Intradialytic haemodynamic instability is a signi/uniFB01cant clinical problem, leading to end-organ ischaemia and contributing to morbidity and mortality in haemodialysis patients. Non-invasive continuous blood pressure monitoring is not part of routine practice but may aid detection and prevention of signi/uniFB01cant falls in blood pressure during dialysis. Brachial blood pressure is currently recorded intermittently during haemodialysis via a sphygmomanometer. Current methods of continuous non-invasive blood pressure monitoring tend to restrict movement, can be sensitive to external disturbances and patient movement, and can be uncomfortable for the wearer. Additionally, poor patient blood circulation can lead to un- reliable measurements. In this feasibility study we performed an initial validation of a novel method and associated technology to continuously estimate blood pressure using pressure sensors in the extra- corporeal dialysis circuit, which does not require any direct contact with the person receiving dialysis treatment. The paper describes the development of the measurement system and subsequent in vivo patient feasi- bility study with concurrent measurement validation by Finapres Nova experimental physiological mea- surement device. We identify a mathematical function to describe the relationship between arterial line pressure and brachial artery BP , which is con/uniFB01rmed in a patient study. The methodology presented re- quires no interfacing to proprietery dialysis machine systems, no sensors to be attached to the patient di- rectly, and is robust to patient movement during treatment and also to the e/uniFB00ects of the cyclical pressure waveforms induced by the hemodialysis peristaltic blood pump. This represents a key enabling factor to the development of a practical continuous blood pressure monitoring device for dialysis patients. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. /one.pnum Introduction Patients receiving hemodialysis treatment as a result of end-stage kidney disease (ESKR) are at a much higher risk of mortality due to cardiovascular disease (CVD) [/one.pnum]. A key factor contributing to CVD is intra- dialytic hypotension, a frequent complication a/uniFB00ecting 1550% of treatments which is associated with subsequent vascular access thrombosis, inadequate dialysis dose, cardiac dysfunction and mortality. The continuous monitoring of blood pressure (BP) during dialysis, particularly with respect to early detection and prediction of hypotension [/two.pnum] has the potential to signi/uniFB01cantly improve patient outcomes [/three.pnum, /four.pnum, /five.pnum] and could ultimately inform the choice of therapeutic intervention via modulation of dialysis time and/or du- ration, dialysate sodium concentration and/or temperature on a per patient basis. Intradialytic hypotension (IDH) is a sudden event, and generally de/uniFB01ned as a decrease in systolic blood pressure greater than 20mmHg or a decrease in mean arterial pressure by 10mmHg [/six.pnum]. Associated symptoms can include dizziness or fainting, anxiety, muscle cramps, abdominal discomfort, nausea and vomiting. In addition to the negative impact on patient well-being, IDH can result in truncated dialysis treatments and increase the risk for coronary and cerebral ischemic incidents. The ability to detect im- 1 pending IDH with su/uniFB03cient time and accuracy to mitigate, is the primary goal of this work to develop a non-invasive continuous estimation of brachial blood pressure. Arterial cannulation is widely regarded as the gold standard reference for continuous measurement of BP [/seven.pnum], (which is referenced to brachial artery BP in common with all the methods discussed here). While a common procedure during high-risk surgery, it is not considered appropriate for haemodialysis patients where non-invasive monitoring is indicated. This is normally achieved in a clinical setting via the use of an air-/uniFB01lled occluding arm cu/uniFB00 that provides a robust, but intermittent measurement that disrupts the normal blood /uniFB02ow, and so requires a signi/uniFB01cant settling time between measurements [/eight.pnum]. Three distinct methods for non-invasive monitoring of BP have occasionally been used in research settings. The /uniFB01rst of these is arterial applanation tonometry [/nine.pnum] where a transducer is positioned above a super/uniFB01cial artery compressing it against an underlying bone. Analysis of the resulting pulse wave has been extended to calculate systolic and diastolic pressure [/one.pnum/zero.pnum].This method has been used in cardiology and anaesthetised procedures to avoid the insertion of an arterial cannula [/one.pnum/one.pnum, /one.pnum/two.pnum], but as these devices are hand-held and are operator dependent, they are unsuitable for continuous monitoring. The second method for non-invasive continuous estimation of BP is Pulse Transition Time (PTT) [/one.pnum/three.pnum] which is based on measured photoplestimography (PPG) and electrocardiogram (ECG) signals