described herein is a method for monitoring cardiac output ({ dot over ( q )} t ) or cardiac index ( i . e ., { dot over ( q )} t divided by body surface area , bsa ) or other variable derived from measured cardiac output . in the described method , which is referred to herein as “ the hybrid method ”, cardiac output is measured simultaneously , or nearly simultaneously , by two or more ( n ) different methods of measurement . the resulting measurements are then combined according to the following formula : q . th = ∑ i = 1 i = n ⁢ α i · q . ti ∑ i = 1 i = n ⁢ α i equation ⁢ ⁢ 2 where { dot over ( q )} t h is the cardiac output calculated by the hybrid method , and { dot over ( q )} ti is a previous ( usually the most recent ) cardiac output measurement made by one of the n methods i , and α i is the corresponding weighting coefficient for the measurement made by method i . in an idealised model where the precision of each method of cardiac output measurement is equal , the measured cardiac output values are statistically distributed according to a gaussian ( normal ) distribution , and the variations between the measurements made by the various methods are entirely random and uncorrelated , then the reduction in standard deviation of measurement of cardiac output ∂ sd expected with the addition of each further method to that of method a , as in equation 2 , is given by : where n is the number of measurement methods employed , assuming all methods are equally weighted . fig1 ( heavy line ) shows this plotted graphically . in its simplest embodiment , the hybrid cardiac output value is the average of the cardiac output values measured by only two methods a and b , so that : relative to the accuracy and precision of measurement of cardiac output by any single method a , the improvement in accuracy and precision obtained from the hybrid method is greatest from the addition of measurement by a second method b . each further additional method can be expected to produce further improvement in accuracy and precision of measurement by the hybrid method , but at the expense of increased complexity and cost associated with the practical conduct of each measurement method . for each additional method involved , this typically involves one or more of : ( i ) additional deployment of measurement devices to the patient care environment , ( ii ) application of the device to the patient via an interface that may involve ( iii ) minimally — or non - invasive devices such as surface electrodes , probes or transducers , or ( iv ) invasive cannulation , and ( v ) collection , calculation , display , assimilation and scrutiny of the resulting data . fig1 ( broken line ) shows the relative reduction in the standard deviation of cardiac output measurement ( as given by equation 3 ) expected with the addition of each further cardiac output measurement method to the calculation of { dot over ( q )} t h by equation 2 using any given number of additional methods ( up to 9 ), where the precision of each method is the same , and all the measurements are equally weighted . it can be seen that the greatest reduction is obtained from the addition of a second method , with progressively reducing additional benefit with each further cardiac output measurement method incorporated into the hybrid cardiac output method . in view of the above , the embodiments described hereinbelow use only two cardiac output measurement methods , as described by equation 4 , which likely represents the most economical and practical embodiments of the hybrid method . however , it will be apparent to those skilled in the art that more generally any number of measurement methods can be used and combined as described herein to provide further reductions in standard deviation . the reduction in standard deviation of measurement of cardiac output expected with the addition of a second measurement method b to that of measurement method a , in accordance with equation 4 , depends on the relative precision of each component method . from equation 3 and fig1 , this reduction is expected to be approximately 30 % where the precision of the second method ‘ method b ’ is the same as that of ‘ method a ’. where the precision of method b is poorer than that of method a , the reduction in standard deviation of measurement of cardiac output { dot over ( q )} t h using equation 4 is expected to be less than the reduction predicted by equation 3 . moreover , use of a method b with very poor precision may potentially worsen the precision of { dot over ( q )} t h obtained using equation 4 , relative to that given by method a alone . for example , fig2 shows the effect of worsening the precision of method b relative to that of method a on the precision of the hybrid cardiac output { dot over ( q )} t h obtained using equation 4 . fig2 shows that the precision of { dot over ( q )} t h remains better than that of method a until the precision of method b is 1 . 