kj · -RRB- when the standard repeats kj times in a window Tj . oj = oj -LRB- t -RRB- , called inherent scale , is a timescale to convert the standard xj -LRB- t -RRB- into the Fourier series of rj components passing through 2rj poles of xj -LRB- t -RRB- . The scale transform τj -LRB- t -RRB- is defined as the composite transform as follows -LRB- Appendix 2 -RRB- : The transformed signal -LRB- x ′ -LRB- τj -RRB- − εj -LRB- τj -RRB- -RRB- / uj -LRB- τj -RRB- occupies rj instantaneous components of the skipped ikjth term in a window Tjincluding kj modulations . While , instantaneous components of the εj -LRB- τj -RRB- / uj -LRB- τj -RRB- scatters into broad components from the 1st to the nth terms . As a result , -LRB- x ′ -LRB- τj -RRB- − εj -LRB- τj -RRB- -RRB- / uj -LRB- τj -RRB- fits the scales τj , uj and εj -LRB- τj -RRB- / uj -LRB- τj -RRB- unfits scales τj , uj , and then , the source x ′ -LRB- t -RRB- is decomposed into two class modulations of x ′ -LRB- τj -RRB- − εj -LRB- τj -RRB- and εj -LRB- τj -RRB- -LRB- Appendix 3 -RRB- . That is , x ′ -LRB- τj -RRB- − εj -LRB- τj -RRB- is extracted by vj -LRB- τj -RRB- = Σuj -LRB- τj -RRB- hij -LRB- τj -RRB- from the ikjth -LRB- i = 1 , . . , rj -RRB- components and εj -LRB- τj -RRB- is extracted by the other εj -LRB- τj -RRB- = Σuj -LRB- τj -RRB- hij -LRB- τj -RRB- except the ikjth components when n instantaneous components of x ′ -LRB- τj -RRB- / uj -LRB- τj -RRB- are defined as hij -LRB- τj -RRB- . The source x ′ -LRB- t -RRB- , therefore , is decomposed into x ′ -LRB- t -RRB- − εj -LRB- t -RRB- and εj -LRB- t -RRB- by inverse scale transform t = t -LRB- τj -RRB- under an adequate uj -LRB- τj -RRB- . The magnitude scale ukj -LRB- τj -RRB- is defined as an expression of the magnitude pattern in each window Tkj when the signals vj -LRB- τj -RRB- -LRB- = x ′ -LRB- τj -RRB- − εj -LRB- τj -RRB- -RRB- , εj -LRB- τj -RRB- and uj -LRB- τj -RRB- are expressed by -LCB- vkj -LRB- τj -RRB- -RCB- k , -LCB- εkj -LRB- τj -RRB- -RCB- k and -LCB- ukj -LRB- τj -RRB- -RCB- k -LRB- k = 1 , . . , kj -RRB- , and each changes its waveform independently . Especially , vj -LRB- τj -RRB- is expressed by a constant value uj -LRB- τj -RRB- = ukj in each window Tkj when its magnitude modulation takes a similar figure with the standard -LRB- Appendix 4 -RRB- . Iterative scale classification of modulating signals The timescale transform of the residual εj -LRB- t -RRB- is defined as τj +1 -LRB- t -RRB- = oj +1 -LRB- aj +1 -LRB- t -RRB- -RRB- when several waves of -LCB- εkj -LRB- t -RRB- / ukj +1 -LRB- t -RRB- -RCB- k in εj -LRB- t -RRB- / uj +1 -LRB- t -RRB- reappears within a window Tj +1 -LRB- Tj +1 ≤ Tj -RRB- . εj -LRB- t -RRB- is analyzed as the j + 1th modulation with the iterative algorithm as εj -LRB- t -RRB- − εj +1 -LRB- t -RRB- and εj +1 -LRB- t -RRB- under aj +1 -LRB- t -RRB- , oj +1 -LRB- aj +1 -LRB- t -RRB- -RRB- , uj +1 -LRB- t -RRB- and xj +1 -LRB- t -RRB- -LRB- Appendix 2 -RRB- . When x ′ -LRB- t -RRB- is m classes of Fourier series with terms of r1 , r2 , ... , rm -LRB- n = r1 + r2 + + rm -RRB- , it expresses Eq . 2 . In Eq . 2 , t = t -LRB- τj -RRB- is the inverse scale transform of the jth scale τj to scale t , vj -LRB- t -RRB- is a Fourier series of the jth class modulation , and εm -LRB- t -RRB- is the mth residual signal . Equation 2 shows that x ′ -LRB- t -RRB- is reconstructed completely by periodic Fourier series vj -LRB- τj -RRB- on scale τj -LRB- j = 1,2 , ... , m -RRB- . Quantity of information on the modulating signal The relation between the quantity of information -LRB- 3 -RRB- and the modulation -LRB- 4 -RRB- is derived from formula -LRB- 2 -RRB- . Since the probability of components on the jth class modulation is to be pj = rj/n , the probability to encounter x ′ -LRB- t -RRB- with m modulations is p -LRB- r1 , r2 , ... , rm -RRB- = p1r1 , p2r2 , ... , pmrm which relates to the geometrical mean . Equation is as follows -LRB- Appendix 5 -RRB- . It clearly shows that the quantity of information on multi-modulating signal is m itself . When hij -LRB- τj -RRB- is the ith instantaneous Fourier component of standard xj -LRB- τj -RRB- in scale τj and hij -LRB- t -RRB- is its modulating component in scale t , the morphological relation is given by the following Formula -LRB- 4 -RRB- : In Eq . 