Patent Publication Number: US-8535234-B2

Title: Apparatus for measuring blood volume and method of evaluating result of measurement by apparatus for measuring blood volume

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to an apparatus for measuring a blood volume which is ejected with each heartbeat, and also to a method of evaluating a result of measurement by such apparatus. 
     In medical facilities, variation in the hemodynamics of a patient in an operating room, an intensive care unit, an emergency room, a dialysis treatment room, or the like needs to be monitored continuously as long as possible. Conventionally, monitoring of the variation in the hemodynamics of such a patient has been predominantly carried out by direct monitoring of a blood pressure. In a living body, a cardiac output and a vascular resistance are regulated such that the blood pressure of the centrum is limited within a predetermined range. In order to know the variation in the hemodynamics of the patient in an early stage, therefore, it is not enough to only monitor the blood pressure directly, and there is a need to know cause of change in the blood pressure when the change in blood pressure is observed. For this reason, there is a need to monitor a change of the cardiac output, in addition to monitoring the change in the blood pressure. 
     A method and apparatus for measuring a blood volume, and a biological signal monitoring apparatus are known in which variation in hemodynamics of the patient can be monitored always and continuously in an noninvasive manner, a skilled technique of a medical person such as insertion of a catheter is not required, less pain is experienced by the patient, there is no threat of infection because it is noninvasive, and the cost is low (see JP-A-2005-312947). 
     JP-A-2005-312947 discloses the principle of measuring the blood volume (cardiac output) which is ejected with each heartbeat in the following manner. 
     When a Windkessel model shown in  FIG. 4  is used, the influx flow volume to the aorta during a systole, that is, the flow volume (SV−Qs) acquired by deducting the efflux flow volume to the periphery during a systole Qs from one stroke volume SV is represented by the aortic compliance C and the pulse pressure PP (see Expression 1). In this description, the narrowly defined pulse pressure (the difference between the systolic blood pressure and the diastolic blood pressure) is indicated by PP, and the broadly defined pulse pressure (the systolic blood pressure (maximum value), the diastolic blood pressure (minimum value), or the difference between them, the mean blood pressure, and the like) is indicated by BP.
 
SV− Qs=C ·PP  (Exp. 1)
 
     The efflux flow volume to the periphery during a diastole Qd is equal to (SV−Qs). 
     Furthermore, Qs and Qd represent values acquired by dividing the systolic and diastolic arterial pressures V by the vascular resistance R and then multiplying by the systolic duration Ts and the diastolic duration Td, respectively. However, as it is estimated, for the matter of simplicity, that the flow volume values are proportional to Ts and Td, respectively, the values may be represented by Expression 2.
 
( Qd =)SV− Qs =SV· Td /( Ts+Td )  (Exp. 2)
 
     From Expressions 1 and 2, Expression 3 is acquired as follows.
 
SV· Td /( Ts+Td )= C ·PP
 
SV= C ·PP·(1+ Ts/Td )  (Exp. 3)
 
     Here, when it is assumed that C and Ts/Td remain constant during the measurement period, and C·(1+Ts/Td) is represented by K, the following is acquired.
 
SV= K ·PP  (Exp. 4)
 
PP=SV/ K   (Exp. 5)
 
     In this way, according to the Windkessel model, the pulse pressure is proportional to SV. 
     In practice, actually measured pulse pressure PP 1  is configured by the pulse pressure PP 2  (although this is represented by PP in Expression 5, hereinafter it will be represented by PP 2 ), and the augmentation PP 3  in the pulse pressure observed upon administration of a vasoconstrictor or the like, as in following Expression 6.
 
PP1=PP2+PP3  (Exp. 6)
 
     In a case where PP 3  is not observed, Expressions 4 and 6 lead to:
 
SV= K ·PP1  (Exp. 7)
 
     Therefore, SV can be directly measured from the measurement of blood pressure. However, since PP 1  already includes PP 3  in the administration of a vasoconstrictor or the like, SV would be overestimated. 
     This has been a problem when SV is calculated from the blood pressure. 
     With regard to the accuracy in measurement of an apparatus which enables calculation of the stroke volume as well as the cardiac output from the waveform of the arterial pressure measured invasively, the following is reported: “For a patient admitted to the ICU (intensive care unit) after a surgery, when the vascular resistance changed by about 60% upon administration of a vasoconstrictor phenylephrine, a remarkably large bias was observed between the measurements by the apparatus described above and the measurements by the cardiac output computer operating in the thermodilution mode used as the standard method, the values of the former being greater than those of the latter. In that case, there is accordingly a need for re-calibration by the blood volume flowmeter operating in the thermodilution mode.” Further, in the administration of a vasoconstrictor, it is known that, in the administration of a vasoconstrictor or the like, the pulse pressure increases by influence of a reflected wave from the periphery, and PP 3  corresponds to this augmentation. 
     In electrocardiography, the pulse wave propagation time (hereinafter, referred to as PWTT), which corresponds to a time taken until the reach of the propagated pulse wave to the SpO 2  at the periphery, is configured by following Expression 8.
 
