METHOD FOR CUFF-LESS BEAT-TO-BEAT BLOOD PRESSURE ESTIMATION USING TWO RELATIVE BLOOD VOLUME SENSORS ON DIFFERENT APPLIED PRESSURES

Abstract

The invention describes a measurement method for the continuous non-invasive determination of blood pressure using two blood volume sensors, which are under two different applied pressures. The non-linear function, which is updated for each cardiac cycle, is used to model the relationship between blood pressure and relative blood volume change. The model depends on relative blood volume changes and applied external pressures to the sensors. The derived model needs one point blood pressure calibration. The blood volume sensor can be optical sensor, such as photoplethysmographic sensor, however, any transducer, which converts blood volume or relative blood volume to electrical signal, is applicable. As one possible application, the method can be used for the blood pressure determination at one finger. However, the method is not limited with the blood volume measurement sites (e.g. radial artery etc.).

Claims

1. A method for continuous non-invasive monitoring of arterial blood pressure based on a beat-to-beat assessment of arterial blood pressure through a dependence function between pressure and volume curves, wherein determining difference signals between the volume curves measured by volume sensors applying different back pressure to an artery arm calculated by formula
V.sub.12=V.sub.1−V.sub.2,  (19) or
V.sub.21=V.sub.2−V.sub.1,  (20) where V.sub.1—signal of volume sensor with higher back pressure, V.sub.2—signal of volume sensor with lower back pressure, and determining amplitudes ΔV.sub.21 or ΔV.sub.12 of the difference signals V.sub.12 or V.sub.21 between the volume curves for each cardiac cycle, and calculating for each cardiac cycle the arterial blood pressure with a predetermined calibration parameter from the amplitudes of the differential signal and the back pressures applied by the sensors by formula $P=P_{s1}-0.5.Math.\left(P_{s1}-P_{s2}\right)-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{21}}{\left(P_{s1}-P_{s2}\right).Math.k.Math.B}\right),$ or by formula $P=P_{s2}-0.5.Math.\left(P_{s1}-P_{s2}\right)-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{12}}{\left(P_{s2}-P_{s1}\right).Math.k.Math.B}\right),$ or by formula $P=P_{s2}+0.5.Math.\left(P_{s1}-P_{s2}\right)-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{21}}{\left(P_{s1}-P_{s2}\right).Math.k.Math.B}\right),$ or by formula $P=P_{s2}+0.5.Math.\left(P_{s1}-P_{s2}\right)-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{12}}{\left(P_{s2}-P_{s1}\right).Math.k.Math.B}\right),$ where P—arterial blood pressure, P.sub.s1—value of higher back pressure applied by volume sensor for each cardiac cycle, P.sub.s2—value of lower back pressure applied by volume sensor for each cardiac cycle, k—compliance index determined for each cardiac cycle, B—parameter determined by previous individual calibration.

2. The method according to claim 1, wherein the dependence function between of the pressure and volume curves is updated for each cardiac cycle by the compliance index k through formula $k=\frac{\ln \left(\frac{\Delta V_1}{\Delta V_2}\right)}{\left(P_{s2}-P_{s1}\right)},$ or of the formula $k=\frac{\ln \left(\frac{\Delta V_2}{\Delta V_1}\right)}{\left(P_{s1}-P_{s2}\right)},$ where ΔV.sub.1—amplitude of the higher back pressure volume sensor signal determined for each cardiac cycle, ΔV.sub.2—amplitude of the lower back pressure volume sensor signal for each cardiac cycle, P.sub.s1—value of the higher back pressure applied by the volume sensor for each cardiac cycle, P.sub.s2—value of the lower back pressure applied by the volume sensor for each cardiac cycle.

3. The method according to claim 1, wherein for each cardiac cycle the dependence function between the pressure and volume curves is updated and the pulse pressure is calculated by the formula $\mathrm{PP}=\frac{\Delta V_1}{\text{?}}$ $\text{?}\text{indicates text missing or illegible when filed}$ or by the formula $\mathrm{PP}=\frac{\Delta V_2}{\text{?}}$ $\text{?}\text{indicates text missing or illegible when filed}$ where k is compliance index determined for each cardiac cycle, B is parameter determined by previous individual calibration, ΔV.sub.1—amplitude of the higher back pressure volume sensor signal determined for each cardiac cycle, ΔV.sub.2—amplitude of the lower back pressure volume sensor signal for each cardiac cycle, P.sub.s1—value of the higher back pressure applied by the volume sensor for each cardiac cycle, P.sub.s2—value of the lower back pressure applied by the volume sensor for each cardiac cycle.

4. The method according to claim 1, wherein the systolic blood pressure for each cardiac cycle is calculated by formula
SBP=P+0.5.Math.PP,
and the diastolic blood pressure by formula
DBP=P−0.5.Math.PP

5. The method according to claim 1, wherein when determining arterial blood pressure for each cardiac cycle the applied pressures of volume sensors are lower than a mean arterial blood pressure.

