the basic concepts of modelling a fluid - filled catheter shall first be explained with reference to fig2 . the recording device according to fig2 has a catheter 4 , which is connected via an extension tube 12 with the pressure sensor 6 . the acquired data may be processed and viewed by means of data processing module 10 . a saline solution 8 can be flushed through the system to keep it clear from air - bubbles and blood clotting . such measuring device is commercially available e . g . from becton dickenson critical care systems . the fluid column in catheter 4 transfers vibrations caused by pressure pulses in the heart to the sensor 6 . the dynamics of the oscillations in the catheter are very similar to a mass - spring system . in particular , the system has a natural frequency f 0 at which it will oscillate when left alone . further , friction will result in damping which may be indicated by a damping coefficient ζ . in the case of a fluid - filled catheter , these parameters will depend on the viscosity of the fluid as well as the dimensions of the catheter tube . by modelling the catheter as a tube with length 1 , radius r and filled with a fluid with a viscosity η , which depends on the temperature of the blood inside the catheter , and by finding values for the hydraulic resistance r h , the hydraulic inertance l h and the hydraulic compliance c h ( equivalent to electric resistance , inductance and capacitance ), a second order differential equation may be derived between the true blood pressure p u and the measured blood pressure p y : p u ⁢ ω 0 2 = ⅆ 2 ⁢ p y ⅆ t 2 + 2 ⁢ ζ ⁢ ⁢ ω 0 ⁢ ⅆ p y ⅆ t + ω 0 2 ⁢ p y ⁢ ⁢ where ( 2 ) f 0 = 1 2 ⁢ ⁢ π ⁢ l h ⁢ c h = 1 2 ⁢ ⁢ π ⁢ π ⁢ ⁢ r 2 ρ ⁢ ⁢ l ⁢ ⁢ c h ⁢ ⁢ and ( 3 ) ζ = r h 2 ⁢ c h l h = 4 ⁢ ⁢ η r 3 ⁢ l ⁢ ⁢ c h ρ ⁢ ⁢ π ( 4 ) the hydraulic resistance r h , inertance l h and compliance c h may be expressed in the terms of the dimensions of the catheter 1 , r and the viscosity η as follows ; r h = 8 ⁢ ⁢ η ⁢ ⁢ l π ⁢ ⁢ r 4 , ( 5 ) l h = ρ ⁢ ⁢ l π ⁢ ⁢ r 2 , ⁢ and ( 6 ) c h = δ ⁢ ⁢ v δ ⁢ ⁢ p , ( 7 ) where δv is the volume of fluid that enters the catheter tube upon application of a pressure change δp . thus , first estimates of the natural frequency f 0 and damping coefficient ζ may be calculated by using the basic dimension of the catheter . as described below , these estimates may be used to find a first approximation of the catheter poles in the z - transform of a high - order filter . alternatively , estimates for f 0 and ζ may be obtained from the step response of the catheter . this embodiment of the invention has the advantage that no assumptions have to be made on the catheter dimensions and the viscosity of blood inside the catheter . instead , the catheter is flushed in vivo with saline . the measured blood pressure at the trailing edge of the pressure step is represented in fig3 . as is evident from fig3 , the blood pressure performs several oscillations with a periodic time t and amplitudes a 1 and a 2 . by inserting these values into a model for a damped oscillatory system , the natural frequency and the relative damping coefficient may be derived as : f 0 = 1 t 1 - ζ 2 ( 8 ) ζ = ln ⁡ ( a 1 a 2 ) π 2 + ln ⁡ ( a 1 a 2 ) 2 ( 9 ) this method provides an easy way to estimate f 0 and ζ . with reference to fig4 to 6 , an embodiment of the actual modelling of the oscillatory artefacts shall now be described . according to this embodiment , the measurement data as well as a model of the measurement data are transformed to the z - domain . in the z - domain , the influence of the catheter oscillations will appear as one or several poles in the complex plane . the basic idea is to identify and separate the catheter poles f ( q ) from the other heart - related poles h ( q ) in a high - order filter t ( q ) and use those poles for compensation . the problem as illustrated in fig4 is to find a filter 16 , or t ( q ), which is the discrete transfer function ( z - transform ) that generates the