Life-threatening complication detection during hemodialysis using fractional order info-gap decision-making

Abstract

Vascular access stenosis and venous needle dislodgement (VND) are frequent and serious life-threatening complications during hemodialysis (HD). According to dialysis survey reports, these complications are key issues for nephrology nurses, medical staff, and patients. Existing detection techniques and early warning tools provide promising solutions in these issues. However, these methods cannot screen for stenosis and VND complications during HD. Clinical examinations show that increases in transverse vibration pressure (TVP) are highly correlated with stenosis screening in arterial anastomosis sites (inflow needle); conversely, TVP drops in the event of a blood leak or VND in venous anastomosis sites (outflow needle). As an early-warning implementation, this study proposes a combination of fractional order integrator (FOI) and info-gap (IG) decision-making to detect these complications. FOI is used to calculate the TVPs’ area under curve (AUC), while AUC ratio (AUCR) quantifies the differences in TVPs between the normal condition and pressure sensor reading. An estimated function of the two-point form shows that AUCRs have a high correlation with TVP variations. Therefore, AUCR is employed to identify changes in TVPs and arrange specific allocations. The IG decision-making scheme produces inference profiles with specific allocations to separate the normal cases from vascular access stenosis or VND/blood leakage. The test results obtained from practical experiments were validated and compared with the results obtained using existing methods such as acoustic techniques, warning products, and homodynamic analysis. The findings also show that the proposed framework employing pressure sensors can be implemented in an early warning monitor for clinical and telemedicine applications.

Keywords

Life-threatening complication fractional order integrator (FOI)info-gap (IG) decision-making transverse vibration pressure (TVP)area under curve ratio (AUCR)

1. Introduction

Hemodialysis (HD) is a routine treatment prescribed three days a week for end-stage renal disease (ESRD) patients. Some life-threatening complications frequen- tly occur during HD, such as vascular access stenosis, venous needle dislodgment (VND), and serious blood loss. These complications cause morbidity and mortality, while early clots and progression of thrombosis result in reduced blood flow through an arteriovenous fistula (AVF) or an arteriovenous graft (AVG) [1, 2]. Blood circuit disconnection and dislodgement of the venous needle from vascular access result in rapid blood loss [3, 4]. Significant stenosis, defined as a decrease of $>$ 50% in normal vascular diameter accompanied by hemodynamic or clinical abnormality, leads to non-substantial intra-graft blood flow; the intra-graft flow thresholds of an AVF and an AVG are $<$ 600 ml/min and $<$ 400–500 ml/min, respectively. Surgical treatment or percutaneous transluminal angioplasty is required to dilate the stenotic access in the case of a $>$ 70% decrease in the lumen diameter.

Other life-threatening complications, such as HD machine stop and VND, result in blood circuit disconnection, blood leak, and blood loss. In HD treatment, a blood flow rate of 400–500 ml/min can loss more than 40% of the adult blood volume in a few minutes [5]. When a VND occurs in the patient, a flow rate of 200–500 ml/min is usually discovered after about 20 s. The loss of $>$ 500 ml of blood when the reaction time is $<$ 2.5 min reaction time is considered a severe case. According to an American Nephrology Nurses’ Association (ANNA) VND survey report [6], more than 75% of the surveyed candidates indicated they had seen VND events, and more than 8% indicated having seen 5 events in the last five years. An HD machine pumps a patient’s blood in a pull-push manner from the arterial anastomosis (inflow) site, passes it through a dialyzer and then returns it to the venous anastomosis (outflow) site. An HD machine has various system malfunction alarms based on inflow/outflow pressures, blood leak, pump flow, and temperature monitors [7, 8]. However, these functions do not permit early detection of the progress in the narrowing of the vascular access and blood leaks during HD. In clinical examinations, AVGs have a higher patency rate in stenosis development at the outflow sites, leading to increased flow resistances, decreased vessel compliances, and high-pressure pulsatile flows, due to venous neo-intimal hyperplasia and thrombosis [9]. Thus, the elastic vascular wall causes vibration behaviors in the vascular access route, while squeezes the low axial blood flow along the axial direction because of transverse vibration pressures (TVPs). A stenotic access causes decreases in vessel compliance as the amplitudes of TVP increase with the degree of stenosis (DOS) [10, 11]. This information is important in the detection of thrombosis or the progress of a stenosis at the inflow site. In addition, a HD machine also has the ability to measure venous pressure to monitor VND with specific alarm ranges, $-$ 30 mmHg/ $+$ 70 mmHg, during the HD [12, 13]. When a venous needle is dislodged, the pressure drops are used to detect VND at the outflow site and to stop the roller pump. Therefore, this information will allow life-threatening complication detection in AVGs and AVFs (end-to-side anastomosis) during routine HD treatment.

Figure 1.

The proposed fractional order info-gap (IG) decision-making model.

Figure 2.

Equivalent human cardiovascular system. (a) In-vitro AVG biophysical experimental model, (b) Venous needles, (c) Stenotic accesses, DOS $=$ 50%–95%.

For clinical examinations of arterial and vascular stenosis, acoustic methods such as phonoangiography (PAG), Doppler ultrasound, and Doppler flowmeter [11, 14, 15] are well-known non-invasive techniques. Previous studies have indicated that PAG can be employed to estimate the DOS at venous anastomosis sites. However, changes in frequency and amplitude are dependent on the numbers of stenosis and monitoring sites, and the degree of severity of stenosis. Ultrasound waves of frequencies 7.5–10 MHz can be used to measure the peak systolic velocity (PSV), peak diastolic velocity (PDV), and heart rate for vessels with a diameter of 5–12 mm [16]. The Reynolds numbers and resistance indexes can be used to identify both cardiovascular diseases and vascular access stenosis by using the PSV and the PDV. However, these techniques cannot be used to detect VND events during HD. For severe blood loss, a pad device can be used as an early warning mechanism, for example, the use of a wetness sensor or an optical sensor (CE Mark, Redsense ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ Monitor, Halmstad, Sweden, FDA-Approved) [3, 17] to detect blood loss at access cannulation sites. However, these devices are not sensitive to clear but conductive fluids such as saline and cannot stop the HD machine because of the absence of a human interface. Therefore, the purpose of this study is to use the fractional order info-gap (IG) decision-making model to identify vascular access stenosis and VND in experimental examinations, as shown in Fig. 1.

A blood pressure wave (BPW) generated by a heartbeat propagates through the arterial vascular system and enters the extracorporeal blood circuit. BPWs can be measured by pressure sensors connected to the arterial and the venous blood circuits. According to previous studies [10, 11], vascular access stenosis leads to an increase in flow resistance and unstable flow. Vascular compliance also varies according to the pressure–blood volume relationship. Elastic vascular walls are subjected to stress under the biomechanical forces acting on them, and vibrations are induced in a stenotic access due to TVP. As the TVP amplitude increases, variations in TVP can be used to evaluate the DOS at the inflow site [18]. In addition, blood leakage or a severe blood loss will cause the TVP amplitude to decrease and has a low correlation with heart pulses at the outflow site. Therefore, TVP variations are used to identify vascular access stenosis and VND events both at the inflow and outflow sites, respectively.