6. The method according to claim 1 wherein for determining the individual calibration parameter B the pressure applied by volume sensors on the artery is increased above the mean arterial blood pressure while the difference of pressures applied by volume sensors maintained, during the increase of the back pressures the amplitude ΔV.sub.21 of the difference signal between the volume curves, compliance index k and time series of the back pressures P.sub.s1, P.sub.s2, are calculated, at the end of back pressures increase the maximum value ΔV.sub.21_max from the time series of the difference signal amplitudes ΔV.sub.21 between the volume curves and value of the compliance index k.sub.max corresponding to this time point and pressures P.sub.s1_max, P.sub.s2_max applied by volume sensors are determined by using the formula $B=\text{?}$ $\text{?}\text{indicates text missing or illegible when filed}$ or formula $B=\text{?}$ $\text{?}\text{indicates text missing or illegible when filed}$

7. The method according to claim 1, wherein for determining the individual calibration parameter B the arterial systolic blood pressure (SBP.sub.m) and diastolic blood pressure (DBP.sub.m) are measured by external blood pressure device and simultaneously with the measurement the time series of the parameters ΔV.sub.21 or ΔV.sub.12, k, P.sub.s1, P.sub.s2, are calculated and after measurement of the blood pressure the mean values of the time series of the parameters ΔV.sub.21_m or ΔV.sub.12_m, k.sub.m, P.sub.s1_m, P.sub.s2_m are calculated by using formula $B=\frac{\Delta V_{21\_m}}{\text{?}}\text{?}$ $\text{?}\text{indicates text missing or illegible when filed}$ or formula $B=\frac{\Delta V_{12\_m}}{\text{?}}.$ $\text{?}\text{indicates text missing or illegible when filed}$

8. A device for continuous non-invasive monitoring of arterial blood pressure based on the dependence function of pressure and volume curves for estimating arterial blood pressure, comprising: two optical sensors consisting of a light source and a photodetector; digital-analogue converters attached to the light sources; transimpedance amplifiers electrically connected to the photodetectors; force transducers attached to the optical sensors; analogue-to-digital converters electrically connected to the force transducers and transimpedance amplifiers; a microcontroller electrically connected to the analogue-to-digital converters and digital-to-analogue converters; a memory electrically connected to the microcontroller; and an external communication port; wherein a sensor housing comprises recesses for one or both optocouples in order to produce differences in the back pressures exerted by the optical sensors.

9. A device for continuous non-invasive monitoring of arterial blood pressure based on the dependence function of pressure and volume curves for estimating arterial blood pressure, comprising two optical sensors consisting of a light source and a photodetector; digital-to-analogue converters connected to the light sources; transimpedance amplifiers electrically connected to the photodetectors; spring loaded force transducers attached to the optical sensors; analogue-to-digital converters electrically connected to the force transducers and transimpedance amplifiers; microcontrollers electrically connected to the analogue-to-digital converters and the digital-to-analogue converters; a memory electrically connected to the microcontroller; and an external communication port; wherein a first spring is mounted between the first optical sensor and the first force transducers, the stiffness of which differs 0.1 to 2 times from the stiffness of the second spring mounted between the second optical sensor and the second force transducers, in order to create differences in the back pressures expressed by the optical sensors.

10. The device according to claim 8, wherein the difference signal V.sub.12 or V.sub.21 between the volume curves and amplitude ΔV.sub.12 or ΔV.sub.21 is calculated in the microcontroller for the determination of arterial blood pressure.

11. The device according to claim 10, wherein the compliance index k of the function between pressure and volume curves is calculated in the microcontroller for each cardiac cycle.

12. The device according to claim 8, wherein the device is automatically switched to calibration mode when an increase in the pressures measured by force transducers is detected or device is switched to the calibration mode through external port, and in which the difference signal amplitude ΔV.sub.12 or ΔV.sub.12, compliance index k and back pressures P.sub.s1 and P.sub.s2 are stored in the memory attached to the controller for each cardiac cycle and simultaneously their values are sent out through external communication port.

13. The device according to claim 12, wherein the device detects a drop of pressures close to the initial level following an increase in the pressures measured by force transducers, as a result of which the recording of parameters ends or recording is terminated via the external communication port and from the time series of amplitudes ΔV.sub.12 the maximum amplitude ΔV.sub.12_max and corresponding compliance index k value k.sub.max and values of pressures P.sub.s1_max ja P.sub.S2_max applied by volume sensors are determined and the calibration parameter is calculated.

14. The device according to claim 8, wherein the device is switched to the calibration mode via the external communication port and during which parameters ΔV.sub.21 or ΔV.sub.12, k, P.sub.s1, P.sub.s2 for each cardiac cycle are stored in the memory attached to the microcontroller.

15. The device according to claim 14, wherein the device is switched off from calibration mode via the external communication port and the systolic (SBPm) and diastolic (DBPm) blood pressure values measured with an external blood pressure device are entered through the said port and based on the time series of the parameters stored in the memory the microcontroller calculates the mean values ΔV.sub.21_m ΔV.sub.12_m, k.sub.m, P.sub.s1_m, P.sub.s2_m after the end of the blood pressure measurement and calculates the calibration parameter B.

16. The device according to claim 13, wherein the arterial blood pressure P, pulse pressure PP, systolic blood pressure SBP and diastolic blood pressure DBP are calculated for each heart cycle in the microcontroller of the device and these values are output via the communication port, respectively.

17. The device according to claim 9, wherein the difference signal V.sub.12 or V.sub.21 between the volume curves and amplitude ΔV.sub.12 or ΔV.sub.21 is calculated in the microcontroller for the determination of arterial blood pressure.

18. The device according to claim 9, wherein the device is automatically switched to calibration mode when an increase in the pressures measured by force transducers is detected or device is switched to the calibration mode through external port, and in which the difference signal amplitude ΔV.sub.12 or ΔV.sub.12, compliance index k and back pressures P.sub.s1 and P.sub.s2 are stored in the memory attached to the controller for each cardiac cycle and simultaneously their values are sent out through external communication port.

19. The device according to claim 18, characterized in that the device detects a drop of pressures close to the initial level following an increase in the pressures measured by force transducers, as a result of which the recording of parameters ends or recording is terminated via the external communication port and from the time series of amplitudes ΔV.sub.12 the maximum amplitude ΔV.sub.12_max and corresponding compliance index k value k.sub.max and values of pressures P.sub.s1_max ja P.sub.s2_max applied by volume sensors are determined and the calibration parameter is calculated.