PWTT=PEP+PWTT1+PWTT2  (Exp. 8)
 
     Here, as shown in  FIG. 9 , PEP is the pre-ejection period of the heart, which is the duration from the initiation of electric stimulation of the heart to the opening of the aortic valve. PWTT 1  is a time taken for the pulse wave to be propagated from its generation in the aorta after the opening of the aortic valve to an artery at the periphery where typically blood pressure measurement is conducted invasively. PWTT 2  is a time taken for the pulse wave to be further propagated from the artery at the periphery to a peripheral blood vessel where photoplethysmogram is measured. 
     The duration of (PEP+PWTT 1 ) from the R wave of electrocardiogram (ECG) to the onset of rising in the pulse wave at the femoral artery was measured using ten adult dogs, and measured the relationship between the duration of (PEP+PWTT 1 ) and the pulse pressure with administration of a vasoconstrictor in the respective cases under conditions such as, administration of a vasodilator, increase of the myocardial contractility, attenuation of myocardiac contractility, and blood removal. In this way, it was found good correlation between the pulse pressure PP 1  and the duration of (PEP+PWTT 1 ). 
       FIG. 5  is a view showing the representative relationship between the PWTT and the pulse pressure PP. 
     Therefore, the relationship between the pulse pressure PP 1  and (PEP+PWTT 1 ) can be represented by following Expression 9.
 
PEP+PWTT1= a ·PP1+ b   (Exp. 9)
 
     Further, the relationship between PWTT 2  and PP 1  is represented by following Expression 10.
 
PWTT2= c ·PP1+ d+e   (Exp. 10)
 
     Since it was discovered that, in a case where PP 3  appears with the use of a vasoconstrictor, PWTT 2  tends to be prolonged as compared to cases under other conditions, a portion corresponding to this prolongation is represented by “e” (where, e is not limited to a constant). 
     Substituting Expressions 9 and 10 for Expression 8, Equation 11 is acquired as follows.
 
PWTT=( a ·PP1+ b )+( c ·PP1+ d+e )
 
PP1=(PWTT− b−d−e )/( a+c )  (Exp. 11)
 
     As PP 2  in Expression 6 is replaced with the right-hand side of Expression 5, following Expression 12 is acquired.
 
PP1=SV/ K +PP3  (Exp. 12)
 
     From Expressions 11 and 12, the following Expression 13 is acquired.
 
PWTT/( a+c )−( b+d )/( a+c )=SV/ K +PP3+ e /( a+c )
 
SV= K ·(PWTT/( a+c )−( b+d )/( a+c ))− K ·(PP3+ e /( a+c ))  (Exp. 13)
 
     As described above, it has been experimentally found that PWTT 2  tends to be prolonged when PP 3  is observed upon use of a vasoconstrictor or the like.  FIG. 8  shows this relationship. 
     When phenylephrine is administered, PP 3  is observed and accordingly PP 1  is increased, as shown in  FIG. 8 . However, the relationship between PWTT 2  and PP 1  which may be observed in cases of blood removal or administration of pentobarbital is no longer observed with the administration of phenylephrine, and PWTT 2  shows a tendency to be prolonged. 
     Therefore, it has been experimentally discovered that, as shown in  FIG. 7 , there is maintained a negative correlation between SV and PWTT even upon administration of phenylephrine, which may be still observed under different conditions, and thus the second term (K·(PP 3 +e/(a+c))) in the right-hand side of Expression 13 may be substantially ignored. 
     Here, taking 1/(a+c)=α and −(b+d)/(a+c)=β, following Expression 14 is acquired.
 
SV= K ·(α·PWTT+β)  (Exp. 14)
 
     where α and β are empirically acquired coefficients that are inherent to the patient. 
     Moreover, the cardiac output can be calculated from following Expression 15.
 
 es CO= K ·(α·PWTT+β)·HR  (Exp. 15)
 
wherein esCO [L/min] is the cardiac output, and K is an empirically acquired constant which is inherent to the patient. HR is a heart rate of the patient.
 
     In addition, Expression 15 may be substituted in the same way as in Expression 16.
 
 es CO=(α K ·PWTT+β K )·HR  (Exp. 16)
 