BPWs can be ascribed to roller pump pressures and arterial access (fistula)/venous access (fistula) pressures through the extracorporeal blood circuit, as shown in Fig. 2. These indicate fluctuations and specific ranges of pressure variations in the BPWs. TVP waves move perpendicular to the direction of propagation of BPWs, and they can be extracted from BPWs. Using the detrending process [19, 20], the arterial/venous pressures, roller pump pressures, and mean vascular access pressures are determined [3] for further analysis. Its process emphasizes the prices fluctuations to separate the trends and variations. For real-time analysis, discrete fractional order integrator (FOI) [21, 22, 23, 24] with finite computations, short-memory requirement, and a finite power series are employed to calculate the TVPs’ area under curve (AUC) [25]. Then, the ratio of the AUC of the measured TVP to that of the normal TVP is determined to identify vascular access stenosis and VND events. The IG decision-making [26, 27, 28] scheme uses a screening model to automatically separate the levels of stenosis: DOS% $=$ 50–70% and DOS $>$ 70%; and VND: blood loss and major blood loss.

Figure 3.

(a) Normalized TVPs versus time interval, (b) Average pressure versus average blood flow for arteriovenous stenosis and venous needle dislodgement.

2. Experimental setup

Figure 2 shows the equivalent human cardiovascular system and the extracorporeal blood circuit for an HD patient, which represent the mock blood circulation in an experimental study. This experimental circulation system uses a roller pump as a pressure source regulator (Precision blood pump, COBE, LAKEWOOD, CO80215, USA), a liquid tank, silicone tubes as arteries and veins, and a stenotic graft. The roller pump simulates (40–80 rpm) various parameters of an adult’s blood circulation, such as heart beat, blood pressure, and pulsatile flow. It is used to control the flow rates, blood pressures, and heart rates during HD with a flow rate of approximately 600–1000 ml/min. A heart rate of 80–120 beats/min was used to drive the blood-mimicking fluid (BMF) through different stenotic grafts, as shown in Fig. 2c. The DOS is defined as follows [14, 15]:

$\textit{DOS}\%=\left[1-\left(\frac{d_{a}}{D_{a}}\right)^{2}\right]\times 100\%$ (1)

where $D_{a}$ is the diameter of the normal access in the direction of the BMF flow and $d_{a}$ is the diameter of the stenotic access. DOS values of 50–95% are considered in this study, while the inner diameters of a normal access were considered to have a circular cross-section with constant wall thickness, $D_{a}=$ 0.635 cm, for simulating arteries and veins [11]. In this study, a mixture of water and glycerin with a hematocrit ratio of 38–62%, kinematic viscosity of 3.2 $\times$ 10 ${}^{-6}$ m ${}^{2}$ /s, density of 1090 kg/m ${}^{3}$ , and temperature 28 ${}^{\circ}$ C was used as adult BMF. As seen in Fig. 2, the blood pressures, 90–150 mmHg, and flow rates, 600–400 l/min through an AVG biophysical model, were also confirmed that were adapted to simulate the various conditions on an in-vitro AVG biophysical experimental model. The DOS% $=$ 50%–95% of stenotic accesses were considered in this study, and the measurement sites were around the inflow sites and outflow sites, as shown in Fig. 2a.

The blood flow rates (ml/min) and blood pressures (mmHg) were measured at the inflow and outflow sites using a pressure monitor equipped with 22G-venous needles (Terumo Surflash), pressure sensors, and flowmeters, while are continually monitored on the BPWs screen, as shown in Fig. 2a and b. The measurement data was transferred to a tablet PC for further analysis using a data acquisition card (National Instruments™ Compact DAQ-9178 card, analog-to-digital converter, 8 channels, and 1 MHz sampling rate). Thus, the BPWs were obtained and distinguished from the roller pump pressures and mean vascular access pressures using the detrending process [19, 20]. As can be seen in Fig. 3a, the normalized TVPs were extracted from BPWs at inflow and outflow sites as follows:

$\displaystyle\textit{TVP}_{\textit{mea}}(t)=\frac{\det\textit{rend}(P_{\textit% {mea}}(t))}{\max(P_{\textit{nor}}(t))}$ $\displaystyle=\frac{\det\textit{rend}(P_{\textit{mea}}(t))}{P_{\textit{nor},% \max}}$ (2)

where detrend ( $\cdot$ ) is a function of the detrending process; $P_{\textit{mea}}(t)$ is the BPW determined from the incoming beat-by-beat measurement; $P_{\textit{nor}}(t)$ is the normal BPW and its average value is $P_{\textit{nor},\max}=$ 150–100 mmHg, which is stored in the database using the average of stable pulses of approximately 1–3 min.

Based on 36 measurements, when a graft’s inflow stenosis is exacerbated, the inflow pressure and flow resistance increase. TVPs induce vibrations of the elastic vascular wall. In contrast to normal TVP, the amplitude of a TVP increases gradually (symbol “ $+$ ”) at the inflow site; in terms of DOS%, the value is 50–90%. In addition, the blood flow rate may be insufficient and reduced during HD, as shown in Fig. 3b. The critical threshold of inadequate dialysis is $<$ 400 ml/min for AVGs. With 28 measurements, when a blood line is disconnected or venous needle is dislodged in the venous return circuit, a blow flow loss or reduction indicates a drop in the TVP amplitude (symbol “ $-$ ”), as shown in Fig. 3a. Thus, TVP amplitude variations can be used to define the risk levels of blood flow loss, with blood flows of $>$ 200 ml/min and reaction times $<$ 2.5 min reaction for an adult [3], as shown in Fig. 3b.

Changes in amplitudes and pulse shapes, andAUC [25] were employed to separate a normal TVP from TVP variations. In this study, the index of AUC ratio (AUCR) is used to evaluate the similarity and is defined as

$\displaystyle\textit{AUCR}=\frac{\textit{AUC}_{\textit{mea}}}{\textit{AUC}_{% \textit{nor}}}=\frac{\int_{t_{0}}^{t_{1}}{\textit{TVP}_{\textit{mea}}(t)dt}}{% \int_{t_{0}}^{t_{1}}{\textit{TVP}_{\textit{nor}}(t)dt}}$ (3) $\displaystyle\Rightarrow\textit{AUCR}=\begin{cases}>1,&\text{Arteriovenous % Stenosis }\\ \approx 1,&\text{Normal}\\ <1,&\text{Venous Needle}\\ &\text{Dislodgement}\end{cases}$ (4) $\displaystyle\textit{TVP}_{\textit{nor}}(t)=\frac{\det\textit{rend}(P_{\textit% {nor}}(t))}{P_{\textit{nor},\max}}$ (5)

where TVP ${}_{\textit{mea}}(t)$ and TVP ${}_{\textit{nor}}(t)$ are the measured TVP and normal TVP, respectively, and [ $t_{0}$ , $t_{1}$ ] is the time interval of each heart beat. An AUCR greater than 1 or less than 1 carry out an “Index” to identify vascular access stenosis and VND.

3. Methodology

3.1 Discrete fractional order integrator (FOI)

Fractional calculus is a generalization formula involving integration and differentiation operations, and its continuous non-integer order operator, $D_{t}^{\alpha}$ , $\alpha\in R$ , is defined as follows [21, 22, 23, 24]:

$_{t_{0}}D_{t}^{\alpha}=\begin{cases}{\displaystyle\frac{d^{\alpha}}{dt^{\alpha% }}},&\alpha>0\\ 1,&\alpha=0\\ \int_{t_{0}}^{t}(d\tau)^{\alpha},&\alpha<0\\ \end{cases}$ (6)

The Riemann-Liouville (R-L), Grünwald-Letnikov (G-L), and Caputo definitions are three well-known methods for derivative and integral numerical approximations.

