Objective: Non-invasive continuous blood pressure monitoring is not yet part of routine practice in renal dialysis units but could be a valuable tool in the detection and prevention of signi/uniFB01cant variations in patient blood pressure during treatment. Feasibility studies have delivered an initial validation of a method which utilises pressure sensors in the extra-corporeal dialysis circuit, without any direct contact with the person receiving treatment. Our main objective is to further develop this novel methodology from its current early development status to a continuous-time brachial artery pressure estimator. Method: During an in vivo patient feasibility study with concurrent measurement validation by Finapres Nova experimental physiological measurement device, real-time continuous dialysis line pressures, and intermittent occluding arm cu/uniFB00 pressure data were collected over the entire period of (typically /four.pnum-hour) dialysis treatments. There was found to be an underlying quasi-linear relationship between arterial line and brachial pressure measurements which supported the development of a mathematical function to describe the relationship between arterial dialysis line pressure and brachial artery BP . However, unmod- elled non-linearities, dynamics and time-varying parameters present challenges to the development of an accurate BP estimation system. In this paper, we start to address the problem of physiological pa- rameter time variance by novel application of an iterative learning run-to-run modeling methodology originally developed for process control engineering applications to a parameterised BP model. Results: The iterative run-to-run learning methodology was applied to the real-time data measured dur- ing an observational study in /nine.pnum patients, supporting subsequent development of an adaptive real-time BP estimator. Tracking of patient BP is analysed for all the subjects in our patient study, supported only by intermittent updates from BP cu/uniFB00 measurements. Conclusion: The methodology and associated technology is shown to be capable of tracking patient BP non-invasively via arterial line pressure measurement during complete /four.pnum-hour treatment sessions. A robust and tractable method is demonstrated, and future re/uniFB01nements to the approach are de/uniFB01ned. Blood pressure measurement, extracorporeal pressure sensors, /uniFB01stula, hemodialysis, continuous blood pressure measurement model parameter optimisation, iterative learning, control engineering run-to-run control, iterative learning /one.pnum Introduction Continuous monitoring of blood pressure (BP) during dialysis [/one.pnum] has the potential to improve patient out- comes [/two.pnum, /three.pnum, /four.pnum] and could ultimately inform treatment regime or close a personalised therapeutic inter- vention loop via modulation of dialysis time and/or duration, dialysate sodium concentration and/or tem- perature on a per patient basis. Of particular interest is intradialytic hypotension (IDH), a decrease in sys- tolic blood pressure [/five.pnum], generally a relatively sudden event with associated symptoms include dizziness or fainting, muscle cramps, abdominal discomfort, nausea and vomiting, often results in truncated dialysis 1 treatments with increased risk of cerebral ischemic incidents. IDH prediction, detection and mitigation is the primary application area of the work described in this paper. BP monitoring is normally conducted in a clinical setting via the use of an air-/uniFB01lled occluding arm cu/uniFB00 that provides a robust, but irregular and intermittent measurement that disrupts the normal blood /uniFB02ow, and consequently requires a signi/uniFB01cant settling time between measurements [/six.pnum]. Additionally, there are three alternative distinct methods for non-invasive monitoring of BP which have occasionally been used in re- search settings. Arterial applanation tonometry [/seven.pnum], where a transducer is positioned above a super/uniFB01cial artery compressing it against an underlying bone [/eight.pnum], has been used in cardiology and anaesthetised proce- dures to avoid the insertion of an arterial cannula [/nine.pnum, /one.pnum/zero.pnum]. Pulse Transition Time (PTT) [/one.pnum/one.pnum] is based on mea- sured photoplestimography (PPG) and electrocardiogram (ECG) signals during several cardiac cycles, which