20. The device according to claim 9, wherein the device is switched to the calibration mode via the external communication port and during which parameters ΔV.sub.21 or ΔV.sub.12, k, P.sub.s1, P.sub.s2 for each cardiac cycle are stored in the memory attached to the microcontroller.

21. Device according to claim 20, wherein the device is switched off from calibration mode via the external communication port and the systolic (SBPm) and diastolic (DBPm) blood pressure values measured with an external blood pressure device are entered through the said port and based on the time series of the parameters stored in the memory the microcontroller calculates the mean values ΔV.sub.21_m ΔV.sub.12_m, k.sub.m, P.sub.s1_m, P.sub.s2_m after the end of the blood pressure measurement and calculates the calibration parameter B.

22. Device according to claim 15, wherein the arterial blood pressure P, pulse pressure PP, systolic blood pressure SBP and diastolic blood pressure DBP are calculated for each heart cycle in the microcontroller of the device and these values are output via the communication port, respectively.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0010] The present invention will be described below in detailed description with reference to the accompanied drawings where:

[0011] FIG. 1 shows the relationship between transmural pressure and blood volume in artery;

[0012] FIG. 2 shows the relationship between transmural pressure and compliance of artery;

[0013] FIG. 3 shows a blood volume change in artery in case mean transmural pressure is zero;

[0014] FIG. 4 shows a blood volume changes in artery for two pressures sensors at different applied pressures;

[0015] FIG. 5 shows a blood volume change in artery between two pressures sensors at different applied pressures;

[0016] FIG. 6 illustrates a block diagram of a non-occlusive and continuous blood pressure sensor device, which is constructed according to the principles of current invention;

[0017] FIG. 7 illustrates a construction principles of the blood pressure sensor device; a) is a cross section of the pressure sensor device, b) is a bottom view of the pressure sensor device;

[0018] FIG. 8 illustrates a construction principles of an alternative solution of blood pressure sensor device; a) is a cross section of the pressure sensor device, b) is a bottom view of the pressure sensor device;

[0019] FIG. 9 illustrates a flowchart of blood pressure monitoring and first calibration manoeuvre;

[0020] FIG. 10 illustrates a flowchart of blood pressure monitoring and second calibration manoeuvre;

[0021] FIG. 11 illustrates calculated volumes ΔV.sub.1, ΔV.sub.2, and ΔV.sub.21;

[0022] FIG. 12 illustrates applied pressures on optical sensors;

[0023] FIGS. 13 to 16 illustrates results of estimated blood pressures using equations according to invention;

[0024] FIGS. 17 to 20 illustrates the Bland-Altman plots of the results illustrated in FIGS. 13 to 16.

DETAILED DESCRIPTION OF THE INVENTION

[0025] The present invention provides for non-occlusive non-invasive continuous imposed arterial blood pressure monitoring. The systolic blood pressure, diastolic blood pressure and pulse pressure are obtained by calculation using arterial blood volume signals from two volume sensors, which are under two different applied pressures. The volume signals are obtained optically using optical sensing technique, which is widely known, and they represent the relative blood volume changes over time. The arterial blood pressure is estimated using the function, which relates the transmural pressure and compliance in the artery, and it is updated for each cardiac cycle. The function is based on the so-called compliance model, which has been discussed earlier in Baker, P. D., Westenskow, D. R. and Kück, K., “Theoretical analysis of non-invasive oscillometric maximum amplitude algorithm for estimating mean blood pressure”, Med. Biol. Eng. Comput. 35, 1997, page 271-278.

[0026] Transmural pressure P.sub.t is the difference between the intra-arterial pressure P and the externally applied pressure P.sub.s (e.g. applied by optical sensor). Transmural pressure is calculated as follows:

P.sub.t=P−P.sub.s  (1)

[0027] The blood volume V in artery and transmural pressure are related to each other through relationship, which is given in FIG. 1. The blood volume in artery is given with the following equation, in case the P.sub.t>0:

[00001]$\begin{array}{cc}V=V_{\max }-\left(V_{\max }-V_0\right).Math.e^{-\frac{C_m}{\left(V_{\max }-V_0\right)}.Math.P_t}& \left(2\right)\end{array}$

where V.sub.max is the is the maximum arterial volume when the artery is fully expanded, V.sub.0 is the arterial volume at zero P.sub.t, and C.sub.m is the maximum compliance. It can be seen that even with the same change of transmural pressure ΔP.sub.t the volume change ΔV is different depending on the operating point of P.sub.t (FIG. 1). ΔV represents the relative volume change or amplitude within one cardiac cycle.

[0028] Through differentiation of equation 9 the analytical form can be obtained for the arterial compliance, in case P.sub.t>0:

[00002]$\begin{array}{cc}C=\frac{dV}{d{P}_t}\approx \frac{\Delta V}{\Delta P_t}=C_m.Math.e^{-\frac{C_m}{\left(V_{\max }-V_0\right)}.Math.P_t}& \left(3\right)\end{array}$

[0029] The relationship is illustrated in FIG. 2.

[0030] Blood volume change in artery is maximal in case mean transmural pressure is zero (see FIG. 3). In such case the externally applied pressure is equal to the mean arterial pressure.

[0031] In the non-occlusive continuous (beat-to-beat) blood pressure estimation system the two blood volume sensors, S1 and S2, which are optical sensors in the present invention, are applied to the artery at two different pressures P.sub.s1 and P.sub.s2. In such case the blood pressure change ΔP in the artery is equal to the pulse pressure. For both blood volume sensors, the pulse pressure is the same; however, the blood volume changes under the sensor are different.

[0032] The blood volume change for volume sensor with applied pressure P.sub.s1 is equal to ΔV.sub.1 and for volume sensor with applied pressure P.sub.s2 is equal to ΔV.sub.2.