4 , ∂ τj / ∂ t is the Jacobian . Therefore , formula -LRB- 4 -RRB- shows that the modulation of every component at scale t is expressed by scale 's modulations on its magnitude uj -LRB- τj -RRB- and its time τj -LRB- t -RRB- = oj -LRB- a -LRB- t -RRB- -RRB- . Especially , the adaptive scale aj -LRB- t -RRB- describes composite transform aj -LRB- t -RRB- = c1 -LRB- c2 -LRB- cn -LRB- t -RRB- -RRB- -RRB- and that of exchanged orders aj -LRB- t -RRB- = cn -LRB- c2 -LRB- c1 -LRB- t -RRB- -RRB- -RRB- , so the sth scale cs -LRB- t -RRB- will express its specific modulation from the standard such as modulations of PQ , QRS , QT and RR . Materials and methods The analysis of scale classification of the three modulating signals on V4 lead was carried out by using the statistical Fourier analysis with maximum terms of 256 with A/D converted 16-bit samples of the sampling frequency 20 kHz over successive 50 s. To gather independent samples with 256 terms , samples needed to be accumulated by the high speed 20 kHz of A/D converter with a large dynamic range of 16 bit to avoid the deform of a tiny respiratory signal -LRB- Fig. 1 -RRB- . Fig. 1Synchronous frequency samplings on scale t and τ The ECG standard xj -LRB- t -RRB- was selected from the source x ′ -LRB- t -RRB- without breathing . On the other hand , x ′ -LRB- t -RRB- with natural breathing and the respiratory flow are recorded simultaneously by using Number 3 Fleisch pneumotachograph . Both the ECG and the respiratory scale transforms were the same as in Fig. 2a , b of Appendix 2 . The ECG x ′ -LRB- t -RRB- − εj -LRB- t -RRB- and its baseline wander εj -LRB- t -RRB- were analyzed when uj -LRB- τj -RRB- = 1 and the respiratory standard xj +1 -LRB- t -RRB- was selected from stationary sequences of εj -LRB- t -RRB- in 16 respiratory cycle . -LRB- εj -LRB- τj +1 -RRB- − εj +1 -LRB- τj +1 -RRB- -RRB- / uj +1 -LRB- τj +1 -RRB- and εj +1 -LRB- τj +1 -RRB- / uj +1 -LRB- τj +1 -RRB- were analyzed when uj +1 -LRB- τj -RRB- of the formula -LRB- 5 -RRB- in Appendix 4 and lung ventilation Vj +1 -LRB- t -RRB- and its residual εj +1 -LRB- t -RRB- were determined . Fig. 2ECG and respiratory standard waves and specific points on scale t. a Cardiac standard , b respiratory standard , and c detecting dots on a part of the source Results Signals corresponding to every process on the scale classification of m = 2 under constant magnitude scale of uj = 1 are illustrated in Fig. 3 with five cardiac periods . That is , intervals among specific points in source x ′ -LRB- t -RRB- in Fig. 3a are transformed into the same intervals of the standard signal with the adaptive scale aj -LRB- t -RRB- to x ′ -LRB- aj -LRB- t -RRB- -RRB- of Fig. 3b and with the inherent scale τj -LRB- t -RRB- to x ′ -LRB- oj -LRB- aj -LRB- t -RRB- -RRB- -RRB- of Fig. 3c . The transformed signal x ′ -LRB- τj -RRB- is decomposed into statistical Fourier components on a fundamental period of 53 cardiac intervals . The transformed signal xj ′ -LRB- τj -RRB- in Fig. 3d is a reconstructed signal from the 53rd , 106th , 159th and 212th components , and its residual εj -LRB- τj -RRB- in Fig. 3e from all other components . The extracted ECG xj ′ -LRB- t -RRB- in Fig. 3f and the base line wander εj -LRB- t -RRB- in Fig. 3g are the inverse scale-transformed signals from scale τj to scale t . When tiny-leak signals on the εj -LRB- t -RRB- synchronized with intervals of QT are replaced with linear trends , the figure of pattern εj -LRB- t -RRB- takes that of the lung ventilation in Fig. 3i . The smoothing signal , Vj -LRB- t -RRB- in Fig. 3h is a filtered signal of εj -LRB- t -RRB- with low-pass filter -LRB- LPF -RRB- under 30 terms -LRB- 0.6 Hz -RRB- . Vj -LRB- t -RRB- is illustrated with enlarged four times . The signal V -LRB- t -RRB- in Fig. 3i is the lung ventilation curve which is an integral signal of the direct measurement of the respiratory flow Fig. 3Classified process of modulating signal of the algorithm Any differences of P ∼ U waveforms between the source x ′ -LRB- t -RRB- and reconstructed ECG x ′ j -LRB- t -RRB- bear getting information , and also the differences between ventilation V -LRB- t -RRB- and baseline wander Vj -LRB- t -RRB- are small when frequencies lower than breathing are neglected . x ′ j -LRB- t -RRB- provides time-interval information on Minnesota codes better than that of x ′ -LRB- t -RRB- clearly in visual . Correlation coefficients ρ between the signal Vj -LRB- t -RRB- and V -LRB- t -RRB- are calculated by each ventilation with scatter plots in Fig. 4a , and are classified by P ∼ U waves of 53 cardiac signals in Table 1a and by respiratory phases of 16 ventilations in Table 1b . Total ρ takes even values -LRB- ρ ≈ 0.82 -RRB- and has less interference between P ∼ U waves in cardiac cycles . However , it takes low values -LRB- ρ ≤ 0.5 -RRB- at the transient regions of I , III between the inspiration and the expiration corresponding to loops in Fig. 4a . The inspiration and the expiration except transient regions are statistically dominant at higher value -LRB- ρ ≈ 0.95 -RRB- . It is clear that the scale classification extracts the electrical activity of the heart with constant magnitude scale of uj -LRB- τj -RRB- = 1 in hole window of Tj . The extracted baseline wander is constructed with lung ventilation and other biological information . Fig. 4X -- Y loop among modulating Vj -LRB- t -RRB- , Vj +1 -LRB- t -RRB- and V -LRB- t -RRB- Table 1Correlation coefficients ρi among Vj -LRB- t -RRB- , Vj +1 -LRB- t -RRB- and V -LRB- t -RRB- on cardiac and respiratory stagesCardiac stagesPQQRSST-TBase lineTotal -LRB- a -RRB- Correlation coefficients ρi between Vj -LRB- t -RRB- and V -LRB- t -RRB- on ECG stages ρi0 .83280.82430.81490.81510.8244 Number of samples13 ,56612,69033,01843,553102,827 Respiratory stagesI