may not be accurate due in part to the unaccounted physiological factors in the blood pressure regulation mechanism and reliance on accurate ECG triggering [/one.pnum/two.pnum]. Finally, the volume clamp (or vascular unloading) method [/six.pnum] utilises an in/uniFB02atable /uniFB01nger-cu/uniFB00 combined with an embedded photodiode to measure the diam- eter of /uniFB01nger artery. Cu/uniFB00 pressure is adjusted to maintain a constant artery diameter, and the changes in cu/uniFB00 pressure are used to calculate a BP curve in the brachial artery. In use, patients frequently report pain or discomfort at the /uniFB01ngertips where cu/uniFB00s are placed, and this device can be unreliable in patients with reduced blood /uniFB02ow to the digits, often manifest in dialysis patients [/one.pnum/one.pnum]. All three non-invasive methods are sensitive to patient movement (especially ECG signals) [/one.pnum/three.pnum] which would result in an unacceptable and uncomfortable restriction placed on patients during a four-hour dialysis treatment. Figure /one.pnum: Sensor and data acquisition signal /uniFB02ow The iTrend (Intelligent Technologies for Renal Dialysis) programme is a long-term collaborative project per- formed by a multidisciplinary research team from the Universities of Derby and Nottingham and the Royal Derby Hospital Renal Unit in the UK [/one.pnum/nine.pnum, /two.pnum/zero.pnum], developing supporting technologies, real-time analysis algo- rithms and heuristics to enable personalised and precision treatment in end-stage kidney disease (ESKD) [/one.pnum/four.pnum, /one.pnum/five.pnum]. Blood pressure monitoring to diagnose hypertension and hypotension [/one.pnum/six.pnum, /one.pnum/seven.pnum] typically relies on plethorperidialytic and intermittent intradialytic BP measurements. The ability to continuously monitor BP both in terms of absolute measures and blood pressure variability could lead to new diagnostic and prognostic criteria for IDH as well as optimal and personalised treatment strategies. A feasibility study of a novel method for continuously monitoring BP has previously been conducted (Fig./one.pnum), which introduced the placement of pressure transducers onto the venous and arterial blood lines that con- nect a patient to a haemodialysis machine during treatment [/one.pnum/eight.pnum], and experimentally derived relationships between pressures in these extra-corporeal blood lines and brachial BP . Pressure sensors were attached to the blood lines rather than making use of the pressure sensors present within the dialysis machines, and utilised the existing ports and connection points which are common and standardised on most dialysis blood line sets. The experimental relationship between brachial cu/uniFB00 MAP and corresponding measured arterial line pres- sure for /one.pnum/one.pnum sessions in the patient study is shown in /uniFB01gure /two.pnum, with a linear least squares /uniFB01t of y= 0:8x1:5e+ 02; (/one.pnum) /two.pnum 50 60 70 80 90 100 110 120 130 140 150 Brachial Cuff MAP (mmHg)-120-100-80-60-40-200Arterial Line Pressure (mmHg)Figure /two.pnum: Brachial cu/uniFB00 MAP vs Arterial line pressures in /one.pnum/one.pnum patient sessions Root Mean Squares Error /one.pnum/zero.pnum./three.pnum, R2/zero.pnum./six.pnum/one.pnum/five.pnum, p-value /six.pnum./three.pnum/five.pnume-/two.pnum/zero.pnum, and is strongly associated with the physical components of the dialysis procedure (pump, pump speed, dialysis line set), with variance from the line dominated by unmodelled physiological and mechanical e/uniFB00ects In order to further examine this hypothesis, 50 60 70 80 90 100 110 120 130 140 150 Brachial Cuff MAP (mmHg)-120-110-100-90-80-70-60-50-40-30-20Arterial Line Pressure (mmHg) Figure /three.pnum: Brachial cu/uniFB00 MAP vs Arterial line pressures in /one.pnum/one.pnum patient sessions, following compensation for time varying e/uniFB00ects during treatment it is possible to negate the time varying e/uniFB00ects in the data by taking a mean value for each individual patient treatment, and recalculating the data scatter, and is shown in /uniFB01gure /three.pnum. A linear least squares /uniFB01t of y= 0:82x1:5e+02, Root Mean Squares Error /six.pnum./five.pnum/four.pnum, R2/zero.pnum./eight.pnum/five.pnum/two.pnum, p-value /two.pnum./nine.pnum/three.pnume-/three.pnum/eight.pnum. There are a number of salient features