[0033] For both volume sensors, the compliances of artery can be calculated as follows:

[00003]$$\begin{gathered} \begin{array}{cc}{C}_1=\frac{\Delta V_1}{\Delta P} \\ {C}_2=\frac{\Delta V_2}{\Delta P}& \left(4\right)\end{array} \end{gathered}$$

[0034] As pulse pressures are equal for both sensors (assuming that pulse pressure is not changing in such a short distance between two sensors) then from equation 4:

[00004]$\begin{array}{cc}\frac{C_1}{C_2}=\frac{\Delta V_1}{\Delta V_2}& \left(5\right)\end{array}$

[0035] By substituting equation 3 to equation 5:

[00005]$$\begin{gathered} \begin{array}{cc}\frac{\Delta V_1}{\Delta V_2}=\frac{C_m.Math.e^{-\frac{C_m}{\left(V_{\max }-V_0\right)}.Math.P_{t1}}}{C_m.Math.e^{-\frac{C_m}{\left(V_{\max }-V_0\right)}.Math.P_{t2}}}=e^{-\frac{C_m}{\left(V_{\max }-V_0\right)}.Math.\left(P_{t1}-P_{t2}\right)} \\ \mathrm{and}& \left(6\right)\end{array} \end{gathered}$$$\begin{array}{cc}\frac{\ln \left(\frac{\Delta V_1}{\Delta V_2}\right)}{\left(P_{t1}-P_{t2}\right)}=\frac{C_m}{\left(V_{\max }-V_0\right)}=k.& \left(7\right)\end{array}$

[0036] The equation 5 can be represented as well with opposite ratios:

[00006]$\begin{array}{cc}\frac{C_2}{C_1}=\frac{\Delta V_2}{\Delta V_1}.& \left(8\right)\end{array}$

[0037] By substituting equation 3 to equation 8:

[00007]$\begin{array}{cc}\frac{\ln \left(\frac{\Delta V_2}{\Delta V_1}\right)}{\left(P_{t2}-P_{t1}\right)}=\frac{C_m}{\left(V_{\max }-V_0\right)}=k.& \left(9\right)\end{array}$

[0038] The difference between transmural pressures of P.sub.t1 and P.sub.t2 (P.sub.t1<P.sub.t2) is equal to the difference between applied pressures of volume sensors P.sub.s1 and P.sub.s2 (P.sub.s1>P.sub.s2), which can be calculated as follows:

P.sub.t1=P−P.sub.s1  (10)

P.sub.t2=P−P.sub.s2,  (11)

P.sub.t1−P.sub.t2=P−P.sub.s1−P+P.sub.s2=P.sub.s2−P.sub.s1 and  (12)

P.sub.t2−P.sub.t1=P−P.sub.s2−P+P.sub.s1=P.sub.s1−P.sub.s2.  (13)

[0039] Therefore, the equations 7 and 9 can be rewritten as follows:

[00008]$\begin{array}{cc}\frac{\ln \left(\frac{\Delta V_1}{\Delta V_2}\right)}{\left(P_{s2}-P_{s1}\right)}=\frac{C_m}{\left(V_{\max }-V_0\right)}=k\mathrm{and}& \left(14\right)\end{array}$$\begin{array}{cc}\frac{\ln \left(\frac{\Delta V_2}{\Delta V_1}\right)}{\left(P_{s1}-P_{s2}\right)}=\frac{C_m}{\left(V_{\max }-V_0\right)}=k.& \left(15\right)\end{array}$

[0040] The compliance model in equation 3 can be rewritten based on the equations 14 and 15:

C=k.Math.(V.sub.max−V.sub.0).Math.e.sup.−k.Math.P.sup.t.  (16)

[0041] By knowing the difference between applied pressures of volume sensors and estimated relative blood volume changes the k can be calculated using equations 14 or 15 and it is dependent on compliance of artery. It is known that the compliance of artery changes due to the slowly varying tonus of the muscles around the vessel driven by the nervous system. Therefore, the calculation of parameter k for each cardiac cycle updates the compliance model. It is assumed that the difference (V.sub.max−V.sub.0) is not changing because maximal volume of artery cannot increase or decrease (during short period of time the artery is not growing bigger) and can be estimated by individual calibration. Therefore, in the following text the difference (V.sub.max−V.sub.0) is substituted by calibration parameter B.

[0042] The difference between transmural pressures is equal to the difference between applied pressures of volume sensors:

ΔP.sub.s12=P.sub.s1−P.sub.s2 or  (17)

ΔP.sub.s21=P.sub.s2−P.sub.s1.  (18)

[0043] The difference between applied pressures of volume sensors corresponds to the measured blood volume difference by volume sensor signals V.sub.1 and V.sub.2, and can be calculated as follows:

V.sub.12=V.sub.1−V.sub.2 or  (19)

V.sub.21=V.sub.2−V.sub.1.  (20)

[0044] The amplitudes ΔV.sub.12 or ΔV.sub.21 of the volume difference signals V.sub.12 or V.sub.21 are detected for every cardiac cycle, respectively, and illustrated in FIG. 5.