Traditional integer integration and differentiation operations use integer-order differential operators with Tustin and Laplace transform methods, and trapezoidal integration methods for geometrical interpretations [21]. According to the G-L definition [24], a generalization formula for $\gamma$ -derivation of a continuous function $P(t)$ , $\gamma\in N$ , $i>\gamma$ , $i=0,2,3,\ldots,n-1$ , is defined as

$\displaystyle\frac{d^{\gamma}}{dt^{\gamma}}P(t)\approx\lim\limits_{\Delta\tau% \to 0}(\Delta\tau)^{-\gamma}\sum\limits_{i=0}^{n-1}(-1)^{i}\binom{\gamma}{i}$ $\displaystyle\quad∼{}P(t-i\cdot\Delta\tau)$ (7)

where $\gamma$ is a negative or positive integer, 0 $<\gamma<$ 1 for differentiation and $-$ 1 $<\gamma<$ 0 for integration, $\Delta\tau=(t_{1}-t_{0})/n$ is time step in time interval [ $t_{0}$ , $t_{1}$ ], and $n$ is the number of sampling data. Equation (3.1) is a linear combination of function values, $P(t)$ , in variable, $t$ . The binomial coefficients of integer $\gamma$ are defined as

$\displaystyle\binom{\gamma}{i}=\frac{\gamma(\gamma-1)(\gamma-2)\ldots(\gamma-i% +1)}{i!}$ $\displaystyle=\frac{\gamma!}{i!(\gamma-i)!},i>\gamma$ (8)

Thus, the FOI can apply all non-integer and irrational numbers to deal with the signal, $P(t)$ , and the summation is computed using the ratios of the Gamma function, $\Gamma(\gamma)$ , incorporating the number of sampling data points in the time interval [ $t_{0}$ , $t_{1}$ ], and the fractional order parameters, $\gamma$ .

For dealing with the time-varying signals such as fluid flows and bio-signals, the G-L definition is used as the basic concept for discrete processing during computations. The fractional-order integral suggests the use of non-integers to deal with bio-signals, and the corresponding binomial coefficients are computed using the ratios of the Euler’s Gamma function, $\Gamma$ , and factorials, as

$\displaystyle\binom{\alpha}{i}=\frac{\alpha!}{i!(\alpha-i)!}=\frac{\Gamma(% \alpha+1)}{\Gamma(i+1)\Gamma(\alpha-i+1)},$ $\displaystyle\quad∼{}\binom{\alpha}{0}=1$ (9)

In this study, the fractional-order derivative of the order parameters, $\alpha$ , is modified as

$\displaystyle D_{t}^{\alpha}P(t)\approx\lim\limits_{\Delta\tau\to 0}(\Delta% \tau)^{-\alpha}$ $\displaystyle\quad∼{}\sum\limits_{i=0}^{\infty}\left|(-1)^{i}\binom{\alpha}{i}% P(t-i\cdot\Delta\tau)\right|$ (10)

where $\alpha<$ 0 for fractional-order integration. Incorporating the number of sampling data points in the time interval [ $t_{0}$ , $t_{1}$ ], the FOI can be presented as

$\displaystyle D^{-\alpha}P(t)\approx\lim\limits_{\Delta\tau\to 0}(\Delta\tau)^% {\alpha}$ $\displaystyle\quad∼{}\sum\limits_{i=0}^{n-1}\left|(-1)^{i}\binom{-\alpha}{i}P(% t-i\cdot\Delta\tau)\right|$ (11)

time step:

$\displaystyle\Delta\tau=\left(\frac{t_{1}-t_{0}}{n}\right)$ (12)

where $n$ is the number of sampling points, $i=$ 1, 2, 3, …, $n$ ; timing parameters $t_{0}$ and $t_{1}$ are the bounds of a time interval. That is, AUCR given by Eq. (3) can be modified as a discrete FOI formulation:

$\displaystyle\textit{AUCR}\approx$ $\displaystyle\frac{\lim\limits_{\Delta\tau\to 0}(\Delta\tau_{\textit{mea}})^{% \alpha}\sum\limits_{i=0}^{n-1}{\left|(-1)^{i}\dbinom{-\alpha}{i}\textit{TVP}_{% \textit{mea}}[i]\right|}}{\lim\limits_{\Delta\tau\to 0}(\Delta\tau_{\textit{% nor}})^{\alpha}\sum\limits_{i=0}^{n-1}{\left|(-1)^{i}\dbinom{-\alpha}{i}% \textit{TVP}_{\textit{nor}}[i]\right|}}$ (13)

where time steps, $\Delta\tau_{\textit{mea}}=(\frac{t_{\textit{mea}}-t_{0}}{n})$ and $\Delta\tau_{\textit{nor}}=(\frac{t_{\textit{nor}}-t_{0}}{n})$ ; the discrete measured TVPs at the inflow or outflow sites are referred to as TVP ${}_{\textit{mea}}$ [ $i$ ]; the normal TVPs are referred to as TVP ${}_{\textit{nor}}$ [ $i$ ], $i\in$ [0, $n-1$ ].

3.2 Info-gap (IG) decision-making

An IG distribution model can be used to represent the uncertainty in a relationship between two parameters or a few key parameters [26, 27, 28]. Its model is a family of nested sets, which represents an infinity of possible realizations of an uncertain entity. A common model can be defined as follows:

$\displaystyle U(\beta,u^{\prime})=\{u:|u-u^{\prime}|\leqslant\beta\},\beta\geqslant 0$ $\displaystyle\Rightarrow U(\beta,u^{\prime})=U(\beta,0)+u^{\prime},U(0,0)=\emptyset$ (14)

where $u^{\prime}$ is the best estimate of an uncertain function $u$ , $\beta$ is the absolute error of an estimation. The set $U(\beta$ , $u^{\prime})$ contains all families of functions, $u$ , while the absolute errors from the best functions $u^{\prime}$ are not greater than $\beta$ .

Table 1

Allocation parameters for info-gap distribution model

Functions	$P_{\max}$	$P_{\min}$	AUCR ${}_{\max}$	AUCR ${}_{\min}$
$U^{+}(\beta^{+}$ , $u^{+}$ )	30	0	4.00	1.25
$U^{0}$ (0, $u^{0}$ )	0	0	1.25	0.90
$U^{-}(\beta^{-}$ , $u^{-}$ )	0	$-$ 16	0.90	0.00

Figure 4.

(a) TVP amplitude variations versus AUCRs, (b) The revenue (pressures) profiles versus the allocation (AUCRs) for screening arteriovenous stenosis and VND.