in this plot. Firstly, the gradient of the /uniFB01t has only changed by 2:5%, indicating a relatively accurate model for the machine and lines system. Secondly, the data R2value has risen by 38:5%to0:852, indicating that it should be possible to design a tractable and useable time-invariant model. The feasibility study con/uniFB01rmed that it is potentially possible to estimate brachial BP continuously and non-invasively during the period of a dialysis session in a clinical setting with measurement of venous and arterial line pressure, and occasional measurement of brachial blood pressure by arm cu/uniFB00. /one.pnum./one.pnum Structure of this paper This paper describes the development, application and performance analysis of an adaptive model param- eter optimisation scheme based on iterative run-to-run learning control. The aim of this development was to compensate for the time-dependent changes of model parameters which describe the arterial line to BP relationship during /four.pnum-hour dialysis treatments. The paper is divided into the following sections: •Section I: Introduction •Section II: Run-to-run BP Estimator describes the application of run-to run iterative learning method- ology /three.pnum •Section III: Method describes the processing methodology for the real-time patient data sets •Section IV: Results examines the e/uniFB00ectiveness of the BP estimation scheme •Section V: Conclusions assesses the overall modeling-predictor method and draws conclusions for further work For clarity, where a patient’s BP is mentioned, this should be taken to mean brachial blood pressure. /two.pnum Run-to-Run BP Estimator The system under consideration (Fig./four.pnum) is discrete-time and non-stationary, with continuous dialysis line pressures sampled at /one.pnumkHz. This measurement constitutes the basis of calculations to estimate instanta- neous, real-time BP . Patient arterial pressure is measured by occluding arm-cu/uniFB00 with an irregular sample rate of approximately /three.pnum/zero.pnum minutes, and this constitutes an accurate, repetitive measurement of BP , albeit at extremely widely spaced time-instances. The challenge addressed in this paper is to devise a method to, as accurately as possible, ’/uniFB01ll in the gaps’ between BP cu/uniFB00 measurements. This is critically important, as patient BP can vary signi/uniFB01cantly at the time-scale of /three.pnum/zero.pnum minute measurement samples. For processes such as this, which are fundamentally repetitive or cyclical by nature and resemble a batch process delineated by cu/uniFB00 measurements, iterative learning approaches are generally tractable approaches to modeling and control [/two.pnum/one.pnum]. These approaches are generally applied to the problem of repetitive refer- ence tracking control for example in the manufacturing of semiconductors [/two.pnum/two.pnum]. In the application described here, the methodology (Fig. /four.pnum) will be adapted to form a model-based BP estimator. Estimation of BP is based on measured arterial line pressure, however, an accurate measurement of BP to update the model parameters is only infrequently available (at best every /three.pnum/zero.pnum mins). Run-to-run control was developed during the /one.pnum/nine.pnum/nine.pnum/zero.pnums [/two.pnum/three.pnum, /two.pnum/four.pnum] for this class of repetitive batch process. The model structure can take any form, how- ever linear regressions and response surface structures are generally implemented [/two.pnum/five.pnum], which assume that the process drift is slow enough to compensate with parameter updates when measurements be- come available. In this application, a model parameter update becomes available at the instant of BP cu/uniFB00 measurement. Figure /four.pnum: BP estimator system A linear regression model of the form y(t) =ax(t) +b(t) +(t) (/two.pnum) is generally implemented, where t= 1;2;:::denotes the time index; yis the model output, estimated BP inmmHg ;xis the input, measured arterial line pressure in mmHg ;ais the slope coe/uniFB03cient ;bis the drift coe/uniFB03cient , andis the disturbance coe/uniFB03cient. The update objective for yisy, and ifaandbare accurately known, then the optimal model for the system is x(t) =a1(yb(t)) (/three.pnum) /four.pnum Model inaccuracies when compared to the system are inevitable, particularly given the non-stationary nature of the physiological