during several cardiac cycles. PTT is then calculated as the time di/uniFB00erence between the ‘R’ peak in the ECG signal and the corre- sponding time instance of the in/uniFB02ection point on the maximum slope of the PPG signal. This method may not be accurate due in part to the unaccounted physiological factors in the blood regulation mechanism and reliance on accurate ECG triggering [/one.pnum/four.pnum] The third alternative is the volume clamp (or vascular unloading) method [/eight.pnum] where an in/uniFB02atable /uniFB01nger- cu/uniFB00 combined with an embedded photodiode measures the diameter of the /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, for ex- ample, dialysis patients [/one.pnum/three.pnum]. All three non-invasive methods are sensitive to patient movement (especially ECG signals) [/one.pnum/five.pnum] which would result in an unacceptable and uncomfortable restriction placed on patients during a four-hour dialysis treatment. /one.pnum./one.pnum The iTrend Renal Dialysis Programme 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. The primary goal of the programme is to develop supporting tech- nologies and real-time analysis of data to enable personalised and precision treatment in ESKD [/one.pnum/six.pnum, /one.pnum/seven.pnum]. Blood pressure monitoring to diagnose hypertension and hypotension [/one.pnum/eight.pnum, /one.pnum/nine.pnum] are typically plethorperidia- lytic 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. In this work, a feasibility study based around a novel method for continuously monitoring BP is described which involves the placement of pressure transducers onto the venous and arterial blood lines that connect a patient to a haemodialysis machine during treatment. The resulting data is compared against standard BP measurements obtained via an occluding arm cu/uniFB00 and the volume clamp method, via the Finometer (FMS, Finapres Measurement Systems, Arnhem, Netherlands), whose accuracy has been studied [/nine.pnum, /one.pnum/zero.pnum] and validated according to the recent British Hypertension Society protocol and the criteria of the Associ- ation for the Advancement of Medical Instrumentation. /one.pnum./two.pnum Structure of this paper This paper describes the development of a continuous, non-invasive method to measure BP during renal dialysis sessions. Design objectives were as follows: •to provide reliable and robust measurement of patient blood pressure before, during and immedi- ately after haemodialysis treatment; /two.pnum •with regards to patient experience, to require no extraneous sensors to be attached directly to the patient; •the measurement method to be robust to patient movement during treatment; •the sensors to be cost-e/uniFB00ective, non-bespoke and readily available as o/uniFB00 the shelf items; •data aquisition and analysis hardware to be low physical footprint and low cost; •the system should not require any special interfaces to and should work equally well with any pro- prietary dialysis machine. The paper is divided into the following sections: •Section II: A generalised parameterised model is derived to describe the approximate relationship between measured brachial cu/uniFB00 pressure measurements and arterial line pressure measurements during hemodialysis treatment. •Section III: The feasibility study data acquisition system and associated hardware is described along with experimental study participants and the dialysis bay experimental setup. •Section IV: Results from the experimental feasibility study are graphically displayed and analysed. •Section V: Conclusions derived from the study are presented, and future work described. For clarity, where a patient’s BP is mentioned, this should be taken to mean brachial blood pressure. /two.pnum Continuous, non-invasive intradialytic BP measurement from dialysis lines Figure /one.pnum: Sensor and data acquisition signal /uniFB02ow The use of pressure signals from the arterial and venous blood lines of a dialysis machine has been shown in principle to enable continuous online monitoring of a patient’s heart rate, even for patients with low cardiac signal amplitude [/two.pnum/zero.pnum, /two.pnum/one.pnum]. The method has been extended to monitor ventricular premature beats [/two.pnum/two.pnum]. Performance was studied for one dialysis /uniFB02ow rate ( 400ml=min ), and results lacked /uniFB01delity where patient heart rate and haemodialysis pump speed coincide. While promising, the method generated to a number of false positive and false negative predictions of IDH. Our approach demonstrates a more robust approach to derive continuous BP signals from the arterial and venous dialysis lines and presents the initial results of its in-vivo veri/uniFB01cation via an on-going patient study in the Renal Unit at Royal Derby hospital. /three.pnum /two.pnum./one.pnum Method The aim of this feasibility study is to identify and experimentally derive relationships between the patient’s brachial BP , and the pressures recorded within the extra-corporeal blood lines