II III VI V Total -LRB- b -RRB- Correlation coefficients ρi between Vj -LRB- t -RRB- and V -LRB- t -RRB- on respiratory stages ρi0 .39900.97880.57720.99700.95460.7273 Number of samples25 ,74725,21025,92814,57411,558103,017 -LRB- c -RRB- Correlation coefficients ρi between Vj +1 -LRB- t -RRB- and V -LRB- t -RRB- on respiratory stages ρi0 .99230.65890.99430.80320.73050.91648 Number of samples25 ,28622,81621,16315,15518,077102,497 I inspirations before midpoints , II inspirations after midpoints , III expirations before midpoints , VI expirations after midpoints , V expirations after inflection points The magnitude scale transform is applied to the scale classification of the base line wander Vj -LRB- t -RRB- with a respiratory standard in Fig. 2b . Scale classification of m = 4 is illustrated in Fig. 5 , the source x ′ -LRB- t -RRB- in Fig. 5a , the extracted ECG xj -LRB- t -RRB- in Fig. 5b , the extracted respiratory signal Vj +1 -LRB- t -RRB- in Fig. 5c , the residual εj +1 -LRB- t -RRB- in Fig. 5d , the leak ECG ε -LRB- t -RRB- over 0.6 Hz of εj -LRB- t -RRB- in Fig. 5e and the ECG of xj -LRB- t -RRB- + ε -LRB- t -RRB- in Fig. 5f . The signal V -LRB- t -RRB- in Fig. 5g is 16 measured respiratory ventilations . The magnitude scale Δuj +1 -LRB- t -RRB- is illustrated in Fig. 5h . Vj +1 -LRB- t -RRB- and εj +1 -LRB- t -RRB- are displayed in the reverse because the extracted respiratory waveform is a visually reversed V -LRB- t -RRB- . εj +1 -LRB- t -RRB- is similar to base-line trends of V -LRB- t -RRB- which relate to the thoracic gas volume -LRB- TGV -RRB- . Fig. 5Scale classification of the four modulating signals in an electro-cardiac signal The scatter plots of 15 lung ventilations between Vj +1 -LRB- t -RRB- and V -LRB- t -RRB- take the similar pattern as illustrated in Fig. 4b . Correlation coefficients ρ in Table 1c takes higher value than the others though transient regions change I , III into II , IV . The frequency distributions of the amplitude components on | V -LRB- f -RRB- | , | Vj +1 -LRB- f -RRB- | , | εj +1 -LRB- f -RRB- | and that of phase shifts Δφ -LRB- f -RRB- between V -LRB- f -RRB- and Vj +1 -LRB- f -RRB- are illustrated in Fig. 6 . On frequency ranges from 0.2 to 0.5 Hz , amplitude distribution in | V -LRB- f -RRB- | and | Vj +1 -LRB- f -RRB- | takes similar pattern and those of phase shifts are invariant near 0 ° . Amplitude distribution in | εj +1 -LRB- f -RRB- | has not only the lower frequency components under 0.06 Hz corresponding to the trends of TGV but also the leak components of the lung ventilation from 0.25 to 0.5 Hz . The components of | εj +1 -LRB- f -RRB- | , moreover , has the harmonics among 0.04 , 0.1 , 0.18 and 0.28 Hz though those harmonics disappear in | V -LRB- f -RRB- | and | Vj +1 -LRB- f -RRB- | at least . Fig. 6Frequency distributions of the measured V -LRB- f -RRB- and the extracted Vj +1 -LRB- f -RRB- , εj +1 -LRB- f -RRB- As a result , the time and magnitude scale is effective to classify modulating signals from the higher frequency Vj +1 -LRB- t -RRB- to the lower frequency εj +1 -LRB- t -RRB- because a residual εj +1 -LRB- t -RRB- has less interference of the higher Vj +1 -LRB- t -RRB- and successive sequential εj +1 -LRB- t -RRB- will supply the signal for detecting other lower modulation . Discussion and conclusion A discrepancy between time domain and frequency domain analysis happens commonly by using biased samplings for discrete signal processing in various way such as Hilbert transform -LSB- 2 -RSB- and wavelet analysis -LSB- 9 -RSB- relating with an unique sampling frequency . Moreover , the mathematical concepts of one-to-one correspondence , n unknown amplitudes and phases are derived from 2n samples , hinders to orientate the statistics in the signal processing . The SFT , however , has no contradiction between Fourier analysis and the statistics which resolute components with the same signal-to-nose ratio -LRB- SNR -RRB- for any signal decreasing amplitude components with order 1/f such as ECG signal , which is unsatisfied in the autoregressive spectral estimation -LSB- 11 -RSB- . The SFT component , moreover , is given independently by a time trace of instantaneous components at each instant as shown in Appendix 1 . That is , its amplitude and phase are not calculated by the inner products between the source and trigonometric bases but by the extracted traces of instantaneous sin-wave themselves -LSB- 12 -RSB- . The concepts of signal arrangements at series -LCB- tk -RCB- is another thing on the SFT because the replacement between ti and tj needs the replacements of all the synchronous frequency samplings between ti and tjto hold the same instantaneous components . The summation of replacements , then , is about . In other words , the SFT supplies a signal ensemble arranging samples of the series -LCB- tk -RCB- . In this study , discrete samples from A/D converter of 20 kHz satisfy the independency as shown in Appendix 6 . As a result , the random noise including a signal is not analyzed as a white noise but