process, unmodelled nonlinearities and stochastic events. Consequently, an iterative parameter adjustment is implemented to update the estimation of aandb b(t) =[y(t1)ax(t1)] + ((1 )b(t1)) (/four.pnum) which is an exponentially weighted moving average /uniFB01lter [/two.pnum/two.pnum], tuned by adjusting variable in the interval 0<< 1. Combining (/four.pnum) with (/three.pnum) gives b(t) =[y(t1)AA1[yb(t1)]] + (1 )b(t1) b(t) =b(t1) +[y(t1)y] (/five.pnum) which, in its general form is x(t) = x(t1)r(t) (/six.pnum) where 0< < 1andr(t)are respectively the forgetting factor andupdate law for the model. Typically the system gain ais modeled in advance via designed experiment [/two.pnum/six.pnum]. In the case under consideration here, the /uniFB01tted linear relationship for the study population has been derived (eq./one.pnum) as y= 0:8x1:5e+02 wherexis the measured variable Brachial cu/uniFB00 BP andyis the corresponding output variable Arterial Line Pressure . Given its successful history in the design and implementation of controllers for batch processes, the methodology has been applied to the design of a real-time BP estimator, which is described in the next section. /three.pnum Method In total /one.pnum/two.pnum participants were recruited with /one.pnum/one.pnum completed monitored dialysis sessions. /one.pnum participant moved out of area before a session could be completed. /five.pnum/eight.pnum./three.pnum% of participants were male, with a median age of /six.pnum/five.pnum (IQR /four.pnum/eight.pnum-/seven.pnum/eight.pnum). All participants had continuous non-invasive monitoring of haemodynamics using pulse wave analysis (Finapres NOVA) during a single dialysis treatment of typically /four.pnum hours duration, and data periodically veri/uniFB01ed by intermittent arm-cu/uniFB00 measurements. Two pressure sensors were attached to the dialysis lines: one between the arterial dialysis needle and dialysis line and the other directly onto the venous-line bubble trap. Data was continuously recorded from all sensors at a sampling rate of /one.pnumkHz. The study protocol was approved by the West Midlands - Coventry and Warwickshire Research Ethics Com- mittee and participants gave written informed consent. A typical real-time data set for a patient study is shown in Figure /five.pnum. Measurements taken during the obser- vational study are acquired and stored for each patient as data sets containing the following datastreams sampled at 1kHz and covering the entire treatment period, typically /four.pnum hours; •Time: continuous from National Instruments board •Arterial line pressure: continuous from pressure sensor •Venous line pressure: continuous from pressure sensor •Occluding cu/uniFB00 BP: intermittent from Finapres Nova •Reconstructed systolic, diastolic and mean arterial pressure: continuous from Finapres Nova /uniFB01nger cu/uniFB00 We will now consider the data from a single typical treatment session for patient IT/five.pnum/four.pnum. Figure (/five.pnum) shows the reconstructed systolic, diastolic and mean arterial pressures calculated by the Finapres Nova unit from a vascular unloading /uniFB01nger cu/uniFB00. It is found in practice that this method causes patient discomfort which generally precludes continuous use, hence in this case approximately /two.pnum hours of data at the beginning of treatment and /three.pnum/zero.pnum mins of data at the end of treatment are recorded. This was the case for all of the participants in the study, with /three.pnum/zero.pnum minute sessions being the average period for /uniFB01nger cu/uniFB00 measurements /five.pnum 0 2000 4000 6000 8000 10000 12000 14000 Time (s)50100150200250Pressure (mmHg)Reconstructed Systolic Pressure Reconstructed Diastolic Pressure Reconstructed MAPFigure /five.pnum: Typical patient real-time data - reconstructed systolic, diastolic and mean arterial pressure (IT/five.pnum/four.pnum) 0 5000 10000 15000 Time (s)-100-50050100150200250300Pressure (mmHg) & Flow (ml/min) Venous Line Pressure Arterial Line Pressure Estimated Blood Pump Flow Rate Figure /six.pnum: Typical patient real-time data - venous and arterial line pressure, estimated blood pump /uniFB02ow rate (IT/five.pnum/four.pnum) before the device causes discomfort. Additionally, as the cu/uniFB00 is /uniFB01tted to a /uniFB01nger on the non-dialysing arm, it can also interfere with run-of-the-mill activities such