75 times worse than that of method a . this represents a very poor level of precision for method b and approximates the worst degrees of imprecision recorded among studies comparing the accuracy and precision of measurement of cardiac output with thermodilution as the reference standard ( see peyton and chong ). this suggests that the hybrid method described herein will provide precision superior to that of a single method using any combinations of the generic methods available in current practice , unless an extremely unreliable method is used as the second method b . any improvement in the precision of measurement will also produce improvement in the mean bias ( accuracy ) relative to the true cardiac output . where two component methods suffer from significant systematic bias but in opposite directions , the hybrid method can be expected to produce a substantial reduction in bias . one technique for obtaining a more precise and accurate measurement of a physiological parameters such as cardiac output is to make repeated measurements closely associated in time , and average the measured values , and it has been suggested that this should be routine practice for some technologies in the field ( see peyton p , bailey m , and thompson b ., reproducibility of cardiac output measurement by the nitrous oxide rebreathing technique , j . clin . monit . comput . 2009 ; 23 : 233 - 6 . 10 . 1007 / s10877 - 009 - 9187 - 7 ). improvement in the precision of measurement is reflected in better reproducibility of measurement , and will obviate some or all of the need for repeated measurements by component technologies . to maximise the precision of hybrid method , the component cardiac output measurement methods chosen for the calculation of { dot over ( q )} t h from equations 2 or 4 should not share common sources of error in the measurement of their raw input data , and should not be subject to mathematical coupling in the derivation of their output measurements . this condition is best obtained by choosing methods or devices from two or more of the different classes of cardiac output measurement technologies . these different classes include , but are not restricted to : ( i ) arterial blood pressure or plethysmographic waveform - derived estimation of stroke volume and cardiac output , including pulse contour methods and pulse wave transit time ; ( ii ) methods based on measurement of blood flow in the heart or great vessels by use of ultrasound , including doppler based measurements as part of echocardiography and use of oesophageal doppler devices ; ( iii ) methods based on pulmonary uptake or elimination of gases such as carbon dioxide ( co 2 ) including differential fick methods such as the partial co 2 rebreathing method , and the capnotracking method ; ( iv ) methods based on transthoracic electrical bio - impedance , or related techniques such as electrical velocimetry and bioreactance ; and ( v ) methods based on imaging of the heart or great vessels such as magnetic resonance imaging or radiology using computerised tomography . these classes of technology for measurement of stroke volume or cardiac output are based on respective different physical and physiological principles , and therefore their measurements of cardiac output are less likely to vary in unison away from the true cardiac output . to put it another way , the sources of error for the different methods that are combined as described herein are ideally not correlated : a stochastic relationship between the measurements obtained from these classes of technology maximises the advantage in precision of measurement obtained from the hybrid method described herein . in ideal embodiments , all of the component methods of cardiac output measurement will have documented accuracy and precision of measurement over a wide range of haemodynamic states and cardiac output values which are comparable to the best published data in the field . to avoid introducing excessive complexity and cost into the hybrid measurement process , one or more of the component methods may be characterised by minimal interference with the usual conduct of patient care and monitoring . ideally , such methods will involve few or no peripheral cables or other attachments to the patient apart from those normally required for patient care and be integrated , by means of plug - in modules for example , into the patient monitoring platform to avoid cluttering of the workspace with stand - alone measurement devices . an example of such a method is the capnotracking method fully integrated into the patient monitoring and ventilation system . where one of a pair of component methods meets these criteria , the cost and complexity of the hybrid method for the clinician or carer is no greater than that of the second method itself , while delivering substantially better accuracy and precision of cardiac output measurement than can be achieved by either component method alone . the choice of weighting coefficients in equations 2 or 4 may be based on a number of factors reflecting the relative accuracy and precision of each component method . examples of these factors include , but are not restricted to , the following : ( i ) data from investigative studies , case reports , reviews , synthesis or meta - analyses on the accuracy and precision of a component method relative to another reference method or to an estimate of the true cardiac output ; ( ii ) data from investigative studies , case reports , reviews , synthesis or meta - analyses on the accuracy and precision of a component method relative to another reference method or to an estimate of the true cardiac output , in certain groups of patients or during certain clinical circumstances or scenarios ; ( iii ) assessment of the accuracy , precision or other index of quality of input data or measurements of raw signals by a component method ; ( iv ) the elapsed time since a prior calibration measurement of the component method has been made ; ( v ) the measured cardiac output itself , where one component method is thought to be more