As seen in Fig. 3b, average TVP amplitude variations gradually increased with blood flow reduction and blood loss. The critical threshold of blood flow reduction was $<$ 200 ml/min (from 600 l/min to 400 l/min) for an AVG, and blood loss of $>$ 200 ml/min with reaction times $<$ 2.5 min was used to indicate the risk level. Therefore, maximum TVP variation, $P^{+}_{\max}\approx$ 30 mmHg, for screening arteriovenous stenosis, and $P^{-}_{\min}\approx-$ 16 mmHg for screening VND could be determined by the biophysical experimental data, as seen in Table 1. Equation (3.1) with the fractional-order parameter, $\alpha=$ 0.20, was employed to compute the AUCRs. In 36 measurements of arteriovenous stenosis, TVPs gradually increased (symbol “ $+$ ”) as AUCR increased within the allocation [1.25, 4.00]. In 28 measurements of VND events, TVPs decreased (symbol “ $-$ ”) within the allocation [0.00, 0.90]. The linear regression can be represented using linear functions involving the AUCRs and the TVP variations. However, TVPs are easily influenced by uncertain conditions, such as arterial/venous needle sizes, blood flow rates, dialysis vascular access (AVG/AVF), flow resistances, and blood viscosity during dialysis [3]. For TVP amplitude variations, $\beta^{+}=\pm 0.2\times|P^{+}_{\max}|$ and $\beta^{-}=\pm 0.2\times|P^{-}_{\min}|$ , the IG model can be used to represent the uncertain conditions, as a set of piecewise linear functions, as shown in Fig. 4a. We have two approximation functions, U ${}^{+}$ ( $\beta^{+}$ , $u^{+}$ ) and U ${}^{-}$ ( $\beta^{-}$ , $u^{-}$ ), within the maximum (max) and minimum (min) interval, as [P ${}_{\min}$ , P ${}_{\max}$ ] and [AUCR ${}_{\min}$ , AUCR ${}_{\max}$ ]. According to the Table 1, we estimated the sets of functions (two point form), as follows:

•

$U^{+}(\beta^{+}$ , $u^{+}$ ): arteriovenous stenosis,

$\displaystyle\mspace{-40.0mu }\frac{u^{+}-P_{\max}^{+}}{\textit{AUCR}-\textit{% AUCR}_{\max}^{+}}=\frac{(P_{\max}^{+}\pm\beta^{+})-P_{\min}^{+}}{\textit{AUCR}% _{\max}^{+}-\textit{AUCR}_{\min}^{+}}$ $\displaystyle\mspace{-40.0mu }\Rightarrow U^{+}(\beta^{+},u^{+})=$ $\displaystyle\mspace{-40.0mu }\quad∼{}\frac{(30\pm\beta^{+})\times\textit{AUCR% }-(30\pm\beta^{+})\times 1.25}{2.75}$ (15)

where $\beta^{+}=\pm$ 6.0 mmHg and $P^{+}_{\max}=30\pm 6$ mmHg.

•

$U^{0}$ (0, $u^{0})=$ 0: normal.

•

$U^{-}(\beta$ , $u^{-}$ ): venous needle dislodgement.

$\displaystyle\mspace{-40.0mu }\frac{u^{-}-P_{\max}^{-}}{\textit{AUCR}-\textit{% AUCR}_{\max}^{-}}=\frac{(P_{\max}^{-}\pm\beta^{-})-P_{\min}^{-}}{\textit{AUCR}% _{\max}^{-}-\textit{AUCR}_{\min}^{-}}$ $\displaystyle\mspace{-40.0mu }\Rightarrow U^{-}(\beta^{-},u^{-})=$ $\displaystyle\mspace{-40.0mu }\quad∼{}\frac{(16\pm\beta^{-})\times\textit{AUCR% }-(16\pm\beta^{-})\times 0.9}{0.9}$ (16)

where $\beta^{-}=$ $\pm$ 3.2 mmHg and $P^{-}_{\max}=-$ 16 $\pm$ 3.2 mmHg.

The boundaries of TVP variations for screening stenosis, DOS% $=$ 50–70% and $>$ 70%, are parameterized with certainty factors (CFs) and can be presented as follows:

$\displaystyle\textit{CF}_{1}=\exp\left(-\frac{1}{2}\times\left(\frac{\textit{% AUCR}-\textit{Mean}_{1}}{\sigma_{1}}\right)^{2}\right),$ $\displaystyle\quad∼{}0\leqslant\textit{AUCR}\leqslant 4$ (17) $\displaystyle\textit{CF}_{2}=\begin{cases}\exp\left(-{\displaystyle\frac{1}{2}% }\times\left({\displaystyle\frac{\textit{AUCR}-\textit{Mean}_{2}}{\sigma_{2}}}% \right)^{2}\right),\\ \qquad\textit{AUCR}<\textit{Mean}_{2}\\ {1,\quad\textit{AUCR}\geqslant\textit{Mean}_{2}}\\ \end{cases}$ (18)

where Mean ${}_{1}=$ 2.50 is the average AUCR for screening DOS% $=$ 50–70%; Mean ${}_{2}=$ 3.50 is the average AUCR for DOS% $>$ 70%; and standard deviations, $\sigma_{j}=$ 0.2 $\times$ Mean ${}_{j}$ , where $j=$ 1, 2. In addition, the VND risk levels can be parameterized as

$\displaystyle\textit{CF}_{3}=\exp\left(-\frac{1}{2}\times\left(\frac{\textit{% AUCR}-\textit{Mean}_{3}}{\sigma_{3}}\right)^{2}\right),$ $\displaystyle\quad∼{}0\leqslant\textit{AUCR}\leqslant 4$ (19) $\displaystyle\textit{CF}_{4}=\begin{cases}1,\quad 0\leqslant\textit{AUCR}% \leqslant 0.40\\ \exp\left[-{\displaystyle\frac{1}{2}}\times\left({\displaystyle\frac{\textit{% AUCR}-\textit{Mean}_{4}}{\sigma_{4}}}\right)^{2}\right],\\ \qquad\textit{AUCR}>0.40\end{cases}$ (20)

where Mean ${}_{3}$ is 0.70 denotes screening blood loss; Mean ${}_{4}$ is 0.40 denotes major blood loss; and standard deviations, $\sigma_{j}=$ 0.5 $\times$ Mean ${}_{j}$ , where $j=$ 3, 4. For four CFs, probability values with range [0, 1] and standard deviations are also assigned for representing the bounds of TVP variations. Thus, the IG decision-making can enhance robustness for screening arteriovenous stenosis and VND.

Figure 4b shows the revenue profiles obtained by for screening vascular stenosis and VND. Therefore, the revenue profiles are relevant combinations of IG distributions and CFs for separating the normal from the arteriovenous stenosis and VND and can be represented as

$\displaystyle\textit{revenous}^{+}=\begin{cases}{U^{+}\times\textit{CF}_{1}}\\ {U^{+}\times\textit{CF}_{2}}\end{cases}\mspace{-18.0mu }=\begin{cases}{U_{1}^{% +}}\\ {U_{2}^{+}}\end{cases}\mspace{-16.0mu }$ $\displaystyle\quad∼{}∼{}\text{for stenosis detection}$ (21) $\displaystyle\textit{revenous}^{0}=U^{0}\text{ for normal}$ (22) $\displaystyle\textit{revenous}^{-}=\begin{cases}{|U^{-}|\times\textit{CF}_{3}}% \\ {|U^{-}|\times\textit{CF}_{4}}\end{cases}\mspace{-18.0mu }=\begin{cases}{U_{3}% ^{-}}\\ {U_{4}^{-}}\end{cases}$ $\displaystyle\quad∼{}∼{}\text{for VND detection}$ (23)

For decision-making applications, revenue profiles with specific allocations are used to present each decision as a function. Then, the “maximum (max)–maximum (max)” composite operations are used to generate logic inferences as follows:

$\displaystyle S_{m}=\max\limits_{0\leqslant\textit{AUCR}\leqslant 4}[\max(U_{1% }^{+},U_{2}^{+}),U^{0},$ $\displaystyle\quad∼{}\max(U_{3}^{-},U_{4}^{-})]$ $\displaystyle=\max\limits_{0\leqslant\textit{AUCR}\leqslant 4}[s_{1},s_{2},s_{% 3}],\text{ Index }m=1,2,3$ (24)

where Index, $m=$ 1, is used in conjunction with the following inequalities to identify vascular stenosis:

•

$U_{1}^{+}>U_{2}^{+}$ : for “DOS% $=$ 50–70%”.