as inherent components characterizing arrangements . Therefore , the reconstructed waveform of a baseline wander holds a prototype even if it includes many random noises . The necessary condition of the spectral analysis known as Nyquist 's condition -LSB- 14 , 15 -RSB- becomes precise on the SFT as shown in Appendix 3 , which confirms its condition statistically . The potentiality to scatter the aliased components impartially discriminates the waveforms under the unsatisfied Nyquist 's condition . In this algorithm , while the inherent scale transform converges to the standard xj -LRB- τj -RRB- with four skipping components , others εj -LRB- τj -RRB- , either continuous or random , disperse components into 256 terms . Since the scale-transformed samples on the SFT are gathered from a whole window at any instant , those samples reflect its scale transform better than any local one . The random and leak signal on the extracted ECG xj ′ -LRB- t -RRB- are reduced into the tiny level under a stable behavior of the random noise . The 256 terms is enough to analyze scale-transformed signal in a window under 53 cardiac cycles because transformed components with the ranges , 8 ≤ kj ≤ 53 , takes almost the same figures . The high-resolution analysis , therefore , is accomplished by the relative high SNR from those instantaneous components . The problem on the scale transforms is to be adequate scales , not to be expressing the true biological modulation . aj +1 -LRB- t -RRB- is , however , selected a traditional scale for non-stationary sequences in each respiratory cycle which carry information stored in Fourier phases as already indicated in -LSB- 6 -RSB- and aj -LRB- t -RRB- is selected from cardiac cycles without breathing in addition to the non-stationary sequences . As a result , oj -LRB- aj -RRB- and oj +1 -LRB- aj +1 -RRB- make those mutual relationship of phases more simple relations . Taking own standard characterized with number of poles is also reasonable to determine the waveform reconstruction and to discriminate the own HRV . Moreover , the lost waveform is scattered into the other components without losing the morphologic information such as the leak ECG waveform . It is well known the volume conductivity of the thorax takes inequality and changes the electro cardiac potentials on the thorax 's surface with respiratory movements -LSB- 1 , 5 -RSB- . In the scale classification of m = 4 , it indicates that a constant magnitude scale ukj = 1 produces unchangeable heart-activity xj ′ -LRB- t -RRB- so that the signal εj -LRB- t -RRB- appears in respiratory modulations from their changes of the conductivity . It suggests that the standard without breathing follows the formula -LRB- 2 -RRB- of the signal classification and the source follows the formula -LRB- 4 -RRB- which expresses the modulating standard with Jacobian , ∂ τj / ∂ t . A composite scale cs -LRB- t -RRB- , therefore , is expected to express the inherent modulation from the standard such as PQ , QT and RR . That is , the spectral analysis of cs -LRB- t -RRB- on RR provides the distribution of the HRV without a tachogram which is expressed in other ways by others -LSB- 2 , 9 , 11 -RSB- . The extracted ECG has the potentiality to detect R -- R modulations of the heart itself . The algorithm extracts the lung ventilation curves -LCB- Vj +1 -LRB- t -RRB- -RCB- k from V4 lead as changing the thoracic gas volume -LSB- 1 , 4 -RSB- . The difference of amplitude distribution between V -LRB- t -RRB- and Vj +1 -LRB- t -RRB- from spectral analysis takes the same pattern around 0.3 Hz -LSB- 8 -RSB- . The phase difference between V -LRB- t -RRB- and Vj +1 -LRB- t -RRB- , however , occurs in the transient regions between the inspiration and the expiration which deduce from inadequate respiratory standards , false respiratory peaks and the gas compression in the thorax -LSB- 7 -RSB- . It is effective to determine specific components , such as harmonics of εj +1 -LRB- t -RRB- around -LRB- 0.04 , 0.1 , 0.18 and 0.28 Hz -RRB- in cardiovascular responses -LSB- 2 , 17 -RSB- . Information of the partial ventilation is also expected from other 12 leads -LSB- 8 -RSB- . The respiratory Jacobian ∂ τj +1 / ∂ t , like that of ECG , has the potentiality to detect respiratory modulation itself as a part of the HRV and uj +1 -LRB- t -RRB- is expected to detect the amplitude modulation such as sighs distribution . The residual εj +1 -LRB- t -RRB- supplies information of waveforms not only of the thoracic gas volume but also of the blood flow relating to cardiovascular responses -LSB- 2 , 11 , 17 -RSB- . It can be concluded that this algorithm reveals the simultaneous measurements of ECG and respiration . The comparison with the frequency distribution and the waveform evaluates new modulations clearly , such as ukj +1 for detecting changes of the tidal volume -LRB- TV -RRB- and for finding TGV and cardiovascular responses . This contribution of the algorithm indicates diagnostic potentials on the sleep apnoea from ECG recordings -LSB- 16 -RSB- .