     where αK and βK are empirically acquired coefficients which are inherent to the patient. 
     When SV and esCO are calculated using PWTT as expressed in Expressions 14, 15 and 16, as shown in  FIG. 7 , there is maintained correlation between SV and PWTT which may be observed under different conditions, even in a case of an augmentation in the pulse pressure associated with the use of a vasoconstrictor, as shown in  FIG. 6 , and thus problems that can be seen with the conventional practice of calculating SV by blood pressure may be solved. 
     Naturally, there is no risk of overestimation of CO. 
       FIGS. 6 and 7  show relationships between SV and PP 1  and between SV and PWTT as measured during vascular constriction, blood removal, and cardiac suppression in an animal test. 
     Incidentally, there occurred an increase in the vascular resistance by more than 60% upon administration of phenylephrine. 
     Next, an example of a biological signal monitoring apparatus to which the conventional method of measuring a blood volume is applied will be described in detail with reference to the drawings. 
       FIG. 10  is a block diagram illustrating the configuration of the example of the conventional biological signal monitoring apparatus, and  FIG. 11  is a diagram illustrating an example of the manner of a measurement in which the conventional biological signal monitoring apparatus.  FIG. 9  is a view showing waveforms of measured pulse waves. 
     A systolic/diastolic blood pressure measuring unit  20  includes a cuff  25 , a compressing pump  27 , a pressure sensor  28 , a cuff pressure detector  29 , an A/D converter  22 , and the like, as shown in  FIG. 10 . 
     Specifically, the cuff  25  is attached to an upper arm of a patient for measurement, as shown in  FIG. 11 . In the cuff  25 , the interior is opened or closed with respect to the atmosphere by an exhaust valve  26  installed in a body  10  of the biological signal monitoring apparatus. Air is supplied to the cuff  25  by the compressing pump  27  installed in the body  10  of the biological signal monitoring apparatus. The pressure sensor  28  (cuff pulse wave sensor) is mounted in the body  10  of the biological signal monitoring apparatus, and an output of the sensor is detected by the cuff pressure detector  29 . 
     An output of the cuff pressure detector  29  is converted into a digital signal by the A/D converter  22 , and input to a cardiac output calculating unit  40  (in  FIG. 11 , the cuff pressure detector  29 , the A/D converter  22 , and the cardiac output calculating unit  40  are included in the body  10  of the biological signal monitoring apparatus). 
     In  FIG. 9 , (a) shows an electrocardiogram waveform, and an aortic pressure wave immediately after the ejection from the heart has a waveform shown in (b) of  FIG. 9 . Further, waveforms of an arterial pressure wave at the periphery and a peripheral pulse wave are acquired as shown (c) and (d) of  FIG. 9 . 
     As shown in  FIG. 10 , a pulse wave propagation time measuring unit  30  includes a time interval detection reference point measuring unit  31 , an A/D converter  32 , a photoplethysmogram sensor  33 , a pulse wave detector  34 , an A/D converter  35 , etc. 
     The time interval detection reference point measuring unit  31  is used for detecting a point of time when an R wave is generated on an electrocardiogram, and an output thereof is converted into a digital signal by the A/D converter  32 , and then input to the cardiac output calculating unit  40 . Specifically, the time interval detection reference point measuring unit  31  is configured by ECG electrodes  31   a  (electrocardiogram measuring unit) which are attached to the chest of the subject, as illustrated in  FIG. 11 . Measurement data is transmitted from a measurement data transmitter  50  which is electrically connected to the ECG electrodes  31   a , to the body  10  of the biological signal monitoring apparatus in a wireless manner. The transmitted measurement data is converted into a digital signal by the A/D converter  32  in the body  10  of the biological signal monitoring apparatus, and then input to the cardiac output calculating unit  40 . In this way, the ECG waveform as shown in (a) of  FIG. 9  is acquired. 
     Meanwhile, the photoplethysmogram sensor  33  is intended to be attached to a peripheral part, such as a finger, of the patient, as shown in  FIG. 11 , and to be used in acquiring the pulse wave propagation time, for example, by performing SpO2 measurement. The photoplethysmogram sensor  33  is electrically connected to the measurement data transmitter  50 , and the measurement data transmitter  50  transmits the measurement data to the main body  10  of the biological signal monitoring apparatus in a wireless manner. When the measurement data is sent to the pulse wave detector  34  in the main body  10  of the biological signal monitoring apparatus, the pulse wave (photoplethysmogram) at the attachment location of the patient is detected. The output of the pulse wave detector  34  is converted into a digital signal by the A/D converter  35  and then input to the cardiac output calculating unit  40 . As such, a waveform of the photoplethysmogram (a waveform at the periphery) such as shown in (d) of  FIG. 9  is acquired. 
     Next, a calculation process of acquiring esCO from the Expressions 15 and 16 will be described with reference to  FIGS. 12 to 15 . 
     First, the procedure in which βK is acquired by calibration using a default value of αK and then esCO is calculated will be described with reference to  FIG. 12 . 
     Reading of the default value of αK is carried out (Step S 1 ). PWTT and HR are acquired (Step S 2 ). Next, it is determined whether βK is available or not (Step S 3 ). If the determination in Step S 3  is NO, then a request for input of cardiac output (CO) value for calibration is displayed (Step S 4 ). It is determined whether the CO value for calibration has been input or not (Step S 5 ). If the determination in Step S 5  is YES, the input CO value, and the acquired PWTT and HR are stored in a register as CO 1 , PWTT 1 , and HR 1 , respectively (Step S 6 ). βK is acquired from following Expression 17 (Step S 7 ).
 
β K =CO1/HR1−α K· PWTT1.  (Exp. 17)
 
     Calculation of acquiring esCO from the Expression 16 is carried out by using the acquired βK (Step S 8 ). If the determination in Step S 3  is YES, likewise, calculation of acquiring esCO from the Expression 16 is carried out (Step S 8 ). The esCO acquired in the calculation is displayed (Step S 9 ). 
     The above procedure is repeated as required. 
     Next, the procedure in which αK and βK are acquired by calibration and then esCO is calculated will be described with reference to  FIG. 13 . Reading of the default value of αK is carried out (Step S 1 ). PWTT and HR are acquired (Step S 2 ). Next, it is determined whether βK is available or not (Step S 3 ). 
     If the determination in Step S 3  is NO, then a request for input of CO value for calibration is displayed (Step S 4 ). It is determined whether the CO value for calibration has been input or not (Step S 5 ). If the determination in Step S 5  is YES, the input CO value, and the acquired PWTT and HR are stored in a register as C 01 , PWTT 1 , and HR 1 , respectively (Step S 6 ). βK is acquired from the Expression 17 (Step S 7 ). Calculation of acquiring esCO from the Expression 16 is carried out by using the acquired βK (Step S 8 ). If the determination in Step S 3  is YES, it is determined whether re-calibration for αK should be carried out or not (Step S 10 ). If the determination in Step S 10  is NO, likewise, calculation of acquiring esCO from the Expression 16 is carried out (Step S 8 ). If the determination in Step S 10  is YES, a request for input of the CO value for calibration is displayed (Step S 11 ). It is determined whether the CO value for calibration has been input or not (Step S 12 ). If the determination in Step S 12  is YES, the input CO value, and the acquired PWTT and HR are stored in the register as CO 2 , PWTT 2 , and HR 2 , respectively (Step S 13 ). αK and βK are calculated from following Expressions 18 and 19 (Step S 14 ).
 