to and from the dialysis machine. Typically, two such blood lines are provided during haemodialysis: an arterial line conducts blood from the patient to the dialysis machine, and a venous line that conducts blood from the dialysis machine back to the patient. Vascular access to the patient is provided by means of two large gauge needles (one on each line) into the patients ‘/uniFB01stula’, a surgically enlarged blood vessel resulting from the connection of a vein onto an artery, typically located within the patients non-dominant arm. In order to develop a non-hardware speci/uniFB01c generalised solution to the problem, additional pressure sen- sors were placed into the blood lines rather than making use of the pressure sensors present within the dialysis machines (as in previous studies) who’s primary function of these safety critical machine sensors is setup monitoring. This study utilised the existing ports and connection points which are common and standardised on most dialysis blood lines sets (Fig /one.pnum). Starting on the blood return side (Fig /one.pnum) venous blood line provides a standard /four.pnummm line connection point on the air trap, which was chosen as the site for the additional venous line pressure sensor. This is typically the /uniFB01nal port on the venous side (Fig /two.pnum). Figure /two.pnum: Pressure sensor connection to venous air trap port As will be seen, the blood /uniFB02ow rate through the extra-corporeal system is critical to analysis of the relation- ship between brachial and arterial line blood pressure measurements. A real-time measurement of blood /four.pnum /uniFB02ow is required for the calculations necessary for BP estimation. Flow rate is generally set at the beginning of treatment, and recorded manually. For various clinical reasons, medical professionals may adjust the /uniFB02ow rate during treatment which may or may not be recorded in patient notes. The pressure waveform measured by the pressure sensor connected to the venous bubble trap is domi- nated by the oscillations introduced by the lobes of the peristaltic blood pump [/two.pnum/three.pnum]. The periodic pressure waveform of such pumps results from alternative compression and relaxation of the dialysis line (typically 8mm diameter at the pump) by the (typically /two.pnum) lobes of the pump. Hence the pump frequency can be derived from a real-time positive pressure sensor sited in the venous air trap by the application of Fourier analysis. By this method, any reasonably well-behaved function can be written in terms of trigonometric or exponential functions. Considering a function f(x)that is periodic on the interval 0xL, Fourier’s theorem states that f(x) can be written as the Fourier trigonometric series for the function as; f(x) =a01X n=1 ancos2nx L +bnsin2nx L (/one.pnum) As2is included in the arguments of the trigonometric functions, then the n= 1 terms have period L, then= 2 terms have period L=2, etc. for higher harmonics. For any integer n, an integral number of oscillations /uniFB01t into the period L. In the case under examination here, the fundamental frequency of the blood pump is sought, so calculations are on for n= 1. The pump frequency is calculated and updated in real-time over a sliding window of data which is /five.pnum/zero.pnum/zero.pnum/zero.pnum samples or/five.pnumswide. As the pump frequency is typically around 1Hz, this ensures su/uniFB03cient data, without including dynamics, so e/uniFB00ectively a quasi steady-state measurement. Frequency is converted to /uniFB02ow in units ofmls1by fl=fr(rads1) 2 60  r2Ln (/two.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. Brachial pressure is regu- larly measured via in/uniFB02atable cu/uniFB00, and data for all the sensors is synchronised and stored via a National Instruments data acquisition device. The additional pressure sensor on the arterial-line should be sited as close as possible to the patient’s vascular access, since the needle sits between positive pulsatile patient blood pressure at one end, and blood-pump dominated negative pulsatile pressure at the other end. Given that no suitable connector exists at the arterial needle end of the line, a ‘Y’ connector with /four.pnummm internal diameter is /uniFB01tted to the tbing of the dialysis needle to allow access to both the dialysis line and the arterial line pressure sensor (Fig. /three.pnum). Modelling the relationship between arterial-line pressure and brachial pressure is extremely complex with high levels of physiological di/uniFB00erences between patients. In order to produce a tractable model, a number of approximations are included. The brachial cu/uniFB00 measurement is, in e/uniFB00ect, a quasi-steady state mea- surement single-instance sample of systolic and diastolic pressure including no dynamic information, and hence the arterial line pressure is /uniFB01ltered by /five.pnum/zero.pnum/zero.pnum/zero.pnum samples moving-average window, similar to the /uniFB01lter applied to the venous-line pressure data. With reference to Fig /four.pnum, datum