accurate or precise within a certain range of haemodynamic states or cardiac output values than the other component method ( s ); ( vi ) the rate of change in measured cardiac output , where one component method is thought to have a faster response time in real - time measurement of changes in cardiac output . incorporation of factors such as these , and others , may involve application of feedback loops in the calculation of { dot over ( q )} t h . thus , the weighting coefficients applied to one or more of the component methods can change between patients or can change over time ( i . e ., can be dynamically generated ) within the course of measurement in a given patient . in some embodiments , the weighting coefficients are retrieved from a database and applied automatically . a coefficient for the cardiac output measurement by a component method can be obtained which applies as , or in place of , the weighting coefficient for that method after ongoing measurements by the other component method ( s ) have been interrupted or ceased . for example , from equation 4 : 1 2 ⁢ ( α + β · q . ⁢ t b q . ⁢ t a ) is the transfer factor t which applies to method a , and is calculated continuously while ongoing measurements by both methods a and b are being made . an average , median or other measure of central tendency for the value for t can be calculated , updated and stored periodically or continuously . when measurement by one or other method ( say , in this example method b ) ceases or is interrupted , the stored value of t can be used as , or instead of , the weighting coefficient for ongoing measurements by method a . this effectively allows method a to be calibrated by the hybrid method in that patient for ongoing measurements . an example of this is the transfer of a patient who has undergone surgery to a high - dependency unit after emergence from anaesthesia and extubation . monitoring of cardiac output may have been done by the hybrid method during surgery while the patient was ventilated using a pulse contour device ( as method a ) and the capnotracking method ( as method b ). after extubation and transfer to the post - anaesthesia recovery or high - dependency unit , continuing monitoring of cardiac output by the pulse contour method ( method a ) alone can continue . the value of t is entered into the monitoring system , by either manual or automated means , and { dot over ( q )} t a is consequently modified to give { dot over ( q )} t h in the postoperative period from equation 5 . this provides a more consistent value of cardiac output than if the result of method a was used directly without scaling , but of course the result no longer benefits from the stochastic advantage of the hybrid method in improving the degree of random intra - patient scatter in subsequent cardiac measurement by method a alone . the hybrid method can be implemented using any combination of component methods , operating either as stand - alone devices or integrated into the patient monitoring platform . by way of example , fig3 is a flowchart of a process of obtaining the hybrid cardiac output { dot over ( q )} t h using equation 4 from two component methods a and b providing cardiac output measurements { dot over ( q )} t a and { dot over ( q )} t b . in some embodiments , following commencement of measurement on either a single , intermittent or continuous basis by either or both of methods a and b , the inputs { dot over ( q )} t a and { dot over ( q )} t b are previous ( usually the most recent and updated ) measurements by the respective methods . the values for the inputs { dot over ( q )} t a and { dot over ( q )} t b are received as data inputs to a computing device , such as exists within the patient monitoring platform , or other related or available computing device . the weighting coefficients α and β to be applied are automatically retrieved from a database by the process . data representing the hybrid cardiac output value { dot over ( q )} t h from equation 4 is automatically generated and displayed , and is updated whenever an updated value for either of the inputs { dot over ( q )} t a and { dot over ( q )} t b becomes available . in some embodiments , data representing a hybrid cardiac index is generated and displayed , either in addition or instead , optionally along with data representing corresponding values of one or more haemodynamic variables which can be determined once a measurement of cardiac output or index is available . in some embodiments , a cardiac output monitoring system is configured to display an indication of “ normal ranges ” for cardiac output , cardiac index and other derived haemodynamic variables , and to trigger an alarm to alert the clinician or carer of any deviation outside these ranges . in some embodiments , a cardiac output monitoring system is a standard computer system 700 , and the hybrid cardiac output monitoring method is implemented in software as one or more cardiac output monitoring modules 702 stored on tangible and non - volatile ( e . g ., solid state or hard disk ) storage 704 associated with the computer system , as shown in fig7 . the cardiac output monitoring modules 702 may include at least one cardiac output measurement component and a cardiac output measurement combining component that generates a signal or data 722 representing the cardiac output of the subject determined by the hybrid cardiac output monitoring method . in some embodiments , the computer system is a component of a patient ventilator . in any case , it will be apparent to those skilled in the art that the various components of the cardiac output monitoring system can be alternatively distributed over a variety of locations and in various combinations , and that in other embodiments at least part of the hybrid cardiac output monitoring method can alternatively be implemented by one or more dedicated hardware components such as application - specific integrated circuits ( asics ) and / or as configuration data for one or more field - programmable gate arrays ( fpgas ), for example . in the described embodiment , the system 700 includes standard computer components , including random access memory ( ram ) 706 , at least one processor 708 , and external interfaces 710 , 712 , 714 , all interconnected by a bus 716 . the external interfaces include universal serial bus ( usb ) interfaces 710 , at least one of which is connected to a keyboard 718 and a pointing device such as a mouse , a network interface connector ( nic ) 712 which connects the system 700 to a communications network 720 such as the internet , and a display adapter 714 , which is connected to a display device such as an lcd panel display 716 . the system 700 also includes an operating system 718 such as linux or microsoft windows . in some embodiments , to reduce the effects of random measurement imprecision on { dot over ( q )} t h , a moving average of { dot over ( q )} t h can optionally be used . this has the effect of delaying the responsiveness of the system to real - time changes in cardiac output , but provides more stable results . alternatively or additionally , the measurement values provided by each of the component methods { dot over ( q )} t a , { dot over ( q )} t b etc can be individually smoothed prior to their combination . technical improvements in the measurement of input parameters for the component methods which reduce random measurement imprecision may allow shorter averaging or none at all , thereby improving the real - time responsiveness of the system . using an idealised monte carlo model where the distribution of measurements by each method follows a gaussian ( normal ) distribution , and the relationship between the measurements made by the various methods is entirely random ( i . e ., the sources of error for the respective methods are uncorrelated or at least substantially uncorrelated ), the improvement in precision of measurement of cardiac output which accompanies the addition of measurements by a method b to that of method a , as in equation 4 , is demonstrated in fig4 . the simulated cardiac output was set at 5 l / min with random variation by a gaussian white noise generator producing 10 6 measurements for each of method a and method b , with a precision ( one standard deviation ) set at 20 % of this value for both , giving 95 % limits of agreement of +/− 40 % or +/− 2 l / min for each component method . the precision of the calculated hybrid cardiac output ( from equation 4 ) is substantially better , with 95 % limits of agreement of +/− 28 . 3 %. the reduction in the standard deviation of the hybrid measurement (∂ sd ) follows the formula ∂ sd = 1 − 1 /√{ square root over ( n )} ( equation 4 ) where in this case n = 2 . published clinical data from botero was used to demonstrate the ability of the hybrid method to produce substantial improvements in the precision of cardiac output measurement using existing component methods which are currently in common clinical use . in their study , the relative accuracy and precision of three methods of measurement of cardiac output were assessed by comparison with a gold standard . with institutional review board approval , sixty - eight consenting patients undergoing cardiac surgery were cannulated , in accordance with standard clinical practice , with a pulmonary artery catheter capable of providing intermittent bolus and continuous thermodilution measurement of pulmonary blood flow via vigilance monitor ( baxter healthcare corporation , irvine , calif ., usa ), as well as non - invasive measurement of pulmonary blood flow by the partial co 2 rebreathing method using a nico ™ monitor ( novametrix medical systems , wallingford , conn ., usa ). for the purposes of the study , the gold standard reference method used was an ultrasonic transit time flow probe ( transonic systems inc , ithaca , n . y ., usa ) applied to the ascending aorta prior to cannulation for cardiopulmonary bypass . contemporaneous measurements were recorded using all four modalities , and the agreement of the three clinical measurement devices with the flow probe was made prior to commencement of and after separation from bypass . raw data for measured cardiac output has been calculated from data points extracted from the bland - altman agreement plots in their paper . the limits of agreement with the flow probe from these extracted data points are as shown in fig5 a ( pre - cardiopulmonary bypass measurements ) and fig5 b ( post - cardiopulmonary bypass measurements ), along with the hybrid cardiac output measurements ( using equation 4 , with equal weighting applied to both component methods ) that can be calculated for the three different combinations of component methods made available from the data . fig5 shows that , for all the methods tested , the agreement with the invasive gold standard reference method was significantly worse than the threshold for acceptability (+/− 30 %) recommended by critchley and critchley . this was particularly true for continuous thermodilution , where limits of agreement pre - and post - cardiopulmonary bypass were 56 . 