CO1=(α K ·PWTT1+β K )·HR1  (Exp. 18)
 
CO2=(α K ·PWTT2+β K )·HR2  (Exp. 19)
 
     Calculation of acquiring esCO from the Expression 16 is carried out by using the acquired αK and βK (Step S 8 ). If the determination in Step S 10  is NO, calculation of acquiring esCO from the Expression 16 is carried out (Step S 8 ). The esCO acquired in the calculation is displayed (Step S 9 ). 
     The above procedure is repeated as required. 
     Then, the procedure in which a is the default value, β and K are acquired by calibration, and then esCO is calculated will be described with reference to  FIG. 14 . The calibration of β is carried out when the pulse pressure is not augmented by administration of a vasoconstrictor or the like. 
     Reading of the default value of a is carried out (Step S 1 ). PWTT and HR are acquired (Step S 2 ). Next, it is determined whether β is available or not (Step S 15 ). If the determination in Step S 15  is NO, then a request for measurement of blood pressure for calibration is displayed (Step S 16 ). It is determined whether measurement of the blood pressure for calibration has been conducted or not (Step S 17 ). If the determination in Step S 17  is YES, the measured PP value, and the acquired PWTT and HR are stored in the register as PP 1 , PWTT 1 , and HR 1 , respectively (Step S 18 ). β is calculated from following Expression 20 (Step s 19 ).
 
β=PP1−α·PWTT1  (Exp. 20)
 
     If the determination in Step S 15  is YES, or after β is calculated in Step S 19 , it is determined whether K is available or not (Step S 20 ). If the determination in Step S 20  is NO, a request for input of CO value for calibration is displayed (Step S 21 ). It is determined whether the CO value for calibration has been input or not (Step S 22 ). If the determination in Step S 22  is YES, the input CO value is stored in the register as CO 1  (Step S 23 ). K is calculated from following Expression 21 (Step S 24 ).
 
 K =CO1/{(α·PWTT1+β)·HR1}  (Exp. 21)
 
     If the determination in Step S 20  is YES, or after K is calculated in Step S 24 , esCO is calculated from the Expression (Step S 25 ). The esCO acquired in the calculation is displayed (Step S 26 ). 
     The above procedure is repeated as required. 
     Then, the procedure in which α, β, and K are acquired by calibration, and then esCO is calculated will be described with reference to  FIG. 15 . The calibration of α and β is carried out when the pulse pressure is not augmented by administration of a vasoconstrictor or the like. 
     Reading of the default value of α is carried out (Step S 1 ). PWTT and HR are acquired (Step S 2 ). Next, it is determined whether β is available or not (Step S 15 ). If the determination in Step S 15  is NO, then a request for measurement of blood pressure for calibration is displayed (Step S 16 ). It is determined whether measurement of the blood pressure for calibration has been conducted or not (Step S 17 ). If the determination in Step S 17  is YES, the measured PP value, and the acquired PWTT and HR are stored in the register as PP 1 , PWTT 1 , and HR 1 , respectively (Step S 18 ). β is calculated from the Expression 20 (Step S 19 ). If the determination in Step S 15  is YES, it is determined whether re-calibration for a should be carried out or not (Step S 27 ). If the determination in Step S 27  is YES, then a request for measurement of blood pressure for calibration is displayed (Step S 28 ). It is determined whether measurement of the blood pressure for calibration has been conducted or not (Step S 29 ). If the determination in Step S 29  is YES, the measured PP value, and the acquired PWTT and HR are stored in the register as PP 2 , PWTT 2 , and HR 2 , respectively (Step S 30 ). α and β are calculated from following Expressions 22 and 23.
 
PP1=α·PWTT1+β  (Exp. 22)
 
PP2=α·PWTT2+β  (Exp. 23)
 
     If the determination in Step S 27  is NO and the processes of Steps S 19  and S 31 , it is determined whether K is available or not (Step S 20 ). If the determination in Step S 20  is NO, a request for input of CO value for calibration is displayed (Step S 21 ). It is determined whether the CO value for calibration has been input or not (Step S 22 ). If the determination in Step S 22  is YES, the input CO value is stored in the register as CO 1  (Step S 23 ). K is calculated from the Expression 21 (Step S 24 ). If the determination in Step S 20  is YES, or after K is calculated in Step S 24 , esCO is calculated from the Expression 15 (Step S 25 ). The esCO acquired in the calculation is displayed (Step S 26 ). 
     The above procedure is repeated as required. 
     Alternatively, the measurement of blood pressure for calibration may not be performed, and a blood pressure value which is measured by another sphygmomanometer may be key-input. Furthermore, the peripheral pulse wave may include also that indicative of a volumetric change in addition to the SpO2 pulse wave. 
     According to JP-A-2005-312947, a method and apparatus for measuring a blood volume, and a biological signal monitoring apparatus can be realized in which variation in hemodynamics of the patient can be monitored always and continuously in an noninvasive manner, a skilled technique of a medical person such as insertion of a catheter is not required, less pain is experienced by the patient, there is no threat of infection because it is noninvasive, and the cost is low. 
     Also in the above-described method and apparatus for measuring a blood volume, and biological signal monitoring apparatus which are disclosed in JP-A-2005-312947, although improvements are made as compared with the conventional art, calibration in which the CO value for calibration is input substantially at least one time is necessary. In view of the requirement of a skilled technique of a medical person, and the high degree of invasion of the patient, therefore, the monitoring cannot be performed in an easy and continuous manner. Therefore, there is a problem in that the method is difficult to monitor always and continuously variation in hemodynamics of the patient. 
     In order to solve the problem, there is a related-art method and apparatus for measuring a blood volume, and biological signal monitoring apparatus in which calibration requiring input of CO for calibration is not necessary. 
     As an example of the related art, an improved example of the procedure shown in  FIG. 14  of the conventional art, and in which α is the default value, β and K are acquired by calibration, and then esCO is calculated will be described together with FIG.  2 . 
     Then, the procedure in which a is the default value, β and K are acquired by calibration, and then esCO is calculated will be described with reference to  FIG. 2 . The calibration of β is carried out when the pulse pressure is not augmented by administration of a vasoconstrictor or the like. 
     Reading of specific information (sex, age, body height, and body weight) of a patient is carried out (Step S 71 ). Reading of the default value of α is carried out (Step S 72 ). PWTT and HR are acquired (Step S 73 ). Next, it is determined whether β is available or not (Step S 74 ). If the determination in Step S 74  is NO, then a request for measurement of blood pressure for calibration is displayed (Step S 75 ). It is determined whether measurement of the blood pressure for calibration has been conducted or not (Step S 76 ). If the determination in Step S 76  is YES, the measured value of the blood pressure PP, and acquired PWTT and HR are stored in the register as PP 1 , PWTT 1 , and HR 1 , respectively (Step S 77 ). β is calculated from the Expression 20 (Step S 78 ). If the determination in Step S 74  is YES, or after β is calculated in Step S 78 , it is determined whether K is available or not (Step S 79 ). If the determination in Step S 79  is NO, CO 1  is calculated by using following Expression 24 (Step S 80 ).
 