[0045] In such case, the compliance can be calculated based on equations 4 and 16 for the transmural pressure P.sub.t1+0.5.Math.ΔP.sub.s12 as follows, in case P.sub.t>0:

[00009]$\begin{array}{cc}\frac{{\Delta V}_{21}}{\Delta P_{s12}}=k.Math.B.Math.e^{-k.Math.\left(P_{t1}+0.5.Math.\Delta P_{s12}\right)}.& \left(21\right)\end{array}$

[0046] By substituting equation 1 into equation 21 it can be rewritten:

[00010]$\begin{array}{cc}\frac{\Delta V_{21}}{\Delta P_{s12}}=k.Math.B.Math.e^{-k.Math.\left(P-P_{s1}+0.5.Math.\Delta P_{s12}\right)}.& \left(22\right)\end{array}$

[0047] The intra-arterial pressure P derives from the equation 22 as follows:

[00011]$\begin{array}{cc}P=P_{s1}-0.5.Math.\Delta P_{s12}-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{21}}{\Delta P_{s12}.Math.k.Math.B}\right).& \left(23\right)\end{array}$

[0048] Similarly, to the equation 21, the compliance model can be rewritten for the amplitude ΔV.sub.12:

[00012]$\begin{array}{cc}\frac{\Delta V_{12}}{\Delta P_{s21}}=k.Math.B.Math.e^{-k.Math.\left(P_{t1}+0.5.Math.\Delta P_{s12}\right)}.& \left(24\right)\end{array}$

[0049] In such case the amplitude ΔV.sub.12 and difference between applied pressures of volume sensors ΔP.sub.s21 are both negative. Based on the equation 1 and 24 the P derives similarly to the equation 23 as follows:

[00013]$\begin{array}{cc}P=P_{s1}-0.5.Math.\Delta P_{s12}-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{12}}{\Delta P_{s21}.Math.k.Math.B}\right).& \left(25\right)\end{array}$

[0050] The P can be also derived from the equations 23 and 25 for the transmural pressure P.sub.t2−0.5.Math.ΔP.sub.s12 as follows, in case P.sub.t>0:

[00014]$\begin{array}{cc}P=P_{s2}+0.5.Math.\Delta P_{s12}-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{21}}{\Delta P_{s12}.Math.k.Math.B}\right),\mathrm{and}& \left(26\right)\end{array}$$\begin{array}{cc}P=P_{s2}+0.5.Math.\Delta P_{s12}-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{12}}{\Delta P_{s21}.Math.k.Math.B}\right).& \left(27\right)\end{array}$

[0051] The equations 23, 25, 26, and 27 can be obtained respectively for the transmural pressures P.sub.t1−0.5.Math.ΔP.sub.s21 and P.sub.t2+0.5.Math.ΔP.sub.s21, in case P.sub.t>0:

[00015]$\begin{array}{cc}P=P_{s1}+0.5.Math.\Delta P_{s21}-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{21}}{\Delta P_{s12}.Math.k.Math.B}\right)& \left(28\right)\end{array}$$\begin{array}{cc}P=P_{s1}+0.5.Math.\Delta P_{s21}-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{12}}{\Delta P_{s21}.Math.k.Math.B}\right)& \left(29\right)\end{array}$$\begin{array}{cc}P=P_{s2}-0.5.Math.\Delta P_{s21}-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{21}}{\Delta P_{s12}.Math.k.Math.B}\right)& \left(30\right)\end{array}$$\begin{array}{cc}P=P_{s2}-0.5.Math.\Delta P_{s21}-\frac{1}{k}.Math.\ln \left(\frac{\Delta V_{12}}{\Delta P_{s21}.Math.k.Math.B}\right)& \left(31\right)\end{array}$

[0052] Intra-arterial pressure P can be estimated equally from equations 23, 25, 26, 27, 28, 29, 30, and 31, in case the calibration parameter B is determined through one point calibration. Therefore, the B is calculated in case the intra-arterial pressure P is known and it is derived from the equations 23 and 25:

[00016]$\begin{array}{cc}B=\frac{\Delta V_{21}}{\left(P_{s1}-P_{s2}\right).Math.k.Math.e^{-k.Math.\left(P-P_{s1}+0.5.Math.\left(P_{s1}-P_{s2}\right)\right)}},& \left(32\right)\end{array}$$\begin{array}{cc}B=\frac{\Delta V_{12}}{\left(P_{s2}-P_{s1}\right).Math.k.Math.e^{-k.Math.\left(P-P_{s1}+0.5.Math.\left(P_{s1}-P_{s2}\right)\right)}}.& \left(33\right)\end{array}$

[0053] Similarly, the calibration parameter B can be derived from all the intra-arterial pressure P equations 26 to 31. However, in the following text all the derivations are based on the equations 23 and 25. The intra-arterial pressure P can be determined using for example an external oscillometric blood pressure measurement device and the systolic blood pressure (SBP.sub.m), diastolic blood pressure (DBP.sub.m), mean blood pressure (MBP.sub.m), and pulse pressure (PP.sub.m) are measured. Any of previously mentioned two measured blood pressures can be selected for the intra-arterial pressure P calculation as they are all related to each other. However, here the intra-arterial pressure P is calculated using systolic and diastolic blood pressure and the calibration parameter B derives as follows based on the equations 32 and 33:

[00017]$\begin{array}{cc}B=\frac{\Delta V_{21\_m}}{\begin{array}{c}\left(P_{s1\_m}-P_{s2\_m}\right).Math.k_m.Math.\\ e^{-k_m.Math.\left({\mathrm{DBP}}_m+0.5.Math.\left({\mathrm{SBP}}_m-{\mathrm{DBP}}_m\right)-P_{s1\_m}+0.5.Math.\left(P_{s1\_m}-P_{s2\_m}\right)\right)}\end{array}},\mathrm{and}& \left(34\right)\end{array}$$\begin{array}{cc}B=\frac{\Delta V_{12\_m}}{\begin{array}{c}\left(P_{s2\_m}-P_{s1\_m}\right).Math.k_m.Math.\\ e^{-k_m.Math.\left({\mathrm{DBP}}_m+0.5.Math.\left({\mathrm{SBP}}_m-{\mathrm{DBP}}_m\right)-P_{s1\_m}+0.5.Math.\left(P_{s1\_m}-P_{s2\_m}\right)\right)}\end{array}},& \left(35\right)\end{array}$

where ΔV.sub.21_m, k.sub.m, P.sub.s1_m, P.sub.s2_m are the average values of parameters ΔV.sub.21, ΔV.sub.12, k, P.sub.s1, P.sub.s2 during the period while blood pressure measurement was carried out by external device.