point 1is de/uniFB01ned as the tip of the arterial line needle, and associate pressure P1and areaA1with it. Similarly, datum point 2is de/uniFB01ned at the pressure sensor, and associate pressure P2and areaA2with it. Assuming steady, incompressible /uniFB02ow with negligible losses, blood /uniFB02ow rate can be expressed using Bernoulli and Continuity equations [/two.pnum/six.pnum] as; f=A22 6642 (P1P2) R 1 A2 A123 7751 2 (/three.pnum) /five.pnum Figure /three.pnum: Arterial line pressure sensor connector where f is /uniFB02uid /uniFB02ow and R is the /uniFB02uid density. A number of assumptions are inherent in this model; horizontal /uniFB02ow and fully developed /uniFB02ow at P1and P2, density and viscosity are constant wrt time. However, many, if not all, of these assumptions are either unmeasurable, or vary in practice from patient to patient, or are time-varying during treatment. Addition- ally, the temporal and physical distance between the /uniFB01stula needle site and the measurement site at the brachial cu/uniFB00 (typically on the opposite arm to the /uniFB01stula) is signi/uniFB01cant ( ~1m). Even for well de/uniFB01ned problems, theoretical /uniFB02ow fis generally 240% lower than empirical due to geometry. Therefore, (/three.pnum) is modi/uniFB01ed as f=A22 (P1P2) C1 2 (/four.pnum) whereCis an experimentally determined lumped-parameter which approximates the unknown and un- modelled features of the system and the unmet assumptions of the analysis. The lumped parameter in- herently includes the e/uniFB00ect of di/uniFB00erent dialysis procedural details such as the needle gauge size that may be used with di/uniFB00erent patients, and blood pump /uniFB02ow-rate according to di/uniFB00erent treatment prescriptions. Individual patient-speci/uniFB01c parameters such as blood viscosity, density and temperature are also implicit. /six.pnum Figure /four.pnum: Arterial line and needle pressure datum points Rearranging for C C=2 (P1P2)  f A22(/five.pnum) the expression allows computation of Cfrom measured values. Assuming P2represents measured arterial line pressure as before, and the lumped unknown parameters coe/uniFB03cient Cincludes the unknown relation- ship between P1and measured brachial pressure Pb, then a quasi-linear relationship between arterial line pressure and brachial pressure can be derived from equation (/five.pnum), if and only if the unknowns represented by the variable Care accurately modelled and time-invariant. The relationship is given by P2= 0:5F A22 CPb (/six.pnum) whereCde/uniFB01nes the gradient of the relationship and can subsequently be used as a predictor between measuredP2and estimated Pb. Given the expectation that C will contain time varying and unmodelled terms, it can be predicted that there will be variation around the mean for individual patient measure- ments. Future and continuing work may identify a more accurate description of the system, however the linear model derived here and presented in the study data con/uniFB01rms the feasibility of the approach. /three.pnum Experimental Hardware Low-cost industrial process control pressure sensors with on-board signal ampli/uniFB01cation and linearization (Honeywell /four.pnum/zero.pnumPC/zero.pnum/one.pnum/five.pnumV/two.pnumA /zero.pnum PSI to -/one.pnum/five.pnumPSI Arterial line, and Honeywell /four.pnum/zero.pnumPC/zero.pnum/one.pnum/five.pnumG/one.pnumA /zero.pnumPSI to /one.pnum/five.pnumPSI Venous line) have been integrated (Fig /one.pnum/one.pnum) with connectors to /uniFB01t ports on standard dialysis lines. The connectors consist of a 4mm internal diameter line, a pressure transducer protector which keeps the blood side of the circuit separated from the sensor, preventing patient cross contamination with blood borne pathogens via a/zero.pnum./two.pnum micron /uniFB01lter. There is also a bespoke membrane barrier (Fig./three.pnum) /uniFB01tted as an extra safety precaution. [/two.pnum/four.pnum, /two.pnum/five.pnum] /one.pnumafter: https://commons.wikimedia.org/wiki/File:Hemodialysis-en.svg /seven.pnum Real-time data acquisition (DAQ) and storage is performed via a National Instruments NI USB-/six.pnum/two.pnum/one.pnum/zero.pnum/two.pnum, /one.pnum/six.pnum input /one.pnum/six.pnum-bit, 250kS=s multifunction I/O device. All acquisition is analogue, sampled at 1kHz on each line. Analogue input lines operate in the range 0to5V. Data from the Finapres Nova is transferred to the National Instruments device via dedicated multicore cable. The following Finapres Nova analogue output lines were acquired by the DAQ hardware: •Reconstructed systolic pressure •Reconstructed diastolic pressure •Finger arterial pressure •ECG II waveform •Reconstituted brachial arterial pressure •Brachial arm-cu/uniFB00 measurements Additionally the venous air trap pressure sensor and Arterial line pressure sensor are connected via ded- icated shielded cables, which include +5Vand0Vsupplies to power the sensors from the acquisition device. All data streams are time synchronised via a common real-time clock. /three.pnum./one.pnum Experimental Study Figure /five.pnum: Dialysis bay experimental setup, (l) foreground /uniFB01napres Nova; (l) background National Instruments device; (r) Dialysis machine Method: Participants >/one.pnum/eight.pnum years were recruited from the prevalent dialysis population at Derby Royal Hos- pital. Patient’s demographics, dialysis background, dialysis prescription, laboratory parameters pre- and post-dialysis at each session were recorded. 