CO1= a+b ·Sex+ c ·Age+ d ·BSA+ e·PWTT 1+ f ·HR1·PP1  (Exp. 24)
 
     where BSA (Body Surface Area)=0.007184·(Body Height) 0.725 ·(Body Weight) 0.425 , and Sex:Male=1, Female=−1. 
     K is calculated from the Expression 21 (Step S 81 ). If the determination in Step S 79  is YES, or after the process of Step S 81  is performed, esCO is calculated from the Expression 15 (Step S 82 ). The esCO acquired in the calculation is displayed (Step S 83 ). 
     The above procedure is repeated as required. 
     In an apparatus for measuring a blood volume which estimates a blood volume by using a parameter relating to the cardiac output of a subject to be measured, such as the above-described related-art apparatus for measuring a blood volume in which calibration requiring input of CO for calibration is not necessary, and the above-described conventional apparatus for measuring a blood volume disclosed in JP-A-2005-312947 in which calibration requiring input of CO for calibration is necessary, due to an artifact of a biological signal or change of a correlation between a monitoring parameter and a biological signal, accuracy of calculation of an estimated value of the monitoring parameter is lowered, and reliability of a result of measurement of the blood volume is lowered. 
     SUMMARY 
     It is therefore an object of the invention to provide an apparatus for measuring a blood volume and a method which can evaluate the reliability of the result of the measurement of the blood volume. 
     In order to achieve the object, according to the invention, there is provided an apparatus for measuring a blood volume, the apparatus comprising: 
     a first calculator which calculates a first blood volume by using information on a cardiac output of a subject; and 
     a second calculator which calculates a second blood volume by using information on oxygen metabolism of the subject. 
     The second calculator may receive the specific information and calculate the oxygen metabolism, and calculate the second blood volume based on the calculated oxygen metabolism. The first calculator may calculate the first blood volume based on a pulse wave propagation time and a heart rate of the subject, from an expression of CO=(αK·PWTT+βK)·HR where CO is the first blood volume, PWTT is the pulse wave propagation time, HR is the heart rate, and αK and βK are coefficients inherent to the subject. 
     The specific information may include at least a sex, age, body surface area, blood pressure of the subject, and the heart rate. 
     The specific information may further include one of the pulse wave propagation time and a pulse wave velocity. 
     The apparatus may further comprise: an evaluator which compares the first blood volume and the second blood volume and evaluates and displays a blood volume calculation function based on comparison result. 
     The blood volume calculating function may be evaluated based on a difference of change rates of the first and second blood volumes which are calculated from a reference time to a calculation time when the first and second calculators calculates the first and second blood volumes. 
     In order to achieve the object, according to the invention, there is also provided an apparatus for measuring a blood volume, the apparatus comprising: 
     a first calculator which calculates a first blood volume by using information on a cardiac output of a subject; and 
     a third calculator which calculates a third blood volume from a change amount of a demand of a blood volume from a reference time to a time, the change amount being estimated by using information on a cardiac output and oxygen metabolism of the subject at the reference time. 
     The third calculator may calculate the third blood volume by using a blood pressure and a heart rate of the subject. 
     The third calculator may further calculate the third blood volume by using a pulse wave propagation time of the subject. 
     The third calculator may calculate the third blood volume based on an expression of CO=CO 1 +e 1 ·(HR·PP−HR 0 ·PP 0 ) where CO is the third blood volume, CO 1  is the cardiac output at the reference time, HR is the heart rate, HR 0  is HR at the reference time, PP is the blood pressure, PP 0  is PP at the reference time, and e 1  is a constant. 
     The third calculator may calculate the third blood volume based on an expression of CO=CO 1 +e 1 ·(HR·PP−HR 0 ·PP 0 )+f 1 ·(PWTT−PWTT 0 ) where CO is the third blood volume, CO 1  is the cardiac output at the reference time, HR is the heart rate, HR 0  is HR at the reference time, PP is the blood pressure, PP 0  is PP at the reference time, PWTT is the pulse wave propagation time, PWTT 0  is PWTT at the reference time, and e 1  and f 1  are constants. 
     The apparatus may further comprise: an evaluator which compares the first blood volume and the third blood volume and evaluates and displays a blood volume calculation function based on comparison result. 
     The blood volume calculation function may be evaluated based on a difference of change rates of the first and third blood volumes which are calculated from the reference time to an estimation time when the first and third calculators calculates the first and third blood volumes. 
     In order to achieve the object, according to the invention, there is also provided a method of evaluating a result of measurement of a blood volume by an apparatus for measuring the blood volume, the method comprising: 
     inputting at least a sex, an age, a body surface area, a blood pressure, and a heart rate as specific information of a subject; 
     calculating oxygen metabolism relating to a cardiac output of the subject and calculating a second blood volume based on the calculated oxygen metabolism; 
     calculating a first blood volume based on a pulse wave propagation time and the heart rate, from an expression of CO=(αK·PWTT+βK)·HR where CO is the first blood volume, PWTT is the pulse wave propagation time, HR is the heart rate, and αK and βK are coefficients inherent to the subject; and 
     performing evaluation based on a difference of change rates of the first and second blood volumes which are calculated from a reference time to an estimation time when the first and second blood volumes are calculated. 