•

$U_{1}^{+}<U_{2}^{+}$ : for “DOS% $>$ 70%”.

Index, $m=$ 2, is used in conjunction with $s_{1}=s_{2}=s_{3}=$ 0 to identify the normal; and Index, $m=$ 3, is used in conjunction with the following inequalities to identify VND:

•

$U_{3}^{-}>U_{4}^{-}$ : for “Blood Loss”,

•

$U_{3}^{-}<U_{4}^{-}$ : for “Major Blood Loss”.

The overall procedure of life-threatening complication detection is shown in Fig. 5.

Figure 5.

The flowchart of life-threatening complication detection.

Figure 6.

Fractional-order integrations with the fractional orders, $\alpha=$ 0.20 $\sim<$ 0.40.

Figure 7.

Experimental results for vascular access stenosis, DOS% $=$ 70%. (a) Inflow BPWs in the time domain; (b) Normalized TVPs between the normal and the vascular access stenosis; (c) AUCR profile (allocations) within 15 detection cycles; (d) Revenue profiles within 15 detection cycles.

4. Experimental results

The experimental system used herein mimics the human cardio-vascular system and extracorporeal blood circuit in the laboratory, as shown in Fig. 2. The inflow and outflow pressures were measured using two 22G-venous needles and two pressure sensors (NOSHOK, Inc.) at the inflow site and outflow site (about 12 cm, two sides of AVG access), respectively. Flow rates of 600–1000 ml/min were used to drive the BMF through the blood circuits and an AVG access by a roller pump (40–80 rpm). BPWs with a sampling rate of 1.0 kHz were obtained from the analog-to-digital(A-D) converter with a compatible PC via a DAQ card. Then, the detrending process was employed to remove the roller pump pressures, and mean vascular access pressures and normalized TVPs (average $P_{\textit{nor},\max}=$ 159.42 mmHg) were obtained using Eq. (2). Three groups of TVPs with an average cardiac cycle of about 0.68 s time interval were obtained, as shown in Fig. 3a.

To identify TVP changes in amplitudes and shapes, fractional-order AUCs were calculated using Eqs (3.1) and (12) with the fractional orders $\alpha=$ 0.20 $-<$ 0.40, as shown in Fig. 6. It can be seen that the distinguishable FOI values had a fractional order $\alpha<$ 0.3. Hence, $\alpha=$ 0.2 was chosen in this study. The AUCRs were calculated to separate normal TVPs from TVP variations using Eq. (3.1), while AUCR $>$ 1 represents vascular access stenosis and AUCR $<$ 1 represents VND. Finally, life-threatening complication detection was performed using the IG decision-making scheme. The overall procedure was designed on a personal computer (PC)-based detection model using LabVIEW (National Instruments™ Corporation, Austin, Texas, U.S.A.) graphical programming software andMATLAB software (MathWorks, Natick, Massachuse- tts, U.S.A.). The results obtained in the two case studies described below, as well as their contrast with the results of hemodynamic analysis, indicate that the proposed detection model is more efficient.

4.1 Case study 1#: Vascular access stenosis

Numerical experiments with DOS $>$ 70% or 50%–70% were performed to verify the proposed detection model. Inflow BPWs in the time domain were measured using pressure sensors, as shown by 15 pressure waves (15 cardiac cycles, about 10 s) in Fig. 7a. For Case Study 1# (DOS% $=$ 70%), the mean vascular access pressure increased from 151.50 mmHg (P𝑛𝑜𝑟,max= 161.39 mmHg) to 160.94 mmHg (P𝑚𝑒𝑎,max $=$ 178.97 mmHg), while the vascular access narrowed. In signal preprocessing, the detrending process was employed to remove the mean vascular access pressures, following which normalized TVPs were calculated using the $P_{\textit{nor},\max}$ , as shown in Fig. 7b. It can be seen that TVPs’ amplitudes and shapes were really different. AUCR was used to identify the differences; thus, the allocation, average AUCR $=$ 2.1915, can be calculated, while can be obtained to separate the normal from the vascular access stenosis or slight stenosis from severe stenosis, as shown in the AUCR profile in Fig. 7c. The procedure of the proposed IG decision-making scheme is as follows:

Step 3) Step 1)
Compute the AUCR, and the allocations can be determined in each detection cycle using Eq. (3.1), as shown in Fig. 7c,
Step 2)
Estimate the TVP amplitude variations using the Eqs (3.2) and (16), as [U ${}^{+}$ , U ${}^{0}$ , U ${}^{-}$ ] $=$ [0.0000, 0.0000, 10.8712], U ${}^{+}>$ 0, this index can identify the vascular access stenosis,
Step 3)
Compute the certainty factors (CFs) using Eqs (3.2) to (20), CF $=$ [CF ${}_{1}$ , CF ${}_{2}$ , CF ${}_{3}$ , CF ${}_{4}$ ] $=$ [0.8794, 0.2012, 0.0001, 0.0000],
Step 4)
Compute the average revenue values of IG distributions as [U ${}_{1}^{+}$ , U ${}_{2}^{+}$ , U ${}^{0}$ , U ${}_{3}^{-}$ , U ${}_{4}^{-}$ ] $=$ [8.4907, 2.1877, 0.0000, 0.0000, 0.0000], average revenue ${}^{+}$ $=$ 8.4907 for “Vascular Access Stenosis”, as shown in Fig. 7d,
Step 5)
Find the maximum revenue value using Eq. (3.2), $S_{1}=$ max[max(U ${}_{1}^{+}$ , U ${}_{2}^{+}$ ) , U ${}^{0}$ , max(U ${}_{3}^{-}$ , U ${}_{4}^{-}$ )] $=$ 8.4907, indicate the possible result: “DOS% $=$ 50%–70%”.

For at least 15 detection cycles, the experimental results of Case Study 1# confirmed the presence of vascular access stenosis. In addition, 21 measurements were made at each inflow site at locations $-l\times D_{a}$ , where $l=$ 5, 10, and 17 and $D_{a}=$ 0.635 cm; “ $-$ ” means a pressure sensor is placed before the stenotic location. When the DOS% was varied from 50% to 95%, positive predictivity was more than 95% for signal identification with 15–45 TVP waves, approximately 10–30 s.

Figure 8.
Experimental results for VND event. (a) Outflow BPWs in the time domain; (b) Normalized TVPs between the normal and VND event; (c) AUCR profile within 15 detection cycles; (d) Revenue profiles within 15 detection cycles.