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 this data was periodically veri/uniFB01ed by intermittent arm-cu/uniFB00 measurements. Two pres- sure sensors were attached to the dialysis lines as described: 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 (Fig./five.pnum). The study protocol was approved by the West Midlands - Coventry and Warwickshire Research Ethics Com- mittee and participants gave written informed consent. /two.pnumhttps://www.ni.com/pdf/manuals//three.pnum/seven.pnum/five.pnum/one.pnum/nine.pnum/four.pnumd.pdf /eight.pnum /four.pnum Results 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). Serial brachial cu/uniFB00 blood pressure values were compared with synchronous pressure sensor data in Matlab (ver. /one.pnum/nine.pnumb). Arterial line pressure sensor data was analysed for dialysis pump /uniFB02ow by /uniFB01tting a Fourier model to the continuous venous line pressure signal. Derived pump /uniFB02ow, arterial and venous line pressures, and brachial cu/uniFB00 pressure measurements for a typical treatment session (Patient IT/five.pnum/seven.pnum) are shown in Fig./six.pnum. Val- ues from the brachial arm cu/uniFB00 ( Systolic, Diastolic and MAP ) are saved to a master record with synchronised time stamps for comparison with the corresponding venous and arterial line pressures. This master record for the patient study enables the calculation of lumped parameter C. In this example (Fig /six.pnum), the dialysis blood pump is enabled at 2000sresulting in divergence of the arterial (ve)and venous ( +ve) line pressures. Subsequently, the Fourier model outputs a /uniFB02ow rate of 325ml=min which remains constant for the duration of the treatment, and agrees with the patient record. Brachial cu/uniFB00 BP measurements are taken from approximately /three.pnum/zero.pnum minutes before the start of treatment and repeated approximately every 30minutes throughout. The cu/uniFB00 measurements of systolic and diastolic BP and MAP are recorded via the DAQ system with a corresponding value for blood /uniFB02ow and for arterial pressure. In this case, it is possible to construct a table of 8measurements for this treatment, and a master data set can thus be constructed for the /one.pnum/one.pnum completed dialysis sessions which allows an analysis to be conducted against a varied participant population. Figure /six.pnum: Typical data output for /four.pnum-hour treatment session: Patient IT/five.pnum/seven.pnum In the Renal Unit at Royal Derby Hospital, where the patient studies are conducted, /one.pnum/four.pnumg is the standard and preferred gauge size for dialysis patients. Smaller diameter (larger gauge size) needles are used for new patients with recent /uniFB01stula, and also for patients with needling problems.The gauge sizes used during this patient study are: •/one.pnum/four.pnum: /one.pnum/four.pnumg Arterial /one.pnum/four.pnumg Venous •/one.pnum/five.pnum: /one.pnum/five.pnumg Arterial /one.pnum/five.pnumg Venous •/one.pnum/six.pnum: /one.pnum/five.pnumg Arterial /one.pnum/six.pnumg Venous where 14is the normal gauge set, and 15;16used for new patients and access issues. With reference to /uniFB01gure /seven.pnum, Cvalues are calculated for every measurement set in each treatment, and grouped according to patient’s needle gauge sizes, which shows the fundamental e/uniFB00ect of needle gauge size on the relationship between PbandP2measurements. Figure /seven.pnum also illustrates a number of salient /nine.pnum features. In particular, a relatively tight core grouping of Cvalues for each needle size set (/one.pnum/four.pnum: 57, /one.pnum/five.pnum: 89, /one.pnum/six.pnum:9:511). A rising mean of this core grouping ( 6,8:5,10:25) indicates the in/uniFB02uence of the reducing available area on the di/uniFB00erence between PbandP2. As expected, the /uniFB01gure shows a number of outlying measurements. In particular for needle gauge size 16, the outliers are all from a patient with a relatively new arteriovenous /uniFB01stulae (AVF), and may indicate that maturation of the blood vessel is not complete [/two.pnum/seven.pnum]. For all gauges, it is salient that the coe/uniFB03cient Cdescribes a range of linear and nonlinear unmodelled e/uniFB00ects beyond needle gauge size and would be expected to contain outliers in a physiologically non homogenous patient study population and can addi- tionally contain time varying e/uniFB00ects experienced over the duration of a /four.pnum hour treatment session. Figure /seven.pnum: Values of Cassociated with Arterial and Venous needle sizes 