O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

fourier transform
scale transform
electrocardiogram
respiratory waveform
heart rate variability


Exploring Barriers to ` Respondent Driven Sampling ' in Sex Worker and Drug-Injecting Sex Worker Populations in Eastern Europe Respondent driven sampling -LRB- RDS -RRB- has been used in several counties to sample injecting drug users , sex workers -LRB- SWs -RRB- and men who have sex with men and as a means of collecting behavioural and biological health data . We report on the use of RDS in three separate studies conducted among SWs between 2004 and 2005 in the Russian Federation , Serbia , and Montenegro . Findings suggest that there are limitations associated with the use of RDS in SW populations in these regions . Findings highlight three main factors that merit further investigation as a means of assessing the feasibility and appropriateness of RDS in this high risk population : the network characteristics of SWs ; the appropriate level of participant incentives ; and lack of service contact . The highly controlled and hidden nature of SW organizations and weak SW social networks in the region can combine to undermine assumptions underpinning the feasibility of RDS approaches and potentially severely limit recruitment . We discuss the implications of these findings for recruitment and the use of monetary and non-monetary incentives in future RDS studies of SW populations in Eastern Europe . Introduction In many countries in Eastern Europe large scale social and economic transition over the past 15 years has been associated with widespread poverty and increasing levels of unemployment and population migration , particularly among women .1,2 Such transition has also been associated with shifts in patterns of sexual behaviour and sexual relationships , including increased commercial sex work , the growth of informal sex work economies and associated human trafficking .3 Additionally , a number of countries in the former Soviet Union have experienced a rapid or explosive spread of HIV associated with injecting drug use .4 -- 7 These epidemics are potentially exacerbated by close links between sex work and injecting drug use .2,8 -- 11 This has caused concerns that high levels of sexual mixing between injecting drug users -LRB- IDUs -RRB- and their sexual partners in settings of high HIV and sexual transmitted infection -LRB- STI -RRB- prevalence may transform HIV infection from concentrated epidemics among risk populations to generalised epidemics .9,10 It is therefore essential to assess the diffusion of HIV and related risk behaviour in hidden vulnerable populations , such as IDUs and sex workers -LRB- SWs -RRB- , as accurately as possible . There has been increased and recent interest in an approach to sampling hidden populations known as respondent driven sampling -LRB- RDS -RRB- .12,13 One of the claimed advantages of RDS over other methods of sampling hidden populations , such as time -- location sampling , is that it requires little in-depth formative research among study populations .13,14 RDS begins with a set number of non-randomly selected seeds -LRB- members of the target population -RRB- . Seeds recruit their peers -LRB- other target population members who make up their social network -RRB- who in turn recruit their peers into the study . This occurs through successive waves of recruits which , it is argued , become increasingly more representative of the underlying population as the recruitment progresses . Since RDS claims to generate a representative sample from non-randomly selected seeds , many researchers have assumed that sampling can proceed without detailed prior knowledge about the local target population .13,14 RDS has proved feasible and successful in recruiting hidden populations of IDUs in a variety of settings , resulting in the rapid acquisition of long and varied recruitment chains .11,14 -- 19 RDS has also been used in several countries to collect both behavioural and biological data from SWs -LRB- e.g. , Vietnam , India -RRB- and men who have sex with men -LRB- e.g. , Bangladesh , Cambodia , Uganda , United States -RRB- .20 -- 24 However , little is known about the feasibility of RDS as a method of recruiting hidden populations of SWs in settings where the organisation of sex work and access to SWs is highly controlled and where there is little or no contact between the target population and local services . Drawing upon three case studies in Eastern Europe targeting SWs and IDUs involved in SW -LRB- IDU/SWs -RRB- , we explore the feasibility of RDS , identifying some barriers to successful recruitment . These findings have implications for the direction of future research exploring the feasibility of RDS methods . Methods Using RDS , data on HIV prevalence and associated risk factors were gathered from SWs in Serbia and Montenegro and from IDUs involved in sex work in Russia -LRB- see Table 1 -RRB- . SWs in Serbia and Montenegro were given three uniquely numbered coupons with which to recruit other SWs . In Russia , although no RDS study directly targeting SWs was carried out , RDS was used to sample SWs/IDUs in an RDS study among IDUs . Incentives were provided to participants completing the survey -LRB- primary incentive -RRB- and for recruiting other eligible participants -LRB- secondary incentive -RRB- . Participants in Belgrade were also offered a rapid HIV test and pre - and post-test voluntary and confidential counselling -LRB- VCT -RRB- . Those with preliminary-positive tests for HIV were referred to a local clinic for confirmatory testing . The studies were undertaken by local fieldwork teams coordinated as part of larger internationally funded research initiatives . Table 1 . Three RDS studies among sex workers and injection drug using sex workersCountryCity -LRB- population size -RRB- Formative researchRecruitment criteria for SWsNumber of seedsSample reached -LRB- target -RRB- Year , study durationSerbiaBelgrade -LRB- about 2 million -RRB- Literature search ; questions on network characteristics and RDS study feasibility posed during individual interviews with SWs in 2005 -LRB- n = 10 -RRB- Exchanged sex for drugs , money or other goods in last 30 days -LRB- irrespective of gender or sexual orientation -RRB- Six initially , six added later209 -LRB- 400 -RRB- 2005 , 2 monthsMontenegroPodgorica -LRB- about 300,000 -RRB- Literature search ; questions on network characteristics and RDS study feasibility