4.2 Case study 2#: VND event

Consider a blood loss rate of $<$ 200 ml/min. A severe case is characterized by $>$ 500 ml of blood loss and a pressure drop (20.15 mmHg) when the reaction time exceeds 2.5 min. In a general case, when a VND occurs in a patient, it could be discovered after about 20 s. For VND detection, the outflow BPWs in the time domain were also measured using the pressure sensors, as shown in Fig. 8a. In Case Study 2#, the DOS% was $<$ 50%, and the normalized TVPs were calculated using $P_{\textit{nor},\max}=$ 160.71 mmHg, as shown in Fig. 7b. For reaction times of 10–30 s, VND occurred in the 9th cardiac cycle, and critical changes in the TVP and pressure drop at the beginning of VND occurrence were noted by observing the AUCR profile, as shown in Fig. 8c. Before VND, the average AUCR $\approx$ 1.0000, and its value dropped suddenly because of blood loss. Thus, the AUCR index (average value $=$ 0.7271) can be used to separate the normal case from blood loss events. For determining the average allocation, the proposed IG decision-making scheme employs the following procedure:

Step 3) Step 1)
Compute the AUCR, and the average allocations can be determined for normal and VND events, as shown in Fig. 8c,
Step 2)
Estimate the TVP amplitude variations, as [U+, U0, U-] = [0.0000, 0.0000, -3.0014], and the index, U ${}^{-}<$ 0, confirms the VND event,
Step 3)
Compute the CFs, CF $=$ [CF ${}_{1}$ , CF ${}_{2}$ , CF ${}_{3}$ , CF ${}_{4}$ ] $=$ [0.0019, 0.0004, 0.9960, 0.2539],
Step 4)
Compute the average revenue values of IG distributions as [U ${}_{1}^{+}$ , U ${}_{2}^{+}$ , U ${}^{0}$ , U ${}_{3}^{-}$ , U ${}_{4}^{-}$ ] $=$ [0.0000, 0.0000, 0.0000, 3.0648, 0.7860], average revenue ${}^{-}$ $=$ 3.0648 for the possible event, as shown in Fig. 8d,
Step 5)
Find the maximum revenue, $S_{3}=\max$ [ $\max$ (U ${}_{1}^{+}$ , U ${}_{2}^{+}$ ), U ${}^{0}$ , $\max$ (U ${}_{3}^{-}$ , U ${}_{4}^{-}$ )] $=$ 3.0648, indicate the possible result: “Blood Loss”.

Twenty-one measurements were recorded at each outflow site at locations $+∼{}l\times D_{a}$ , where the symbol “ $+$ ” means a pressure sensor is placed after the stenotic location. Positive predictivity $>$ 95% was used to quantify the performance of signal identification without or with a slightly noisy background. The case studies confirm that the proposed detection model enables the examination of vascular access stenosis, blood loss, and major blood loss.

Table 2
Experimental results for stenosis and VND detections using the proposed screening model

Class DOS % Blood reduction Blood loss $\Delta P$ (mmHg) $V_{\textit{est}}$ (m/sec) Res AUCR IG decision-making

(ml/min) (ml/min) U ${}^{+}$ U ${}^{0}$ U ${}^{-}$

Vascular 95 193.30 ( $-$ ) $\times$ 31.43 ( $-$ ) 2.80 0.89 3.6757 26.46 0.00 0.00

access 90 80.10 ( $-$ ) $\times$ 12.42 ( $-$ ) 1.76 0.82 2.5434 14.05 0.00 0.00

stenosis 80 24.10 ( $-$ ) $\times$ 8.98 ( $-$ ) 1.49 0.79 2.2163 8.97 0.00 0.00

70 7.40 ( $-$ ) $\times$ 7.74 ( $-$ ) 1.39 0.78 1.9180 3.70 0.00 0.00

50 3.80 ( $-$ ) $\times$ 2.25 ( $-$ ) 0.75 0.59 1.8305 2.58 0.00 0.00

VND $<$ 50 $\times$ 10.00 ( $+$ ) 1.66 ( $+$ ) 0.64 – 0.8438 0.00 0.00 0.92

(blood loss) $<$ 50 $\times$ 11.90 ( $+$ ) 3.32 ( $+$ ) 0.91 – 0.8092 0.00 0.00 1.54

$<$ 50 $\times$ 25.86 ( $+$ ) 6.64 ( $+$ ) 1.28 – 0.5804 0.00 0.00 5.36

$<$ 50 $\times$ 62.45 ( $+$ ) 9.97 ( $+$ ) 1.57 – 0.4330 0.00 0.00 8.19

$<$ 50 $\times$ 94.83 ( $+$ ) 13.30 ( $+$ ) 1.82 – 0.3280 0.00 0.00 10.17

Note: (1) $V_{\textit{est}}=\sqrt{\frac{(P_{\textit{High}}-P_{\textit{Low}})}{4}}=\sqrt{% \frac{\Delta P}{4}}$ , (2) Resistive index, $\textit{Res}=\frac{V_{\textit{est}}-V{}_{0}}{V_{\textit{est}}}$ , where $V_{\textit{est}}$ is the estimated peak systolic velocity (m/sec), $V_{0}=$ 0.3 m/sec [11] is the peak systolic velocity under the “flow rate, 600 ml/min”, (3) Symbol “ $-$ ” are the pressure or flow rate changes in inflow site; and symbol “ $+$ ” is change in the outflow site.

Table 3
Compare the detection tasks with the proposed method and existing techniques

[dir=NW]TaskMethod [c]The proposed

method [c]Wetness sensing

pad [4] [c]Optical sensing

pad [4] [c]Acoustic

method [9, 10, 11, 12] Auscultation method [14, 15] [c]Photoplethysmography

(PPG) [24]

Detector Pressure sensor Wetness sensor Optical sensor Ultrasound Electronic stethoscope Bilateral optical sensor

(7.5–10.0 MHz)

Technique Pressure signal Voltage Infrared (IR) Ultrasound image Phonoangiography PPG signal

Decision-making FOI and IG $\times$ $\times$ Physician Frequency analysis, artificial Bilateral timing differences,

method decision-making intelligent method artificial intelligent method

Duty During HD During HD During HD Routine examination Routine examination Routine examination,

during HD

Stenosis detection $\circ$ $\times$ $\times$ $\circ$ $\circ$ $\circ$

VND detection $\circ$ $\circ$ $\circ$ $\times$ $\times$ $\times$

4.3 Discussion

Class	DOS %	Blood reduction	Blood loss	$\Delta P$ (mmHg)	$V_{\textit{est}}$ (m/sec)	Res	AUCR	IG decision-making
Vascular	95	193.30 ( $-$ )	$\times$	31.43 ( $-$ )	2.80	0.89	3.6757	26.46	0.00
access	90	80.10 ( $-$ )	$\times$	12.42 ( $-$ )	1.76	0.82	2.5434	14.05	0.00
stenosis	80	24.10 ( $-$ )	$\times$	8.98 ( $-$ )	1.49	0.79	2.2163	8.97	0.00
	70	7.40 ( $-$ )	$\times$	7.74 ( $-$ )	1.39	0.78	1.9180	3.70	0.00
	50	3.80 ( $-$ )	$\times$	2.25 ( $-$ )	0.75	0.59	1.8305	2.58	0.00
VND	$<$ 50	$\times$	10.00 ( $+$ )	1.66 ( $+$ )	0.64	–	0.8438	0.00	0.92
(blood loss)	$<$ 50	$\times$	11.90 ( $+$ )	3.32 ( $+$ )	0.91	–	0.8092	0.00	1.54
	$<$ 50	$\times$	25.86 ( $+$ )	6.64 ( $+$ )	1.28	–	0.5804	0.00	5.36
	$<$ 50	$\times$	62.45 ( $+$ )	9.97 ( $+$ )	1.57	–	0.4330	0.00	8.19
	$<$ 50	$\times$	94.83 ( $+$ )	13.30 ( $+$ )	1.82	–	0.3280	0.00	10.17