measured pressure waveform p y when fed with a stochastic signal such as white noise e ( t ). white noise may be used because it contains all frequencies and therefore maximally excites the system throughout all frequency components . in the transfer function t ( q ), the catheter dynamics are included as c ( q ). c ( q ) may be described as a quotient of the polynomials b ( q ) and f ( q ). since in this case the transfer function ( z - transform ) of the catheter is a second order model ( see equation ( 2 )), b ( q ) can be approximated by a constant . f ( q ) however , includes the poles of the catheter transfer function . according to an especially preferred embodiment , t ( q ) can be written as an auto - regression ( ar ) model . an auto - regression model is a model that regresses on the passed values of itself . if t ( q ) is chosen to be a 9 th order auto - regression model , it may be written as follows : p y ( t )+ a 1 p y ( t − 1 )+ . . . + a 9 p y ( t − 9 )= e ( t ), ( 10 ) is the parameter vector of ( in this case ) 9 unknown parameters that needs to be adapted to the measured data . the order of the model is determined by the number of delayed input signals that are considered . a 9 th order model has proven to give good results , however , any order from 4 to 14 may also be considered . preferably the order is 7 to 11 , most preferred 8 , 9 or 10 . by a recursive algorithm , the parameter vector θ is then adapted to the measured data such that the sum of squared prediction errors is minimized . any recursive estimation method may be used , for example a least mean square algorithm or a recursive least square algorithm . the effect of such iterative estimation is shown in fig5 and 6 , showing a representation of t ( q ) in the z - plane after 0 . 4 seconds in fig5 and after 10 seconds of computation in fig6 . in fig5 , 9 poles 22 of t ( q ) are distributed over the complex plane . from the estimated values of f 0 and the damping coefficient ζ , as explained above , estimates for the position of the catheter poles 18 have been previously calculated and are represented in fig5 and 6 by larger crosses 18 . these poles are surrounded by rectangular areas 20 , which represent the region in which a pole 22 of t ( q ) would be identified as a catheter pole . in fig5 , none of the 9 poles 22 are within the rectangular areas 20 . however , after 10 seconds of computation time , the auto - regressive model has been so far adapted that 2 poles 24 and 26 have moved inside the rectangular areas 20 and are situated very close to the estimated positions 18 . thus , these poles 24 , 26 may be identified as originating from an influence of the fluid - filled catheter . when the poles of f ( q ) have been identified in t ( q ), better estimates of the true values for the natural frequency f 0 and the damping coefficient ζ may be obtained from the position of the poles . by rewriting equation ( 2 ) as a difference equation , solving for p u and inserting the values for f 0 and ζ , the desired pressure p u ( t ) can be derived by inverse filtering as follow : p u = ( 1 + 2 ⁢ ⁢ ς t ⁢ ⁢ ω 0 ) ⁢ p y ⁡ ( t ) - 2 ( t ⁢ ⁢ ω 0 ) 2 ⁢ ( 1 + ζ ⁢ ⁢ ω 0 ⁢ t ) ⁢ p y ⁡ ( t - t ) + 1 ( t ⁢ ⁢ ω 0 ) 2 ⁢ p y ⁡ ( t - 2 ⁢ ⁢ t ) ( 12 ) however , other know inverse filtering techniques using the numerator and denominator of the transfer function t ( q ) may be used as well , such as the filter function in matlab .
the invention relates to a method for removing oscillatory artefacts caused by pressure waves in a fluid - filled trans - luminal catheter from invasive blood pressure measurement data , including the steps of setting up a model for the measurement data , fitting the model to the measurement data , identifying the model components , representing the oscillatory artefact , and removing the oscillatory artefact from the measurement data . the invention also relates to a respective device for acquiring and correcting invasive blood pressure measurement data .