posed during in-depth interviews with SWs in 2005 -LRB- n = 4 -RRB- Exchanged sex for drugs , money or other goods in last 30 days -LRB- irrespective of gender or sexual orientation -RRB- One to start with , one added later2 -LRB- 150 -RRB- 2005 , 2 monthsRussian FederationTogliatti -LRB- 740,636 -RRB- Literature search -LSB- relied on previous qualitative study of IDUs conducted in 2001 -LRB- n = 57 -RRB- and epidemiological survey of IDUs including SWs -LRB- n = 426 -RRB- -RSB- Exchanged sex for drugs , money or other goods and injected drugs in last 4 weeksOne , 35 SWs recruited by a female non-SW IDU seed36 -LRB- not set -RRB- 2004 , 1.5 months All studies were approved by appropriate local ethical committees and international human subject review boards . Participants were required to agree to an informed consent before participating . Participants were not linked to the study with any personal identifiers , and all participant information was kept confidential and anonymous . Prior to data collection , formative research , comprising a combination of key informant interviews and a literature review , was undertaken to assess the local feasibility of the RDS study identifying the optimal study set up -LRB- Table 1 , column 3 -RRB- . The formative research elicited data on size estimates of the sex work population ; description of how sex work is organised -LRB- sectors of sex work , freedom of movement , average earnings and prices charged for services in each sector -RRB- ; and the legal situation surrounding sex work . In Serbia and Montenegro , researchers also asked SWs about the size of their social networks in order to fine-tune questions on which RDS analysis would be based . A social network was defined as the number of SWs , 18 years and older , each SW knows and has seen in the past week , month , three months , six months , or year . Results As shown in Table 1 , a total of 209 SWs were recruited in Belgrade -LRB- Serbia -RRB- , two in Podgorica -LRB- Montenegro -RRB- and 36 in Togliatti -LRB- Russian Federation -RRB- . Case 1 : Serbia RDS was conducted in the autumn of 2005 in Belgrade , Serbia 's capital , by a local fieldwork team with a limited access to SW networks . Estimates of the size of the SW population in the municipality , based on police records and anecdotal estimates , vary widely from 900 to 3,000 SWs .2,24,25 Sex work is illegal . Findings from in-depth interviews of SWs suggest that there are approximately ten areas located near the main transit routes in and out of Belgrade where street SWs operate in small groups . Qualitative data suggests that the majority of SWs operate independently , advertising their services in newspapers or through referrals via existing client networks , potentially making them harder to reach through RDS . Formative interviews also found that there was little mixing of SWs across different sex work sectors -LRB- street , agency , and SWs working independently -RRB- , among street SWs themselves -LRB- transvestite , Roma and Serbian/Montenegrin heterosexual SWs -RRB- and among SWs working independently . However , in addition to a lack of strong connection among SWs and their independent working situations , the study team undertaking formative qualitative research associated SWs ' reluctance to participate in the study to perceptions of inadequate incentive -LRB- 10 euros for 1 hour of their time -RRB- and a general mistrust associated with coming into contact with ` official ' agencies . However , the same interviews suggested that in principle SWs would be interested in participating in a survey involving the collection of both behavioural and biological data through HIV testing . Interviewees indicated that they knew approximately 20 other SWs , which again suggested that RDS would be feasible . The RDS study had a target of 400 SWs , both male and female . The sample needed to be large enough for a statistically reliable analysis of risk factors and HIV prevalence , should RDS analysis show that the sample is reasonably representative . The interview site was on the premises of a non-governmental organisation -LRB- NGO -RRB- located in central Belgrade easily accessible by public transport . It was a part of a large apartment block with a separate entrance . The site was open everyday from 3 to 9 p.m. and could accommodate three to four participants an hour because of the computer administered questionnaire . After two months , the study ceased , having reached only 209 SWs . In total , 12 seeds were used during the study . Of the initial six seeds only three produced any subsequent waves . The rate of recruiting increased noticeably after an RDS study of IDUs being implemented at the same site had ceased . Due to the difficulties experienced by the research team in locating new seeds through other means , four participants with dense social networks were drawn from the seventh wave of two of the most productive recruitment chains and used as new seeds . This resulted in two more productive chains that ultimately reached seven waves . The average SW network size reported during the study was 12 . In response to the question , `` where do you most often solicit your clients ? , '' the majority of SWs replied that they solicited on the street -LRB- 43 % -RRB- , followed by referral from an agency , pimps , friends or other SWs -LRB- 28.9 % -RRB- and by telephone -LRB- 25.2 % -RRB- . Importantly , the take-up of VCT provided as part of the RDS study was high -LRB- 71.8 % -RRB- , and SWs indicated that they participated because of the HIV testing , rather than the monetary incentive . Case 2 : Montenegro There are no estimates of the number of SWs in Podgorica , the Republic 's capital . Sex work is ostensibly illegal . Through formative rapid assessment no street-based SWs were identified and the majority of SWs were found to work independently from their homes . Key informant interviews -LRB- IDUs , ex-IDUs , taxi drivers , public health officials , NGO representatives and journalists -RRB- identified the only semi-public sex work sites as being approximately six illegal brothels , registered as lap dancing venues , in which most of the SWs also lived . At least one such brothel was found not to allow SWs to leave the premises . Indications were that local police also ` moonlighted ' as security guards in these brothels . Other links between brothels and public services included taxi drivers , beauty salons and hotels . The intersection