[dir=NW]TaskMethod	[c]The proposed
method	[c]Wetness sensing
pad [4]	[c]Optical sensing
pad [4]	[c]Acoustic
method [9, 10, 11, 12]	Auscultation method [14, 15]	[c]Photoplethysmography
(PPG) [24]
Detector	Pressure sensor	Wetness sensor	Optical sensor	Ultrasound	Electronic stethoscope	Bilateral optical sensor
				(7.5–10.0 MHz)
Technique	Pressure signal	Voltage	Infrared (IR)	Ultrasound image	Phonoangiography	PPG signal
Decision-making	FOI and IG	$\times$	$\times$	Physician	Frequency analysis, artificial	Bilateral timing differences,
method	decision-making				intelligent method	artificial intelligent method
Duty	During HD	During HD	During HD	Routine examination	Routine examination	Routine examination,
						during HD
Stenosis detection	$\circ$	$\times$	$\times$	$\circ$	$\circ$	$\circ$
VND detection	$\circ$	$\circ$	$\circ$	$\times$	$\times$	$\times$

HD is one of the treatment choices for ESRD patients and has become routine therapy in Taiwan. Vascular access stenosis occurs more frequently complications and has higher patency and thrombosis rates [10, 18] in patients with AVGs. VND occurs less frequently, but it is a severe complication in chronic HD ( $>$ 70%) and acute cares ( $>$ 40%). More than half of the surveyed candidates, including nephrology nurses/staff and patients were concerned about VND very often ( $>$ 30%), often ( $>$ 20%), or seldom/occasionally( $>$ 20%) [4, 6]. Six risk factors were issued and identified in the ANNA VND survey results, and 4 risks for a VND event depended on the likelihood of a needle becoming dislodged and the likelihood of stopping blood loss to prevent serious harm. Recommendations have also implemented to prevent VND [4, 12, 29], such as selecting an access cannulation site beforehand, taping the needles securely, assuring access visibility, monitoring dialysis catheters, monitoring pressure variations in bloodlines, and monitoring pressure/moisture during HD. Easy-to-use assistance tools are promising for reducing the risk of VND in patients. As listed in Table 2 the rises and drops in the mean arterial access (symbol “ $-$ ”) and venous access (symbol “ $+$ ”) pressures can be used to separate vascular access stenosis events from VND events. Pressure differences were used to estimate the velocity $V_{\textit{est}}$ (m/s), and the resistive index (Res $>$ 0.55) was to evaluate the DOS through the stenotic access. However, mean pressure variations were influenced by patients’ movements, height changes, cannula sizes, blood flow rates, dialysis access (AVG/AVF), flow resistance, and blood viscosity. Hence, pressure variation is not the only index used for attribute screening during dialysis. To ensure routine HD care, dialysis organizations or manufacturers have established evidence-based HD procedures and early warning devices for blood leakage and blood loss detection, such as wetness sensor or optical sensor [4, 30]. However, additional electronic devices with two spaced out designs may limit the patient movements and dialysis settings and cause a patient to be restless, stressed, and worried about moving. In addition, these devices cannot be used for the detection of two events, as seen in Table 3.

Acoustic methods [9, 10, 11, 12] such as the Doppler sonography, ultrasound imaging, and ultrasound flowmeter, and auscultation method [14, 15], were reliable ways of detecting the presence of stenosis inside vascular accesses in clinical examinations. Ultrasound imaging examinations with B-mode operation have also been applied to visualize the structure of vascular structures, and aneurismal and thrombotic tissues. A-mode operation provides acoustic signals for monitoring various blood flow velocities such as peak-systolic velocity, peak-diastolic velocity, and mean velocity. These techniques can serve as a reference for therapeutic decisions before surgical treatments and are used for assessing access creation before HD cares and for locating stenotic sites. However, they have limitations, including being unsuitable for usage during HD and for early warning of blood leak and acute care, as seen in Table 3. Auscultation techniques with phonoangiography and frequency analysis [14, 15, 31] have been used to estimate frequency domain features. Artificial intelligent methods are designed as a decision-making manner for stenosis evaluation. However, phonography techniques are affected by the measurement site, size of the sampling window, and time-frequency parametric model choices. Photoplethysmography (PPG) is an optical measurement technique that can be used to non-invasively detect blood volume changes [24]. PPG signals carry information about the cardiovascular risk factors, atherosclerosis, arterial stiffness, and peripheral vascular diseases. This technique allows continuous measurement and temporal analysis using the intelligent decision-making methods during HD treatment. However, auscultation and PPG techniques can not detect the blood leakage and blood loss.

For puncture venous needles and pressure sensors at the inflow site and outflow sites, both inflow and outflow pressures can be recorded continuously to a Tablet PC or a monitor device. Using the measurement data, the proposed detection model separated the normal cases from vascular access stenosis with DOS% $=$ 50–90%, and normal cases from VND events with DOS $<$ 50% and blood loss $<$ 200 ml ( $<$ 2 min). It provided promising results in terms of accurate detection in the event of a life-threatening complication, as shown in Table 2. Discretization FOI with fractional order $\alpha=$ 0.2 and the Gamma function were applied using Eqs (3.1) and (3.1) to deal with TVP signals, incorporating the number of sampling data and the fractional order parameters [19]. Hence, the distinguishable features can be extracted in time-domain analysis. The IG decision-making-based screening model required no optimization methods to assign the model’s parameters, and it overcame the problems of iteration computation mechanism, such as updating or refining the model’s parameters. The model uses straightforward mathematical computations to arrive at the inference procedure for real-time applications. The embedded system (NI™ myRIO-1900, Austin, Texas, USA) can be applied to develop an early warning monitor within a short design cycle, including (1) connectivity measurements (via analog inputs) from the pressure sensors, (2) built-in digital signal processor, (3) easily implementation of the FOI and the IG decision-making algorithm in a programmable processor (dual-core ARM Cortex), and (4) monitoring of the information via wired or wireless (built-in Wi-Fi) communication in a tablet PC. Its framework could be implemented in a standalone device using graphical programming software and the portable embedded design device in real-time (RT) applications. In addition, the remote monitor’s function can also be used in telemedicine and telecare applications in home-based HD and public HD rooms.

5. Conclusion

In Taiwan, there are more than 77,000 patients with ESRD and chronic kidney failure, and life-threatening complications during HD treatment have attracted the attention of dialysis organizations and medical staff. In this study, we proposed an assistant tool based on discretization FOI and IG decision-making that can screen for frequent or severe complications. The FOI formulation can be designed by power series expansion and Gamma function, and it can be applied to real-time signal processing. It was employed to identify the categories using the AUCR index during allocation: AUCR $>$ 1.25, for vascular access stenosis and AUCR $<$ 0.90 for VND events. Then, the IG decision-making model needed to assign fewer model parameters and acted as an inference mechanism to identify critical revenues. In practical measurements, the experimental results showed that the proposed model was highly accurate, and positive predictivity greater than 90% was used to identify the possible results within specific revenues versus allocations. Under the ES design environment, we used four fundamental operations of arithmetic and logical inference to embed the proposed algorithms in a dual-core programmable processor. In addition, further studies should consider the approval of hospital research ethics committee and Institutional Review Board (IRB), and clinical investigations with enrolled patients are used to verify the proposed model in ESRD on HD. Hence, the proposed model employing pressure sensors can be integrated into dialysis machines made available in clinical and telemedicine applications.

Footnotes

Acknowledgments

This work was supported by the research grant of National Cheng Kung University, under contract number: NCKUH-103-05001, duration: January 1, 2014 $\sim$ December 31, 2014, and was supported in part by the Ministry of Science and Technology, Taiwan, under contract number: MOST 105-2218-E-075B-001, duration: March 1 2016 $\sim$ February 28 2017.