     The second blood volume may be calculated by an expression of CO 2 =a 1 +b 1 ·Sex+c 1 ·Age+d 1 ·BSA+e 1 ·HR·PP where CO 2  is the second blood volume; Sex is the sex, when the subject is male, Sex=1, and when the subject is female, Sex=−1; Age is the age; BSA is the body surface area; HR is the heart rate; PP is the blood pressure; and a 1 , b 1 , c 1 , d 1 , and e 1  are constants. 
     The second blood volume may be calculated by an expression of CO 2 =a 2 +b 2 ·Sex+c 2 ·Age+d 2 ·BSA+e 2 ·HR·PP+f 2 ·PWTT where CO 2  is the second blood volume; Sex is the sex, when the subject is male, Sex=1, and when the subject is female, Sex=−1; Age is the age; BSA is the body surface area; HR is the heart rate; PP is the blood pressure; PWTT is a pulse wave propagation time of the subject; and a 2 , b 2 , c 2 , d 2 , e 2 , and f 2  are constants. 
     According to the invention, there is also provided a computer-readable recording medium in which a computer program causing the apparatus to execute the method according to claim  14  is recorded. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating the configuration of a biological signal monitoring apparatus of the present invention. 
         FIG. 2  is a flowchart showing a procedure in a related-art example in which a default value of α is used, β and K are calibrated, and esCO is calculated. 
         FIG. 3  is a flowchart showing a procedure in the invention in which a default value of α is used, β and K are calibrated, and esCO is calculated. 
         FIG. 4  is a diagram showing a Windkessel model. 
         FIG. 5  is a view showing a representative relationship between PWTT and a pulse pressure PP. 
         FIG. 6  is a view showing relationships between SV and PP 1  measured in cases of vasoconstriction, blood removal, and cardiac suppression in an animal test. 
         FIG. 7  is a view showing relationships between SV and PWTT measured in cases of vasoconstriction, blood removal, and cardiac suppression in an animal test. 
         FIG. 8  is a view showing relationships between PP 1  and PWTT 2  measured in cases of vasoconstriction, blood removal, and cardiac suppression in an animal test. 
         FIG. 9  is a view showing relationships among PEP, PWTT 1 , PWTT 2 , and PWTT. 
         FIG. 10  is a block diagram illustrating the configuration of a conventional biological signal monitoring apparatus. 
         FIG. 11  is a view showing an example of a state in which an electrocardiogram measuring unit and a peripheral-pulse wave detecting unit are attached to the patient. 
         FIG. 12  is a flowchart showing a procedure in a conventional art in which a default value of αK is used, βK is calibrated, and esCO is calculated. 
         FIG. 13  is a flowchart showing a procedure in a conventional art in which αK and βK are calibrated, and esCO is calculated. 
         FIG. 14  is a flowchart showing a procedure in a conventional art in which a default value of α is used, β and K are calibrated, and esCO is calculated. 
         FIG. 15  is a flowchart showing a procedure in a conventional art in which K, α, and β are calibrated, and esCO is calculated. 
         FIG. 16  is a flowchart showing a procedure in a second embodiment of the invention in which esCO is calculated. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     First, individual specific information which relates to a cardiac output used in the present invention, and which relates to oxygen metabolism of a patient will be described. In the cardiac output, a stroke volume of blood containing oxygen from the heart is controlled in accordance with oxygen metabolism of a living body. Although information relating to the oxygen metabolism of the living body does not directly reflect the cardiac output, therefore, the information relates the cardiac output. 
     In the invention, as the individual specific information which relates to the oxygen metabolism of the patient, the body surface area, the age, the sex, the blood pressure, and the heart rate are used. Also one of the pulse wave propagation time and a pulse wave velocity may be used. 
     It is seemed that the cardiac output is governed mainly by the oxygen consumption or rate of metabolism of the human body, and the rate of metabolism is best corrected by the body surface area. The rate of metabolism of the human body depends on the age, is maximum in childhood, and further decreases as the age is more increased. The cardiac output and the cardiac index are inversely correlated with the age. The cardiac index is a value which is acquired by dividing the cardiac output by the body surface area. A female is lower in basal rate of metabolism than a male. Usually, the myocardial oxygen consumption uses a product (i.e., a double product) of the heart rate and the systolic blood pressure, as an index. As the movement intensity is more increased, the mean blood pressure is gradually increased. Particularly, the systolic blood pressure is remarkably raised, and the diastolic blood pressure is raised by only a low degree. Therefore, the myocardial oxygen consumption can be the that it is equal to a product of the heart rate and the difference between the systolic blood pressure and the diastolic blood pressure, or the pulse pressure and the heart rate. The pulse wave velocity is the reciprocal of the pulse wave propagation time. The pulse wave velocity is indicated in the following manner. 
     Pulse wave velocity=3.57/(Square root of Percentage of increase of capacity with respect to increase of blood pressure) 
     When a blood vessel has a high extensibility, the percentage of increase of the capacity with respect to increase of the blood pressure is large, and the pulse wave velocity is reduced. In the case where the same blood pressure change occurs, namely, the degree of change of the cardiac output is reflected in the pulse wave velocity. In other words, a change of the cardiac output is reflected in the pulse wave propagation time. Furthermore, it is known that the pulse wave velocity changes with aging. 
     The process procedure of the method in which a result of measurement by the apparatus for measuring a blood volume of the invention is evaluated, and which includes a procedure in the invention in which a default value of α is used, β and K are acquired by calibration, and then esCO is calculated will be described with reference to the flowchart of  FIG. 3 . 
     In advance of description of flowcharts, the technical meanings of K, α, and β will be described. 
     From the Expression 4, the following expression is acquired.
 