[0054] The calibration parameter B is derived as well in case the transmural pressure is zero (P−P.sub.s1+0.5.Math.ΔP.sub.s12=0) in equation 22. In such case the amplitudes ΔV.sub.12 or ΔV.sub.21 of the volume difference signals are maximal ΔV.sub.12_max or ΔV.sub.21_max. This situation is achieved by increasing the pressure, which is applied on volume sensors. The calibration parameter B is derived from the equation 22 for ΔV.sub.12_max or ΔV.sub.21_max:

[00018]$\begin{array}{cc}B=\frac{\Delta V_{21\_\max }}{\left(P_{s1\_\max }-P_{s\mathrm{2\_}\max }\right).Math.k_{\max }}\mathrm{or}& \left(34\right)\end{array}$$\begin{array}{cc}B=\frac{\Delta V_{12\_\max }}{\left(P_{s2\_\max }-P_{s\mathrm{1\_}\max }\right).Math.k_{\max }},& \left(35\right)\end{array}$

where k.sub.max, P.sub.s1_max and P.sub.s2_max are the values of k, P.sub.s1, and P.sub.s2 at the situation when ΔV.sub.12 or ΔV.sub.21 are maximal.

[0055] The compliance model is used for the intra-arterial pressure P calculations once the calibration parameter B is estimated. Based on the calculated intra-arterial pressure P, the pulse pressure (PP) is calculated by combining equations 4, 10, 11, and 16:

[00019]$\begin{array}{cc}PP=\frac{\Delta V_1}{k.Math.B.Math.e^{-k.Math.\left(P-P_{s1}\right)}},& \left(36\right)\end{array}$$\begin{array}{cc}\mathrm{PP}=\frac{\Delta V_2}{k.Math.B.Math.e^{-k.Math.\left(P-P_{s2}\right)}}.& \left(37\right)\end{array}$

[0056] Systolic blood pressure is calculated based on equations 23, 36, and 37 as follows:

SBP=P+0.5.Math.PP.  (38)

[0057] Similarly, diastolic blood pressure is calculated based on equations 23, 36 and 37 as follows:

DBP=P−0.5.Math.PP.  (39)

[0058] In the present invention, the device for non-occlusive non-invasive continuous pressure monitoring is shown in FIG. 6. The dependence between the transmural pressure and compliance for each cardiac cycle is performed by updating the function (compliance model) adopted for sensor device. The sensor device comprises two pairs of photoplethysmographic sensors 1, 2 arranged side by side in one sensor device housing 3 as optical sensor comprising of a light source 4, 5 and a photodetector 6, 7, digital-to-analogue converters (DACs) 8 electrically connected to light source, transimpedance amplifiers 9, 10 electrically connected to the photodetector, analogue-to-digital converters (ADCs) 11 electrically connected to the force transducers 12, 13 and the transimpedance amplifiers, a microcontroller 14 electrically connected to the analogue-to-digital and digital-to-analogue converters, an electrically connected memory 15 and external communication port 16 to the microcontroller. A force transducer is attached to each optical sensor. The back pressure exerted on the artery by both optical sensors can be measured with a force transducer. The sensor housing 17, shown in FIG. 7, comprises one or both optical sensors 18, 19 in the case of cavities. The sensor housing is designed so that the surfaces of the optical sensors are not in the same level. The surface of one optical sensor is located in relation to the surface of the other sensor in the cavity. Thereby, the optical sensor in the cavity exerts a lower back pressure than the sensor not in the cavity. The optical sensor and force transducer in the cavity is attached to the housing so that the arterial pressure exerted by the optical sensor can be recorded. The signals from the optical sensors and force transducers are supplied to the other electrical components of device 20. In alternative embodiment, shown in FIG. 8, in order to produce differences in the back pressures exerted by the optical sensors, a first spring 21 is attached between the first optical sensor 22 and the force transducer 23, the stiffness of which differs from that of the second spring 24 attached between the second optical sensor 25 and the force transducer 26.

[0059] The light from light emitting diodes (LEDs) is absorbed and scattered in the artery or microvascular bed of tissue and fraction of photons are detected by photodiode (photodetector). The current signal from photodiodes of optical sensors are supplied to transimpedance amplifiers that convert the photocurrents of the photodiodes to the voltage signals. The back pressure exerted on the artery by both optical sensors is measured with a force transducer. The output voltage of the transducer is in known relation with the applied force on the transducer. The outputs of the two transimpedance amplifiers and force transducers are supplied to the analogue-to-digital converters, where the signals are digitized for application to the microcontroller.

[0060] The microcontroller turns the LEDs on alternately through the DAC and the intensity of the LEDs are set based on the received voltage signals of photodetectors from the transimpedance amplifier. The driving frequency of the LEDs is at least 1 kHz and the duty cycle is between 25% to 50%. The microcontroller assembles the light intensity signals based on the voltage signals received for each photodetector, while the LED is turned on. Microcontroller may cancel the ambient light by using the voltage signal while the LED is turned off and subtracting it from the signal while the LED is turned on. The relative volume signals V.sub.1 and V.sub.2 are computed using the principles of Beer-Lamber law:

I=I.sub.0.Math.e.sup.−μ.Math.V,  (40)

where I.sub.0 is emitted light intensity by LED, I is detected light intensity by photodiode, V is tissue volume and μ is absorption. In diastole, the arterial blood volume in tissue is minimal V.sub.min and the detected light intensity is maximal I.sub.max. Beer-Lambert law is as follows:

I.sub.max=I.sub.0.Math.e.sup.−μ.Math.V.sup.min  (41)

[0061] In systole, the arterial blood volume in tissue is maximal and the detected light intensity is minimal. For such case the Beer-Lambert law is as follows:

I.sub.min=I.sub.0.Math.e.sup.−μ.Math.V.sup.max.  (42)

[0062] Therefore, the relative blood volume change in tissue is:

[00020]$$\begin{gathered} \begin{array}{cc}\frac{I_{\max }}{I_{\min }}=\frac{I_0.Math.e^{-\mu .Math.V_{\min }}}{I_0.Math.e^{-\mu .Math.V_{\max }}}=\frac{e^{-\mu .Math.V_{\min }}}{e^{-\mu .Math.V_{\max }}}=e^{-\mu .Math.V_{\min }+\mu .Math.V_{\max }} \\ \ln \left(\frac{I_{\min }}{I_{\max }}\right)=-\mu .Math.V_{\min }+\mu .Math.V_{\max }=V_{\max }-V_{\min }=\Delta V.& \left(43\right)\end{array} \end{gathered}$$

[0063] Microcontroller detects for each cardiac cycle the minimal and maximal values of light intensities for both sensors and calculates volume changes ΔV.sub.1 and ΔV.sub.2 using the equation 43.

[0064] For the optical sensor S1 the relative blood volume can be calculated as follows:

I.sub.1=I.sub.01.Math.e.sup.−μ.Math.V.sup.1  (44)

where I.sub.01 is the emitted and I.sub.1 is detected light intensity of optical sensor S1. Similarly, the light intensity can be calculated for the second optical sensor S2:

I.sub.2=I.sub.02.Math.e.sup.−μ.Math.V.sup.2.  (45)

[0065] The difference between blood volumes underneath the sensors are calculated as follows:

[00021]$\frac{I_1}{I_2}=\frac{I_{01}.Math.e^{-\mu .Math.V_1}}{I_{02}.Math.e^{-\mu .Math.V_2}}=\frac{I_1}{I_2}.Math.e^{-\mu .Math.V_1+\mu .Math.V_2}$$\begin{array}{cc}\ln \left(\frac{I_1.Math.I_{02}}{I_2.Math.I_{01}}\right)=V_2-V_1=V_{21}\mathrm{or}& \left(46\right)\end{array}$$\begin{array}{cc}\ln \left(\frac{I_2.Math.I_{01}}{I_1.Math.I_{02}}\right)=V_1-V_2=V_{12}.& \left(47\right)\end{array}$

[0066] Microcontroller calculates according to the equation 46 or 47 the difference between blood volumes underneath the optical sensors and detects the amplitude ΔV.sub.21 or ΔV.sub.12 for each cardiac cycle, respectively. Furthermore, microcontroller calculates for each cardiac cycle pressures of the sensors P.sub.s1 and P.sub.s2 using the output voltages from force transducers, volume changes ΔV.sub.1 and ΔV.sub.2, parameter k (compliance index), intra-arterial blood pressure P, pulse pressure PP, systolic blood pressure SBP, and diastolic blood pressure DBP, and supplies the values together with parameters ΔV.sub.21 or ΔV.sub.12 via external communication port.

[0067] During calibration procedure the microcontroller stores the parameters ΔV.sub.21 or ΔV.sub.12, k, P.sub.s1, P.sub.s2, for each cardiac cycle to the memory of the device. There is possibility to initiate and to terminate the calibration manoeuvre via external communication port. The parameter B is calculated and stored to the memory of the device after calibration manoeuvre by microcontroller.

[0068] Use of blood pressure monitoring device will now be described. The device is placed on surface of the skin 26 above the subject's artery 27 or microvascular bed of tissue under interest (FIG. 6). An external force is applied to the device, which may be exerted, for example, by a strap attached around the device and the body to be examined. Firstly, the calibration parameter B is determined through calibration manoeuvre. There are two possible calibration manoeuvres.

[0069] The first possible calibration manoeuvre includes the external device that determines the arterial blood pressure, e.g. oscillometric blood pressure device. The arterial blood pressure is measured by external blood pressure device and at the same time the calibration manoeuvre is initiated in the device via external communication port. During the calibration manoeuvre amplitudes ΔV.sub.12 or ΔV.sub.21 of the relative volume change differences, parameter k, and applied pressure signals P.sub.s1 and P.sub.s2 are recorded to the memory. The recording is terminated in the microcontroller via external communication port after the blood pressure measurement is finished with the external device. As follows, the systolic blood pressure (SBP.sub.m) and diastolic blood pressure (DBP.sub.m) are supplied to the microcontroller via external communication port. The calibration parameter B is calculated based on the average values of the recorded parameters ΔV.sub.12 or ΔV.sub.21, parameter k, and applied pressure signals P.sub.s1 and P.sub.s2, and blood pressure values SBP.sub.m and DBP.sub.m.

[0070] The second possible calibration manoeuvre is initiated, when the microcontroller detects the rise in the force that is applied to the optical sensors or initiated via external communication port. The volume difference signal amplitude ΔV.sub.12, arterial compliance index k, and applied pressure signal values P.sub.s1 and P.sub.s2 are recorded to the memory for each cardiac cycle. The applied forces on the optical detectors can be monitored via external communication port. The applied pressure by the optical sensors is increased (e.g. manually) and it exceeds the mean arterial blood pressure. Thereafter, the applied pressure is decreased back to the initial level, which is detected by the microcontroller, and the recording of the parameters to the memory is terminated automatically or via external communication port. The maximal values ΔV.sub.12_max or ΔV.sub.21_max of amplitudes ΔV.sub.12 or ΔV.sub.21 from the recorded time series is detected. Based on this point in the time series, the arterial compliance index k.sub.max and pressure sensor values P.sub.s1_max and P.sub.s2_max are detected and calibration parameter B is calculated.