9 % and 64 . 8 % respectively . however , the hybrid cardiac output measurements calculated for the three combinations had significantly better agreement with the reference method . for the nico / bolus thermodilution hybrid , the limits of agreement closely approached the +/− 30 % threshold for acceptability ( 31 . 9 % and 31 . 7 % pre - and post - cardiopulmonary bypass ). it should be noted that even for the hybrid combinations involving the continuous thermodilution component , the precision of agreement of the hybrid was not significantly worse than that of the other , more precise , component . note that bias relative to the reference method was also significantly improved by the hybrid method in the post - cardiopulmonary bypass measurements . data from the published meta - analysis by peyton and chong allows an estimate to be made of the expected precision of the hybrid method using currently available component cardiac output measurement technologies . these authors reviewed published papers from the 10 years 2000 - 9 and included papers where comparison was made with bolus thermodilution with results presented as bias and precision according to the method of bland and altman . fig6 lists the precision these authors found for four generic classes of cardiac output measurement technologies using a pooled weighted meta - analysis of published data on the precision of agreement with bolus thermodilution of four generic classes of technology for measurement of cardiac output , expressed as 95 % limits of agreement ( two standard deviations of the difference between paired measurements ). using monte carlo modelling as employed in fig4 and fig2 , the expected precision of hybrid measurements obtained from the possible combinations of these four groups were calculated . fig6 shows that the precision expected from the hybrid method using these component methods was substantially better in all six possible combinations of two methods . for all combinations of currently available generic technology , the hybrid method achieved precision of agreement with bolus thermodilution that exceeded or closely approached the +/− 30 % criterion for acceptability stipulated by authorities ( see critchley and critchley ). the hybrid method was tested by comparing the accuracy and precision of cardiac output measurement relative to simultaneous bolus thermo - dilution measurements ( average of 3 bolus measurements on each occasion ) via a pulmonary artery catheter , using combinations of three component cardiac output measurement methods . with approval from the local institutional ethics committee , 30 patients scheduled for either elective cardiac surgery or liver transplantation were studied at the austin hospital , melbourne , australia . pulmonary capnotracking ( qtco 2 ) measurements of cardiac output were combined with either : ( i ) continuous thermodilution measurements of cardiac output ( qtcco ); or ( ii ) vigeleo / flotrac pulse contour measurements of cardiac output ( qtft ) to determine corresponding hybrid values of cardiac output as described herein . the agreement of these hybrid values with cardiac output measurements by thermodilution was assessed . the measurements and assessments were done pre - and post - cardiopulmonary bypass or pre - and post - reperfusion of the donor liver . a total of 50 sets of measurements were collected . agreement with thermodilution was assessed for the two hybrid combinations , and compared with that of the component methods alone , using bland altman statistics , as shown in fig8 . for each method and hybrid combination , the standard deviation and variance of the difference between paired measurements was calculated , along with the percentage error (% error : 2 standard deviations divided by the mean cardiac output ), as shown in fig9 . the statistical significance of the differences in variances was determined using either the f - test for normally distributed data , or by levene &# 39 ; s robust test for equality of variances , which does not assume normality of data distributions . hybridization of qtco 2 (% error 42 . 2 %) and qtcco (% error 51 . 3 %) achieved significantly better precision (% error 31 . 3 %) than the component methods ( p = 0 . 0004 and p = 0 . 0195 ). due to the poor inherent precision of qtft (% error 82 . 8 %), hybrid combination of qtft with qtco 2 did not result in better precision than qtco 2 alone . the hybrid measurement can approach a percentage error of +/− 30 % which is recommended as the criterion for acceptability . many modifications will be apparent to those skilled in the art without departing from the scope of the present invention .
a computerized method for monitoring cardiac output of a subject by a processor executing the method , the method comprising the steps of : determining first values of cardiac output of the subject for a first period of time using respective different cardiac output measurement methods having respective first measurement errors ; and combining the determined first values of cardiac output to determine a second value of cardiac output of the subject for the first period of time , such that the second value of cardiac output has a second measurement error that is less than any of the first measurement errors ; and at least one of storing , outputting , and displaying data representing the determined second value of cardiac output of the subject .