 K =SV/PP
 
     Therefore, K is the reciprocal of the ratio of SV (one stroke volume of the heart) to PP (pulse pressure). In a person in which the blood vessel is more rigid, K is smaller. When K is acquired, it is possible to correct individual differences of the relationship between one stroke volume of the heart and the pulse pressure. 
     From the expression, PP=α·PWTT+β, the following expression is acquired.
 
α=ΔPP/ΔPWTT
 
     Therefore, α is the ratio of the variation of PP to that of PWTT. In a person in which the blood vessel is more rigid, α is larger. When a is acquired, it is possible to correct individual differences of the relationship between the variations of PWTT and PP due to the rigidity of a blood vessel. Although the degree of α is different depending on the kind of the animal, there arises no serious problem even when it is deemed to be constant in the same kind. 
     From the expression, PP=α·PWTT+β, the following expression is acquired.
 
β=PP−α·PWTT
 
     The length and rigidity of a blood vessel are reflected in β. When β is acquired, it is possible to correct individual differences of the length and rigidity of a blood vessel. 
     From the Expression 14, the following expression is acquired.
 
 K α=ΔSV/ΔPWTT
 
     Therefore, Kα is the reciprocal of the ratio of the variation of PWTT to that of SV. In a person in which the blood vessel is more rigid, K is smaller, and in contrast α is larger. Therefore, Kα is a coefficient in which individual differences due to the rigidity of a blood vessel are absorbed. When Kα is acquired, it is possible to correct individual differences of the relationship between the variations of SV and PWTT. 
     From the Expression 14, the following expression is acquired.
 
 K β=SV− K ·α·PWTT
 
     The length and rigidity of a blood vessel are reflected in Kβ. When Kβ is acquired, it is possible to correct individual differences of the length and rigidity of a blood vessel. 
     The process procedure of the method in which a result of measurement by the apparatus for measuring a blood volume of the invention is evaluated, and which includes a procedure in the invention in which a default value of α is used, β and K are acquired by calibration, and then esCO is calculated will be described with reference to the flowchart of  FIG. 3 . The calibration of β is carried out when the pulse pressure is not augmented by administration of a vasoconstrictor or the like. 
     Reading of specific information (sex, age, body height, and body weight) of a patient is carried out (Step S 71 ). Reading of the default values of α and γ1 is carried out (Step S 72 ′). γ1 is a number which is to be used as a threshold used in the evaluation of a result of measurement. PWTT and HR are acquired (Step S 73 ). Next, it is determined whether β is available or not (Step S 74 ). If the determination in Step S 74  is NO, then a request for measurement of blood pressure for calibration is displayed (Step S 75 ). It is determined whether measurement of the blood pressure for calibration has been conducted or not (Step S 76 ). If the determination in Step S 76  is YES, the measured value of the blood pressure PP, and acquired PWTT and HR are stored in the register as PP 1 , PWTT 1 , and HR 1 , respectively (Step S 77 ). β is calculated from the Expression 20 (Step S 78 ). If the determination in Step S 74  is YES, or after β is calculated in Step S 78 , it is determined whether K is available or not (Step S 79 ). If the determination in Step S 79  is YES, esCO is calculated from the Expression 15 (Step S 82 ). The esCO acquired in the calculation is displayed (Step S 83 ). If the determination in Step S 79  is NO, then a request for input of CO value for calibration is displayed (Step S 90 ). It is determined whether the CO value for calibration has been input or not (Step S 91 ). If the determination in Step S 91  is YES, the input CO value is stored in a register as CO 1  (Step S 92 ). K is calculated from the Expression 21 (Step S 93 ). CO 2  is calculated by using following Expression 25 (Step S 94 ).
 
CO2= a+b ·Sex+ c ·Age+ d ·BSA+ e ·PWTT1+ f ·HR1·PP1  (Exp. 25)
 
     where BSA (Body Surface Area)=0.007184·(Body Height) 0.725 ·(Body Weight) 0.425 , and Sex:Male=1, Female=−1. 
     After esCO which is acquired in the calculation of Step S 82  is displayed, CO 3  is calculated by using following Expression 26 (Step S 95 ).
 
CO3= a+b ·Sex+ c ·Age+ d ·BSA+ e ·PWTT+ f ·HR·PP  (Exp. 26)
 
     where BSA (Body Surface Area)=0.007184·(Body Height) 0.725 ·(Body Weight) 0.425 , and Sex:Male=1, Female=−1. 
     The evaluation value γ which is the degree of coincidence between CO 2  and CO 3  that are calculated in Steps S 94  and S 95  is calculated by using following Expression 27 (Step S 96 ).
 