[0071] Possible recalibration may be needed periodically depending on the time period that the device has been used continuously.

[0072] After calibration the function (compliance model) between blood pressure and relative blood volume change is determined based on the calibration parameter B for particular patient and for every cardiac cycle updated compliance index k. The calculated systolic blood pressure, diastolic blood pressure, and pulse pressure values in the microcontroller are supplied via external communication port.

[0073] In FIG. 9 is presented flowchart of the method according to present invention with first calibration manoeuvre where: device is attached to the individual and process starts with detection of optical and applied pressure signals, which is followed by detection of cardiac cycle, and based on obtained data parameters ΔV.sub.21, P.sub.s12, and compliance index k are calculated, which is followed with systolic (SBPm) and diastolic (DBPm) blood pressure measurement with external device, and detection and recording of parameters ΔV.sub.21, P.sub.s12, and compliance index k in case calibration is started from external communication port, thereafter detection and recording of parameters is finished in case calibration is terminated from external communication port, which is followed with calculation of recorded parameters' average values and calibration coefficient B, in case calibration is not started or terminated from external communication port it is followed with intra-arterial blood pressure, systolic, diastolic and pulse pressure calculation.

[0074] In FIG. 10 is presented flowchart of the method according to present invention with second calibration manoeuvre where: device is attached to the individual and process starts with detection of optical and applied pressure signals, which is followed by detection of cardiac cycle, and based on obtained data parameters ΔV.sub.21, P.sub.s12, and compliance index k are calculated, which is followed with applied pressure change on optical sensors and detection and recording of parameters ΔV.sub.21, P.sub.s12, and compliance index k in case applied pressure increase on optical sensors is detected or calibration is started through external communication port, thereafter detection and recording of parameters is finished in case calibration is terminated from external communication port or applied pressure on optical sensors is returned to initial level, which is followed with detection of maximal amplitude of V.sub.21 with other parameters from recorded time series and calculation of calibration coefficient B, in case calibration is not started or terminated from external communication port it is followed with intra-arterial blood pressure, systolic, diastolic and pulse pressure calculation.

[0075] It is to be understood that the above-described arrangements are only illustrative of the application of the principles of the present invention. Numerous modifications and alternative arrangements may be devised by those skilled in the art without departing from the spirit and scope of the present invention and the appended claims are intended to cover such modifications and arrangements. For example, sensing light transmitted through rather than back scattered from an artery or microvascular bed of tissue could be utilized to determine relative volume of the artery. Furthermore, any transducer, which converts blood volume or relative blood volume to electrical signal (e.g. bioimpedance), is applicable. The method is not limited with the blood volume measurement sites (e.g. radial artery etc.).

[0076] The method according to present invention was tested on three different subjects using two optical sensors, which were attached on the first finger. The applied pressures were different and lower than mean arterial pressure of the finger. The applied pressures were measured and recorded during the experiment. The Finapres system was used for the reference blood pressure measurement. The finger cuff was placed around middle finger. The optical signals were registered with sampling rate of 1 kHz. During the experiment the subject was in supine position. The subjects were asked to carry out hand-grip test in order to change the arterial blood pressure during the recording time. After the recording of the signals the post processing was carried out in MATLAB.

[0077] In FIG. 11 are given volumes Δ.sub.V1, ΔV.sub.2, and ΔV.sub.21. The recorded pressure signals applied on the sensor are given in FIG. 12. The calibration parameter B was determined using equation 32, according to the measured reference arterial systolic (SBPm) and diastolic (DBPm) blood pressures.

[0078] As follows, the blood pressures were estimated using equations 22, and 36 to 39. The results for first subject (subject nr. 1) are illustrated in FIGS. 13 to 16, where the Finapres measured and estimated blood pressures are given. The peaks can be observed from the Finapres measured blood pressure values. Those peaks are related to the sensor calibration of the Finapres device, which occurs after certain period of time. Those Finapres blood pressure values were excluded from the analysis. The Bland-Altman plots of the results are given in FIGS. 17 to 20. The bias (BIAS) and standard deviation (SD) values for each subject and blood pressure are given in Table 1.

TABLE-US-00001 TABLE 1 Bias and SD values of the estimated blood pressures for each subject. Subject nr. 1 Subject nr. 2 Subject nr. 3 SBP BIAS, mmHg 0.013 0.026 0.874 SD, mmHg 6.3 6.2 6.7 DBP BIAS, mmHg 0.01 −0.024 −1.368 SD, mmHg 2.5 2.4 5.5 PP BIAS, mmHg 0.003 0.05 2.24 SD, mmHg 4.7 5.8 6.2 P BIAS, mmHg 0.011 0.001 −0.247 SD, mmHg 4.2 3.7 5.3

LIST OF DETAILS

[0079] 1, 2—two pairs of photoplethysmographic sensors [0080] 3—sensor device housing [0081] 4, 5—light source [0082] 6, 7—photodetector [0083] 8—digital-to-analogue converters (DAC) [0084] 9, 10—transimpedance amplifiers [0085] 11—analogue-to-digital converters (ADCs) [0086] 12, 13—force transducers [0087] 14—microcontroller [0088] 15—memory [0089] 16—external communication port [0090] 17—sensor housing [0091] 18, 19—optical sensors [0092] 20—electrical components of device [0093] 21—first spring [0094] 22—first optical sensor [0095] 23—first force transducer [0096] 24—second spring [0097] 25—second optical sensor [0098] 26—second force transducer [0099] 26—subject skin [0100] 27—subject artery