as refreshment breaks and reading. Figure (/six.pnum) shows the directly measured venous and arterial line pressures, along with estimated blood pump /uniFB02ow rate which is derived from the venous line pressure data. Figure (/six.pnum) reveals a venous line pressure waveform which is time varying with respect to both mean and amplitude. This measurement is taken at a port on the venous bubble trap which is situated close to the dialyser blood pump. As is to be expected, the waveform dynamics are dominated by the action of the two lobes of this peristaltic pump Fig. (/seven.pnum). This dominating waveform shape should be closely related to the angular speed of the pump and hence should support the derivation of /uniFB02ow rate through the dialysis lines. The time varying nature of the waveform renders this derivation potentially problematic, leading to the application of Fourier modelling to calculate the fundamental frequency of the pump. This method supports the derivation of instantaneous, and hence, time varying pump speed [/two.pnum/seven.pnum]. The problem can be posed as a moving window length Lover the real-time venous line pressure data stream which is periodic over the interval 0xL, thenf(x)can be derived as f(x) =a0+1X n=1 ancos2nx L +bnsin2nx L (/seven.pnum) /six.pnum 6909 6909.5 6910 6910.5 6911 6911.5 6912 Time (s)160165170175180Venous Line Pressure (mmHg)Figure /seven.pnum: Typical patient real-time data - venous line pressure detail (IT/five.pnum/four.pnum) which is the Fourier trigonometric series for the function f(x). In the case under examination here, the fundamental frequency of the blood pump is sought, so calculations are constrained to n= 1. Examination of Figs. (/five.pnum - /seven.pnum) reveals waveforms which comprise cyclical elements which are varying in both amplitude and mean in addition to measurement noise. In order to smooth the signals to facilitate real time calculations, moving average /uniFB01lters with a window length of /five.pnum/zero.pnum/zero.pnum/zero.pnum samples or/five.pnumswas implemented on all data lines with the exception of BP which has a single value at each measurement event. The win- dow length was chosen as being over twice the length of the period of a slow heart rate (HR) of /three.pnum/zero.pnumbpm in order to avoid aliasing. The pump frequency is calculated and updated in real-time over this sliding win- dow. Additionally, arm cu/uniFB00 measurements are characterised as steady-state phenonomena as they are discrete measurements without dynamics. Derived pump frequency is converted to /uniFB02ow in units of mls1 by fl=fr(rads1) 2 60  r2Ln (/eight.pnum) whereflis /uniFB02ow inmls1,fris pump frequency in rads1,ris the radius of the dialysis line within the pump inmm andLnis the e/uniFB00ective length of line within the pump in mm. In the example shown in Fig. (/six.pnum) the estimate of 290ml=min agrees with the /uniFB02ow rate recorded in the patient’s record. 0 5000 10000 15000 Time (s)-100-50050100150200Pressure (mmHg)Arm Cuff Mean Arterial Pressure Mean Arterial Line Pressure Mean Reconstructed Arterial Pressure Figure /eight.pnum: Typical patient real-time data - occluding arm cu/uniFB00 pressure, mean arterial line pressure, mean reconstructed arterial pressure (IT/five.pnum/four.pnum) /seven.pnum Table /one.pnum: Baseline participant characteristics VARIABLE (n=/seven.pnum) Age (years) /five.pnum/three.pnum (*IQR /four.pnum/nine.pnum to /seven.pnum/zero.pnum) Male [n (%)] /three.pnum (/four.pnum/three.pnum) White ethnicity [n (%)] /five.pnum (/seven.pnum/one.pnum) Current smoking [n (%)] /one.pnum (/one.pnum/four.pnum) Diabetes [n (%)] /two.pnum (/two.pnum/nine.pnum) Ischaemic heart disease [n (%)] /two.pnum (/two.pnum/nine.pnum) Dialysis vintage (months) /six.pnum (/six.pnum to /two.pnum/three.pnum) Dialysis adequacy ( Kt=V ) /one.pnum./two.pnum/four.pnum (/zero.pnum./nine.pnum/seven.pnum to /one.pnum./four.pnum/six.pnum) Fistula blood /uniFB02ow assessment ( QA) /six.pnum/seven.pnum/zero.pnum (/six.pnum/three.pnum/five.pnum to /one.pnum/zero.pnum/seven.pnum/two.pnum) Vascular access type Brachiocephalic arteriovenous /uniFB01stula [n (%)] /four.pnum (/five.pnum/seven.pnum) Radiocephalic arteriovenous /uniFB01stula [n (%)] /three.pnum (/four.pnum/three.pnum) Needle gauge /two.pnumx /one.pnum/four.pnumg [n (%)] /three.pnum (/four.pnum/three.pnum) /two.pnumx /one.pnum/five.pnumg [n (%)] /three.pnum (/four.pnum/three.pnum) Arterial /one.pnum/five.pnumg; Venous /one.pnum/six.pnumg [n (%)] /one.pnum (/one.pnum/four.pnum) Post-dialysis weight ( kg) /seven.pnum/eight.pnum./six.pnum (/six.pnum/four.pnum./one.pnum to /nine.pnum/eight.pnum./two.pnum) Body mass index ( kg=m2) /two.pnum/six.pnum./three.pnum (/two.pnum/four.pnum./four.pnum to /three.pnum/four.pnum./four.pnum) *IQR, interquartile range Filtered mean arterial line pressure and reconstruced arterial waveforms are shown in Fig. (/eight.pnum) with corre- sponding arm cu/uniFB00 MAP measurements during the treatment period. Real-time code has been developed in Matlab/Simulink [/two.pnum/eight.pnum] to perform calculations on patient measure- ment data streams acquired during dialysis treatment. The algorithm is structured as follows; /one.pnum. pre-calculate recursive least /uniFB01t for the patient populations previously measured and recorded BP - arterial line pressure pairs Fig. (/two.pnum). In this case, with xas the measured variable arterial line pressure andyas the predictor variable BP, we derive the relationship of the form y(t) =ax(t)+b(t)+(t)) Eq. /two.pnum asy= 0:619x+ 138:8 + /two.pnum. the acoe/uniFB03cient in Eq.(/two.pnum) is thus /uniFB01xed as 0:619for this patient and will be updated for future treat- ments as more data is acquired /three.pnum. initial estimates of BP are conducted with the population derived /uniFB01t until the /uniFB01rst new BP/line pres- sure measurement is received /four.pnum. the relationship y(t) =ax(t) +b(t) +(t))is updated according to Eq. /four.pnum /five.pnum. estimates of BP are conducted with the updated estimator /six.pnum. new measurements received /seven.pnum. repeat from item /four.pnum /four.pnum Results /nine.pnum complete treatment data sets were processed and subsequently analysed, characteristics of the patients in the study are given in Table /one.pnum Fig. /nine.pnum shows the typical updating of the model over an approximately /four.pnum-hour treatment period as new BP/line pressure measurements are acquired. The associated BP estimator for this treatment is shown in Fig. /one.pnum/zero.pnum. Blood pump /uniFB02ow for this treatment is consistent at 280ml=min . The initial estimate at /three.pnum/five.pnum/zero.pnum/zero.pnums is based upon the initial population /uniFB01t model and exhibits a relatively wide divergence from the incoming accurate BP measurement. Subsequent pairs show the incoming BP mea- surement, with the estimate from the predictor model prior to update, and exhibit improved accuracy /eight.pnum -140 -120 -100 -80 -60 -40 -20 Arterial Line Pressure (mmHg)406080100120140BP (mmHg)Initial Population Fit Fit 1 Measurement 1 Fit 2 Measurement 2 Fit 3 Measurement 3 Fit 4 Measurement 4 Fit 5 Measurement 5 Fit 6 Measurement 6 Fit 7 Measurement 7Figure /nine.pnum: IT/six.pnum/two.pnum Initial population /uniFB01t predictor, incoming measurements and predictor updates over /four.pnum hour treatment 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Time (s)-100-50050100150200250300Pressure (mmHg) Flow (ml/min)Brachial Cuff Measurement Predicted BP Arterial Line Pressure Dialyser Blood Pump Flow Figure /one.pnum/zero.pnum: IT/six.pnum/two.pnum measured and predicted BP , arterial line pressure and blood pump /uniFB02ow over /four.pnum hour treat- ment when compared to the /uniFB01rst estimate in all patients. Performance of the estimator scheme for patients in the study is shown in Table /two.pnum. Maximum errors are exclusively associated with the initial estimates derived from the population model. Errors then tend to decrease signi/uniFB01cantly after the /uniFB01rst BP update. The average RMS error for all the sessions analysed here (including initial modelling error) is 11:5mmHg . Eliminating the initial modeling error reduces the average RMS error to 7:9mmHg Finally for completeness, we can examine the performance of the estimator against dynamic, continuous BP measurement (Fig. /one.pnum/one.pnum). There is reasonable performance in tracking the cu/uniFB00 BP measurements, how- ever, with the continuous BP measurement provided by the Fiapres Nova /uniFB01nger cu/uniFB00 there are obvious shortcomings. This is to be expected when comparing the performance of a steady-state linear model against the output of a dynamic non-linear system. /nine.pnum Table /two.pnum: Estimator performance