γ=( es CO−CO1)/CO1−(CO3−CO2)/CO2  (Exp. 27)
 
     It is determined whether the absolute value of the calculated evaluation value y is larger than the threshold y 1  which is previously input or not (Step S 97 ). If the determination in Step S 97  is YES, “Low reliability” is displayed (Step S 98 ). 
     The above procedure is repeated as required. 
     In the above description of  FIG. 3 , it is assumed that the example to which the apparatus for measuring a blood volume of the invention and the evaluation method for the evaluation are applied corresponds to  FIG. 14  of the conventional art. It is a matter of course that the example may correspond to  FIG. 12 ,  FIG. 13 , or  FIG. 15 . 
     In the invention, as a second embodiment, information relating to a change amount of a demand of the blood volume from a reference time, and estimated by using information of the cardiac output and oxygen metabolism of the patient at the reference time may be used in place of information relating to oxygen metabolism of the living body. 
     As the information relating to the estimated change amount, the pulse wave propagation time, the blood pressure and the heart rate are used. Also the pulse wave propagation time may be excluded. 
     More specifically, it is preferable to calculate the information relating to the estimated change amount from one of the following expressions.
 
CO2= a 1+ b 1·Sex+ c 1·Age+ d 1·BSA+ e 1·HR1·PP1
 
     where CO 2  is a cardiac output, Sex is the sexuality (Male=1, Female=−1), Age is the age, BSA is the body surface area, HR 1  is the heart rate, PP 1  is the pulse pressure, and a 1 , b 1 , c 1 , d 1 , and e 1  are constants, and
 
CO2= a 2+ b 2·Sex+ c 2·Age+ d 2·BSA+ e 2·HR1·PP1+ f 2·PWTT1
 
     where CO 2  is a cardiac output, Sex is the sexuality (Male=1, Female=−1), Age is the age, BSA is the body surface area, HR 1  is the heart rate, PP 1  is the pulse pressure, PWTT 1  is the pulse wave propagation time, and a 2 , b 2 , c 2 , d 2 , e 2 , and f 2  are constants. 
     The process procedure of the method evaluating a result of measurement by the apparatus for measuring a blood volume of the second embodiment of the invention will be described with reference to  FIG. 16 . The constants and the like which are used hereinafter are identical with those described above unless otherwise specified. 
     Reading of specific information (sex, age, body height, and body weight) of a patient is carried out (Step S 71 ). Reading of the default values of α and γ1 is carried out (Step S 72 ′). γ1 is a number which is to be used as a threshold used in the evaluation of a result of measurement. PWTT and HR are acquired (Step S 73 ). Next, it is determined whether β is available or not (Step S 74 ). If the determination in Step S 74  is NO, then a request for measurement of blood pressure for calibration is displayed (Step S 75 ). It is determined whether measurement of the blood pressure for calibration has been conducted or not (Step S 76 ). If the determination in Step S 76  is YES, the measured value of the blood pressure PP, and acquired PWTT and HR are stored in the register as PP 1 , PWTT 1 , and HR 1 , respectively (Step S 77 ). β is calculated from the Expression 20 (Step S 78 ). If the determination in Step S 74  is YES, or after β is calculated in Step S 78 , it is determined whether K is available or not (Step S 79 ). If the determination in Step S 79  is YES, esCO is calculated from the Expression 15 (Step S 82 ). The esCO acquired in the calculation is displayed (Step S 83 ). If the determination in Step S 79  is NO, then a request for input of CO value for calibration is displayed (Step S 90 ). It is determined whether the CO value for calibration has been input or not (Step S 91 ). If the determination in Step S 91  is YES, the input CO value is stored in the register as CO 1  (Step S 92 ). K is calculated from the Expression 21 (Step S 93 ). CO 1  which is stored in the register in Step S 92  is substituted into CO 2  (step S 94 ′). After esCO which is acquired in the calculation of Step S 82  is displayed, CO 3  is calculated by using one of following Expressions 28 and 29 (Step S 95 ′).
 
CO3= CO 1+ e 1·(HR·PP−HR0·PP0)  (Exp. 28)
 
     where CO 1  is a cardiac output at a reference time, HR 0  is a heart rate at the reference time, PP 0  is a blood pressure at the reference time, and e 1  is the constant, and
 
CO3=CO1+ e 1·(HR·PP−HR0·PP0)+ f 1·( PWTT−PWTT 0)  (Exp. 29)
 
     where CO 1  is a cardiac output at a reference time, HR 0  is a heart rate at the reference time, PP 0  is a blood pressure at the reference time, PWTT 0  is PWTT at the reference time, and e 1  and f 1  are the constants. 
     It is preferable that the reference time is a time when CO 1  is measured. 
     The evaluation value y which is the degree of coincidence between CO 2  and CO 3  that are calculated in steps S 94 ′ and S 95 ′ is calculated by using the Expression 27 (Step S 96 ). It is determined whether the absolute value of the calculated evaluation value y is larger than the threshold γ1 which is previously input or not (Step S 97 ). If the determination in Step S 97  is YES, “Low reliability” is displayed (Step S 98 ). 
     The above procedure is repeated as required. 
     Also in the above description of  FIG. 16 , it is assumed that the example to which the apparatus for measuring a blood volume of the invention and the evaluation method for the evaluation are applied corresponds to  FIG. 14  of the conventional art. It is a matter of course that the example may correspond to  FIG. 12 ,  FIG. 13 , or  FIG. 15 . 
     According to an aspect of the invention, it is possible to evaluate that the accuracy of the calculation of the estimated value of the monitoring parameter is lowered and that the reliability of the result of the measurement of the blood volume is lowered. 
     In the case where the reliability of the result of the measurement of the blood volume is lowered, therefore, the measurement system may be readjusted, calibration may be again performed, or the measurement method may be changed to another one.