References

Tordolr Jan

. Dialysis: Early pre-emptive intervention might reduce AVF access loss. Nature Reviews, Nephrology January 2014; 1(10): 9-10.

Stanziale

Lodi

D’Andrea

Sammartino

Luzio

. Arteriovenous fistula: End-to-end or end-to-side anastomosis? Hemodialysis International January 2011; 15(1): 100-103.

Polaschegg

. Venous needle dislodgement: The pitfalls of venous pressure measurement and possible alternatives, a review. Journal of Renal Care2010; 36(1): 41-48.

Axley

Speranza-Reid

Williams

. Venous needle dislodgement in patients on hemodialysis. Nephrology Nursing Journal November–December 2012; 39(6): 435-445.

Reines

Gutierrez

. Clinical review: Hemorrhagic shock. Critical Care2004; 8(5): 373-381.

American Nephrology Nurses’ Association (ANNA). https://www.annanurse.org/resources/venous-needle-dislodgement.2012.

Misra

. The basics of hemodialysis equipment. Hemodialysis International2005; 9: 30-36.

Paulson

Ram

Work

Conrad

Jones

. Inflow stenosis obscures recognition of outflow stenosis by dialysis venous pressure: Analysis by a mathematical model. Nephrol Dial Transplant2008; 23: 3966-3971.

Manos

Sokolis

Giagini

Davos

Kakisis

Kritharis

Stergiopulos

Karayannacos

Tsangaris

. Local hemodynamics and intimal hyperplasia at the venous side of a porcine arteriovenous shunt. IEEE Trans Infomation Technology in Biomedicine2010; 14(3): 681-90.

10.

Leea

Fischerb

Lotha

Royston

Grogan

Bassiouny

. Flow-induced vein-wall vibration in an arterio-venous graft. Journal of Fluids and Structures2005; 20(6): 837-852.

11.

Chen

Lin

Kan

Lin

. Assessment of flow instabilities in in-vitro stenotic arteriovenous grafts using an equivalent astable multivibrator. IET Science, Measurement & Technology September 2015; 9(6): 709-716.

12.

Mactier

Worth

. Minimizing the risks of needle dislodgement during haemodialysis. Artery2007; 41(3): 9-13.

13.

Waeleghem

Chamney

Lindley

Olausson

Pancirova

. Venous needle dislodgment: How to minimize the risks. Journal of Renal Care2008; 34(4): 163-168.

14.

Chen

Kan

Lin

Chen

. A rule-based decision-making diagnosis system to evaluate arteriovenous shunt stenosis for hemodialysis treatment of patients using Fuzzy Petri nets. IEEE Journal of Biomedical and Health Informatics March 2014; 18(2): 703-713.

15.

Chen

Lin

Kan

. Residual stenosis estimation of arteriovenous graft using a dual-channel phonoangiography with fractional-order features. IEEE Journal of Biomedical and Health Informatics March 2015; 19(2): 590-600.

16.

Huynh

Brott

Ito

Cheng

Shih

Allon

Anayiotos

. Turbulent flow evaluation of the venous needle during hemodialysis. Journal of Biomechanical Engineering2005; 127: 1141-1146.

17.

Hurst

. It can happen without warning: Venous needle dislodgement. Renal Business Today2009; 4(9): 18-22.

18.

Asif

Gadalean

Merrill

Cherla

Cipleu

Epstein

Roth

. Inflow stenosis in arteriovenous fistulas and grafts: A multicenter, prospective study. Kidney International2005; 67: 1986-1992.

19.

Syntax: detrend. https://www.mathworks.com/help/matlab/ref/detrend.html#syntax.

20.

MATLAB

{}^{\@setsize{\tiny}{6pt}{\vpt}{\@vpt}\textregistered}

Data Analysis, MathWorks, Inc. https://www.mathworks.com/help/pdf_doc/matlab/data_analysis.pdf.

21.

Das

. Functional fractional calculus for system identification and control. Springer Berlin Heidelberg, New York, Chapter 1. 2008.

22.

Krishna

. Studies on fractional order differentiators and integrators: A survey. Signal Processing2011; 91(3): 386-426.

23.

Petras

. Fractional-order nonlinear systems: Modeling, analysis and simulation. Nonlinear Physical Science, Springer 2011. ISSN 1867-8440.

24.

Huang

Lin

. Bilateral photoplethysmography analysis for peripheral arterial stenosis screening with a fractional-order integrator and info-gap decision-making. IEEE Sensor Journal April 2016; 16(8): 2691-2700.

25.

Integral, Wikipedia, https://en.wikipedia.org/wiki/Integral.

26.

Chen

Zhang

Sun

. Robust restoration decision-making model for distribution networks based on information gap decision theory. IEEE Trans on Smart Grid March 2015; 6(2): 587-597.

27.

Hayes

Barry

Hosack

Peters

. Severe uncertainty and info-gap decision theory. Methods in Ecology and Evolution July 2013; 4(7): 601-611.

28.

Ben-Haim

. Info-gap decision theory. Design Under Severe Uncertainty. 2

{}^{\rm nd}

ed. San Diego, CA, USA: Academic Press February 2006.

29.

Sandroni

. Venous needle dislodgement during hemodialysis: An unresolved risk of catastrophic hemorrhage. Briefing paper presented for discussion for the EDTNA/ERCA Journal Club2005.

30.

Rognvaldsson

Engvall

. Human status and activity during hemodialysis. Center for Applied Intelligence Systems Research (CAISR), Research Profile, Annual Report2012; 44-45.

31.

Chen

. Arteriovenous access stenosis detection for hemodialysis patients using phonoangiography techniques: From clinical to physical model. The Degree of Doctor of Philosophy in Department of Biomedical Engineering, National Cheng Kung University May2015.

Class	DOS %	Blood reduction	Blood loss	$\Delta P$ (mmHg)	$V_{\textit{est}}$ (m/sec)	Res	AUCR	IG decision-making
		(ml/min)	(ml/min)					U ${}^{+}$	U ${}^{0}$	U ${}^{-}$
Vascular	95	193.30 ( $-$ )	$\times$	31.43 ( $-$ )	2.80	0.89	3.6757	26.46	0.00	0.00
access	90	80.10 ( $-$ )	$\times$	12.42 ( $-$ )	1.76	0.82	2.5434	14.05	0.00	0.00
stenosis	80	24.10 ( $-$ )	$\times$	8.98 ( $-$ )	1.49	0.79	2.2163	8.97	0.00	0.00
	70	7.40 ( $-$ )	$\times$	7.74 ( $-$ )	1.39	0.78	1.9180	3.70	0.00	0.00
	50	3.80 ( $-$ )	$\times$	2.25 ( $-$ )	0.75	0.59	1.8305	2.58	0.00	0.00
VND	$<$ 50	$\times$	10.00 ( $+$ )	1.66 ( $+$ )	0.64	–	0.8438	0.00	0.00	0.92
(blood loss)	$<$ 50	$\times$	11.90 ( $+$ )	3.32 ( $+$ )	0.91	–	0.8092	0.00	0.00	1.54
	$<$ 50	$\times$	25.86 ( $+$ )	6.64 ( $+$ )	1.28	–	0.5804	0.00	0.00	5.36
	$<$ 50	$\times$	62.45 ( $+$ )	9.97 ( $+$ )	1.57	–	0.4330	0.00	0.00	8.19
	$<$ 50	$\times$	94.83 ( $+$ )	13.30 ( $+$ )	1.82	–	0.3280	0.00	0.00	10.17