over treatment sessions when compared to incoming BP measurements (mmHg) Patient RMS Error Max Error Min Error IT/six.pnum/two.pnum /one.pnum/two.pnum./two.pnum/seven.pnum /two.pnum/six.pnum./three.pnum/eight.pnum /zero.pnum./seven.pnum/one.pnum IT/five.pnum/eight.pnum /seven.pnum./four.pnum/seven.pnum /one.pnum/four.pnum./eight.pnum/nine.pnum /two.pnum./zero.pnum/eight.pnum IT/five.pnum/seven.pnum /one.pnum/one.pnum./one.pnum/nine.pnum /two.pnum/one.pnum./one.pnum/seven.pnum /zero.pnum./three.pnum/eight.pnum IT/five.pnum/four.pnum /two.pnum/eight.pnum./four.pnum/eight.pnum /five.pnum/one.pnum./four.pnum/five.pnum /one.pnum./seven.pnum IT/six.pnum/two.pnum /one.pnum/one.pnum./five.pnum/one.pnum /two.pnum/eight.pnum./six.pnum/eight.pnum /zero.pnum./three.pnum/eight.pnum IT/six.pnum/zero.pnum /seven.pnum./four.pnum/seven.pnum /one.pnum/eight.pnum./nine.pnum /one.pnum./two.pnum/two.pnum IT/five.pnum/seven.pnum /one.pnum/two.pnum./nine.pnum/four.pnum /two.pnum/five.pnum./six.pnum/eight.pnum /one.pnum./zero.pnum/six.pnum IT/five.pnum/six.pnum /six.pnum./seven.pnum/six.pnum /one.pnum/three.pnum./zero.pnum/eight.pnum /zero.pnum./seven.pnum/seven.pnum IT/five.pnum/five.pnum /five.pnum./five.pnum/six.pnum /one.pnum/four.pnum./three.pnum/three.pnum /two.pnum./zero.pnum/one.pnum 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Time (s)-100-50050100150200250Pressure (mmHg) / Flow (mL/min)Arterial Line Brachial MAP Estimated MAP Reconstructed MAP Blood Pump Flow Figure /one.pnum/one.pnum: IT/five.pnum/seven.pnum measured and predicted static and dynamic BP , arterial line pressure and blood pump /uniFB02ow over /four.pnum hour treatment /five.pnum Conclusion A non-invasive, recursive BP estimator has been designed and analysed on real-time data sets from an observational patient study. The parameterised run-to-run adaptive model described is initially /uniFB01tted to data from the study population, and subsequently updated with the individual’s line and BP data when it is available. The problem of de/uniFB01ning initial conditions for the estimator model and reliance on sparse update data is extremely challenging. There are a number of signi/uniFB01cant outcomes from this phase of the research programme. Firstly, in this study, and a previous /five.pnum/zero.pnum patient study which examined heart rate and blood pressure variability in dialysis treatment [/two.pnum/nine.pnum], it is apparent that continuous monitoring technology currently faces challenges in applications with long treatment times. The method described in this paper successfully conducts estimation of BP based only on the pressure measurements from sensors placed in the dialysis lines, and intermittent BP measurements. As such it ful/uniFB01lls the requirements of a usable non-invasive, continuous estimator. In its current form, the estimator can track trends in patient BP albeit with an average RMS error of 7:9mmHg between prediction and updated BP measurement. Consequently, it represents a signi/uniFB01cant step forward in this area as the ability to repeatably track changes in BP rather than measure instantaneous BP with high levels of accuracy is currently a critical necessity during treatment. Examination of Fig. /one.pnum/one.pnum reveals the mis- match between the performance of the linear steady-state model and the non-linear dialyser-physiological patient dynamics. Future work will develop a non-linear parameterised model estimator, which will still utilise measured BP updates, but will have more reliance on the complex interaction between the venous and arterial lines real-time pressure measurements. In this way, the model will have less reliance on a pop- ulation model for initial conditions, and in particular will be able to estimate both steady-state and dynamic BP response, which should enable more accurate real-time estimates rather than trend estimation from /one.pnum/zero.pnum the current estimation scheme. Acknowledgments The authors would like to thank Mel Morris and the MStart Foundation for funding the iTrend research programme, and the support of the Royal Derby Hospital Renal Unit. US Patent O/uniFB03ce & Overseas License /six.pnum/two.pnum//eight.pnum/five.pnum/five.pnum/zero.pnum/six.pnum/nine.pnum MEASURING PRESSURE WAVES IN DIALYSIS LINES TO DE- RIVE CONTINUOUS ARTERIAL BLOOD PRESSURE Prof Paul Stewart, Prof Jill Stewart, et al. iTrend Medical Research Ltd.