of the police and sex work networks , the small size of the city and the high number of implicated actors suggested that SWs could be easily monitored and controlled . Previous attempts by the local NGOs to conduct research among SWs in Podgorica had failed . Key informants , interviewed during formative rapid assessment , reported knowing at least one SW or their pimps but in almost all cases introductions were denied or never materialized . Those conducting the formative rapid assessment received strong advice from local experts and key informants -- including NGOs , police , and taxi drivers -- against approaching brothel owners because of the highly controlled nature of SW venues in the city . After two weeks of trying to make a contact , four SWs were accessed via their drug user networks , the only entry points into SW networks available to researchers . These SWs were interviewed at their place of work -LRB- brothel and pimp 's flat -RRB- . Each of the four interviewed SWs independently estimated that there were approximately 200 SWs in the city , many of them also drug injectors , most of whom worked independently , advertising their services via newspapers and television and via client recommendation but who were not open about their SW status . All four SWs interviewed indicated that they would participate in a RDS study and would invite others to do so , and each estimated they had personal regular contact with between five and ten SWs . The four SWs participating in the formative rapid assessment were invited to participate in the RDS study as seeds . Only one of the four participated but failed to recruit anyone else . She reported having had contact with ten SWs in 4 weeks , but no additional seeds were secured . Despite recruiting an additional SW -LRB- who required complete anonymity fearing being identified as a SW by others to his family and who had not seen other SWs in the past month -RRB- , the RDS study failed to identify a sufficient pool of seeds willing to participate . Case 3 : Russia The RDS study of IDUs and IDU/SWs was conducted in May 2004 in Togliatti City . Togliatti City is the second city of Samara Region situated approximately 1,000 km south of Moscow . Togliatti was selected as a study site because evidence suggests a recent increase in the number of IDUs and SWs and an explosive spread of HIV associated with injecting drug use .6,11 Approximately 2,000 SWs are estimated to operate in Togliatti , half of whom work from the street .6 Despite ambiguous Russian legislation towards sex work , it is not tolerated by the wider community or the police . The city has been noted for its intense street policing of drug users and SWs , often involving fines levied under administrative codes , such as possession of drugs , causing a public nuisance , or lack of official residency permit , rather than criminal codes .26,27 Street-based SWs in Togliatti operate openly along the main roads and highways . Two popular locations are Moskovsky Prospect where approximately 70 women are working at any one time , and Pobeda Street where about 100 women work . In a study conducted in Togliatti City in 2001 , 50 % of female IDUs -LRB- n = 155 -RRB- reported ever exchanging sex for goods or money , of whom 86 % -LRB- n = 66 -RRB- were currently SWs .6 Although no stand-alone RDS studies of SWs have been conducted in Russia , attempts have been made to boost participation of IDU/SWs in RDS studies of IDUs motivated by the evidence of high proportion of SWs who also inject drugs in other cities .28 -- 30 A cross-sectional survey of IDUs and female IDU/SWs was undertaken in Togliatti in 2004 as a follow up to the 2001 baseline survey . A total of 476 IDUs were sampled during a 5-week period in May 2004 using RDS . Among these , 55 -LRB- 11 % -RRB- reported ever exchanging sex for money , drugs or goods , and of these , 36 in the past month , which was lower than expected . At the start of the field work , seven seeds were selected , of which one seed was female who had exchanged sex in the past month . SWs were explicitly asked to recruit other SWs , and non-SWs were encouraged to recruit either SWs or non-SWs -LRB- Table 1 , column 4 -RRB- . This first SW seed produced no recruits and was lost to follow up . Another female non-SW started a chain that recruited a total of 22 female IDUs who had ever exchanged sex , of whom 13 had exchanged sex in the past month . This female non-SW seed produced a total of 135 recruits by the end of the study equivalent to 28 % of the total sample , of which 15 % -LRB- 20 -RRB- were SWs and who reported working on the street . Among the other seeds , only a handful of current SWs were recruited -LRB- n = 4 -RRB- . Towards the end of the project more coupons were distributed to female SWs in an attempt to increase the SW sample -LRB- n = 5 -RRB- , none of which produced any recruits . In order to increase the sample of SWs in the survey , 21 SWs were subsequently identified and interviewed without coupons . Data on the number of female SWs within an individual 's IDU network were unfortunately not provided . The mean IDU network size among SWs was 19.5 -LRB- SD 14.2 -RRB- and among non-SWs 27.1 -LRB- SD 33.0 -RRB- . Only one SW recruited through RDS reported working from an apartment ; all others were street-based SWs . We expected that RDS would enable us to recruit more hidden populations of SWs such as those working from apartments or hotels . The fact that SW seeds failed to produce any waves of SWs or were lost to follow up , indicates that SW networks may not be as well connected . Field notes show that initial attempts to access street SWs at Moskovsky Prospect and Pobeda Street had failed primary because of intensified police action in the area . A local officer of the Federal Security Service believed he had been recently infected with HIV by a SW from the area , and , in revenge , he and his colleagues enforced a repressive policy of fines and arrests among SWs . Recruiting SWs towards the end of the survey was more successful when policing practices returned to normal . Meanwhile , the sample target was reached for non-SW IDUs . Discussion Despite undertaking formative research in the planning of these RDS studies , we found that RDS methods were unable to attain sufficient samples of SWs in Serbia , Montenegro , and Russia . A number of inter-related factors emerged as important to the success of RDS : low motivation of SWs to participate due to