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 /eight.pnum. A linear least squares /uniFB01t of y= 0:8x1:5e+02, 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. As predicted, the /uniFB01gure displays a correlated scatter for the population around a linear least squares /uniFB01t with a gradient which represents a fundamen- tal relationship between PbandP2. This is common to all members of the study, and hence 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 e/uniFB00ects. This is a signi/uniFB01cant outcome for the project, as it means that the process of real-time prediction can be decomposed into two separate functions. Namely, updating the machine mean relationship to take account of any hardware variances between machine sets (new machine and or lines can be modelled into a library), and learning the rela- tionship to the machine line on a per patient basis (which again can be an updateable model). In order to further examine this hypothesis, it is possible to negate the time varying e/uniFB00ects in the data by taking a mean value for Cfor each individual patient treatment, and recalculating the data scatter. This should reduce data variance since the scatter around the least squares /uniFB01t line consists of two components: time varying e/uniFB00ects, and unmodelled physiological e/uniFB00ects, and also to a certain extent negate the time varying e/uniFB00ects in the data by taking a mean value for Cfor each individual patient treatment, and recalcu- late the data scatter. This is shown in /uniFB01gure /nine.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 a tractable and useable time-invariant model can be constructed. Finally, although the majority physical systems can be modelled adequately by linear, time-invariant models, there is much to be gained in future work develop- ing time-variant, non-linear models of these speci/uniFB01c systems. Overall, data from this /uniFB01rst feasibility study indicates that a linearised model for individual patients, patient populations and machine sets can be calcu- /one.pnum/zero.pnum Figure /eight.pnum: Brachial cu/uniFB00 MAP vs Arterial line pressures in /one.pnum/one.pnum patient sessions (o) with least squares linear /uniFB01t (+) lated which de/uniFB01nes a linear relationship between measured arterial line pressure and measured brachial artery pressure. The feasibility study thus con/uniFB01rms that it is practically possible to estimate brachial BP continuously and non-invasively during the period of a dialysis session in a clinical setting with measure- ment of venous and arterial line pressure, and occasional measurement of brachial blood pressure by arm cu/uniFB00. /five.pnum Conclusion The objective of this patient study was to answer a pressing question in dialysis treatment, whether a method could be developed which demonstrates the feasibility of continuous non-invasive blood pressure monitoring, without compromising patient experience and without requiring bespoke interfacing to the dialysis machine, or any additional sensing to be worn by the patient beyond current arm cu/uniFB00 monitoring requirements. An approximate mathematical model relating arterial line pressure, blood pump /uniFB02ow rate and brachial pressure was derived, which predicts a quasi-linear relationship between arm cu/uniFB00 measured pressure, and corresponding pressure measured in the arterial line near to the /uniFB01stula. Interfaces, measurement devices and a data acquisition were designed and built to support an observational study during renal dialysis treatment. The results from this observational study suggest that it is feasible to derive a continuous measurement of brachial pressure from continuous measurements of arterial and venous line pressures via an empirically based and updated mathematical model. Potential exists to identify a more complex and hence more accurate parametric model. The study presented here is critical to con/uniFB01rming that the fundamentals of this approach are feasible, and the results have con/uniFB01rmed that the methodology and technology has a practical future in renal units. There are a number of challenges following directly from this work which will be addressed in current and future algorithmic/technological developments and studies. In particular, iterative learning algorithms to update the mathematical models based upon incoming cu/uniFB00 BP measurements, improved mathematical models to increase estimation accuracy, and predictive models for hypotension. Patient studies are about to start at Royal Derby Hospital to demonstrate, analyse and improve the continuous estimation of brachial BP in real-time for the complete duration of dialysis treatments. Further work will report on the outcome of /one.pnum/one.pnum Figure /nine.pnum: Brachial cu/uniFB00 MAP vs Arterial line pressures in /one.pnum/one.pnum patient sessions (o) with least squares linear /uniFB01t (+) following compensation for time varying e/uniFB00ects during treatment these studies. 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.