their perception of inadequate incentive ; low-density SW networks combined with high level of independence in the organisation of sex work ; a tightly controlled small number of sex work venues ; lack of contact between SWs and local services in the context of high levels of mistrust of ` official ' agencies ; and difficulties emerging in the organisation of the RDS studies of SWs at the same time as a parallel RDS study of IDUs . Whereas in other settings -LRB- e.g. , Vietnam , north-eastern India , Brazil -RRB- SWs have reacted favourably to nominal monetary incentives in RDS studies , including incentives which fall below the rate charged for sex ,1617 it is possible that the incentives offered were perceived as being too low . In order to earn primary and secondary incentives , which together in all three studies amounted to about a half-an-hour SW 's rate , they had to leave their work and travel to and from the fixed interview site at least twice plus spend at least an hour involved in the study . It is possible that SWs in Eastern Europe may be less interested in the incentives offered since they have comparatively higher earnings . Indications are that free HIV/STI health assessments and referral for treatment should be explored in addition to the incentive . The high acceptance of VCT in Belgrade , for example , is a good example of how provision of services can be more effective than monetary incentives in recruiting survey participants . If incentives are purely monetary , they should be adequate to entice SWs to participate ; yet this is often not feasible given the risk of high incentives also encouraging the attempted participation of non-SWs . Unlike other RDS studies conducted in Vietnam ,16 SWs in Belgrade felt uncomfortable being interviewed at a location where a concurrent study of IDUs was being conducted . Based on anecdotal information and the fact that SWs in Belgrade started participating in the study once the IDU study had finished , we believe that SWs were dissuaded from going to a location that was used by IDUs . This problem can be assessed during formative research using focus groups with SWs to assess whether they would feel comfortable sitting in a waiting room with a group of male and female IDUs . Perhaps the main reason for the poor success of RDS recruitment among SWs in these three settings is the characteristics of SW networks . RDS methodology requires that the target population form sufficiently large and dense networks . However , the information on the network sizes of a few SWs gathered through our formative research are not easy to interpret since there is no known cut-off point for determining an appropriate network size or density for RDS . Based on the results of our studies , SWs in our three study areas often work independently , thus forming smaller , more isolated , networks . Those working on the street and in brothels are also under tight control by managers , pimps and police thus restricting their movement and weakening network density . On the other hand , prevalent societal norms -- a form of social control -- prevent SWs who work independently from revealing their SW status and participating . The low recruitment rate encountered in our studies might be overcome by allowing studies to run for a much longer time -- perhaps as long as six months or a year -- allowing SWs to gain trust in the investigators . In the studies described above , interview sites were rented and staff employed for a fixed amount of time . A preferable setting is one with on-going services for SWs that can be used as an interview site for a long period of time allowing recruits to come at a slow rate . However , time was unlikely a major factor contributing to difficulties in RDS recruitment in the cities where our studies were conducted . The dearth of well-established projects targeting SWs in Eastern Europe means that greater effort should be invested prior to RDS studies to identify a greater number of seeds and engender SWs ' trust . In some cases existence of a well-established service with established contacts with local SW communities might be a decisive factor . For example , this was the case in a RDS study among SWs in Tbilisy , Georgia -LRB- January 2006 , written communication , Johnston LG -RRB- . In addition to promoting trust , such service organisations can provide additional networking opportunities for loosely connected SWs . Conclusion Given the cost of conducting second-generation sero-surveillance among highly vulnerable populations , formative research is important for establishing the appropriate type of sampling and reward system . We found the making available free and confidential HIV testing services was an effective incentive , and perhaps more so than monetary incentives alone . Although formative research would require some additional costs , it can increase efficiency in a more extensive and successful study . During formative research , we suggest that policy makers , service providers and target populations be consulted to determine the visibility of sex work , as low visibility can be associated with tight control of the sex work industry and weak networking among SWs , indicating difficulties using RDS . If researchers find it difficult to recruit SWs for formative study , the RDS study is likely to fail . Depending on the timescale , funding and interest among existing service providers , additional services may be provided well ahead of a RDS study in order to access SW respondents . Further investigation is needed into the ethnography of SW networks in this region , especially on network composition and service access . In the case of IDUs who exchange sex for money , goods , or drugs , it is important to understand their primary network linkage -- injecting drug use or sex work -- and how they represent their `` other identity '' within each network . Incentives need to be better identified in advance of RDS studies , specifically as they relate to level of income , opportunity costs , and trust in the investigators and seeds . Without this cultural and legal sensitivity , surveillance for HIV among this vulnerable population will not provide adequate information on epidemic spread or program effectiveness .

O O O O B I I O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O B O O O O O O O O B O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

respondent driven sampling
hidden populations
russia
serbia
montenegro
sex workers