Wireless Sensor Networks in Application to Patients Health Monitoring

Wireless Sensor Networks in Application to Patients Health Monitoring Stanislaw Rajba, Ph.D.

Teresa Rajba, Ph.D.

Department of Electrical Engineering and Automation University of Bielsko-Biaáa, Bielsko-Biaáa, Poland [email protected]

Department of Mathematics and Computer Science University of Bielsko-Biaáa, Bielsko-Biaáa, Poland [email protected]

Pawel Raif, Ph.D.

Mufti Mahmud, Ph.D.

Dept. of Biosensors and Biomedical Signals Processing Silesian University of Technology, Gliwice, Poland [email protected]

NeuroChip Laboratory University of Padova, Padova, Italy [email protected] using some probabilistic solutions that can be applied to both randomized algorithms access, process control network [8] and probabilistic analysis on the wireless network [9]. Randomized algorithms play an important role in any type of distributed system, they lead to faster and simpler solutions [10],[11],[12]. In the case of wireless networks there are essentially four main topics of probabilistic analysis: (1) related to energy saving [13], (2) related to design and analysis - random access or random sending [14], (3) probabilistic network performance analysis (assuming random network topology), and (4) probabilistic analysis of randomized algorithms [15],[16]. In this study we propose the use of a single-hop network to monitoring of patients in a hospital ward, using network access technology models based on Poisson Arrivals See Time Averages (PASTA).

Abstract—This work presents an application of Wireless Sensor Network (WSN) of random access with one-way transmission to the monitoring of hospital patients. In the paper, we consider WSN single-hop network using one single radio frequency, such that all nodes are divided into several groups depending on the average time between the transmission due to the different state of health of patients. We apply the Poisson Arrivals See Time Averages (PASTA) to modeling of WSN. We present formula for the probability of collisions which has been verified by simulation studies of network. Key words—Wireless Sensor Network (WSN), Poisson Arrivals See Time Averages (PASTA system), probability of collision, random control monitoring of hospital patients

I.

INTRODUCTION

II.

The wireless measurement is a very fast growing area of research. The wireless sensor network (WSN) is a specific use of radio communications systems where many stations nodes transmit the information to a base station (sink) [1]. It requires a completely different approach to radio communications than traditional systems, or even ad hoc networks [2]. You can list a number of important factors affecting the design of the WSN network. These are: bands and communication frequencies, the demand for power supply (for example: for the purposes of communication and data processing), reducing external (environmental) as well as, hardware limitations, scalability, fault tolerance range [3]. On the one hand the WSN network is characterized by the architectural and communication specificity associated with the system requirements, and on the other hand with the requirements of the radio propagation conditions. Among them: the mobility of the network nodes, configuration changes, the changing environmental conditions, algorithms for single-hop and multi-hop networks, often selflearning [4],[5],[6]. Basically, the use of WSN in specific applications often requires individual solutions to many complex problems [7]. A specific class of network WSN are

c 978-1-4673-5883-5/13/$31.00 2013 IEEE

PROBLEM FORMULATION.

The proposed solution is based on the idea that the patient's bed is equipped with wireless measurement node. The use of radio communication allows to maintain mobility of hospital beds. Measurement node is associated with a hospital bed and is equipped with five inputs for sensors used for monitoring the health of patients (Table I). A characteristic feature of the measuring nodes is ability to transmit wirelessly the information about patient’s state of health to the database in the information system. What’s important: the transmission time is chosen randomly. The average time a node generates broadcast depending on the values of the monitored parameters and their dynamics. Average broadcasting delay time is chosen according to one of three groups to which the specified node is classified at any given time. This classification depends on the patient state of health. This paper presents an application of WSN networks with random access nodes to monitor hospital patients. Our previous research on the single-hop, one-way radio transmission WSN networks that uses one radio frequency has been presented in the papers [17],[18]. The main features of the proposed wireless network are, in particular, the independence of the

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nodes that support sensors (plug and play), one-way transmission using only one frequency (resulting in simplicity of both software and hardware of the nodes) and extremely narrow radio band needed make this solution to be useful in patient monitoring in the hospital. The detailed requirements for monitoring hospital ward patients were established on base research presented in [19] (and after the consultation with the doctors on duty at the city hospital in Bielsko-Biala, Poland. These requirements were taken into consideration before the setting parameters of the proposed wireless network. Hospital patients can be divided into three groups (Table I): (1) the first group consists of patients in a stable state, where surveillance need not be too frequent, (2) the second group of patients with a slow deterioration of the parameters determining the state of health, and finally, (3) a third group of patients, whose health deteriorated sharply. This classification allows to determine the average time at which the base station (sink) information should receive messages from each node measuring supervised patients. It was also found the percentage (average) distribution of the above-mentioned groups across the number of monitored patients. The Table I shows the percentage distribution of these groups of patients in the standard case. There are situations "more difficult for the hospital," for example in case of more serious diseases and injuries, but this cases are not considered in this work (as differing from normal situation). The Table I contains five parameters which are monitored in patients in the order of importance from the standpoint of patient safety risks. The table shows how often the node examines the chosen parameters, and the frequency of transmission of radio messages depends on the classification of patients into one of three groups based on the results of measurements by the node. The radio communication is based on sending short packets of information. From the point of view of the methods of access to the network node, presented probabilistic model protocol should be as short as possible, but it must contain the necessary information. This information should contain: the number of the node (sender), which will be associated with particular patient, the identification number of the medical test. For each number field test data should be provided with a fixed length. In our case, the data field length is one octet. Taking into account that in the one octet data field is one bit for parity at the disposal of 7 bits, 128 levels determine the value of a given size. This option is the minimum that it can always be expanded at the expense of longer duration of the protocol or at the expense of the occupied bandwidth. It is recommended that a fixed length protocol, which somewhat simplifies operation algorithm and provides a simple mechanism for some kind of validation controls communication with the parity bits. In the proposed model, the duration of the protocol is tp = 3,2 × 10-5 s. Excessive expansion of the protocol is not necessary and not advisable because it deteriorates the quality of network communication. The base station performs a new analysis of incoming messages and generates alarm for individual patients whose health-related safety or survival is threatened. Emergency information for the service, in addition to the alarm signal from base station, automatically generate messages sent to a GSM SMS notifications to SMS with medical surveillance of

selected individuals to take immediate action. The scheme of the proposed monitoring system, based on using WSN, is shown in Figure 1. TABLE I.

No. of test

Determining the type of test

TRANSMISSION PARAMETERS The requi red frequ ency of test [s]

able abnormali ties (changes slowly varying)

able deviatio n from the norm (Quickchange)

60%

30%

10%

1

3600 (1hour)

30

5

1

3600 (1hour)

30

5

1

3600 (1hour)

30

5

900

21600 (6 hour) 21600 (6 hour)

900

60

21600 (6 hour)

1800

Percentage of patients in the specified state of the health (standard situation)

1 2 3 4 5

oxygen saturation pulse rate respiratory rate arterial pressure the body temperature

Frequency of sending a message [s]

3600

average transmission time

In the steady state

T1= 3600s

T2=30s

T3=5s

(source: own elaboration)

The aim of this study is to investigate the suitability of using WSN with random access to the monitoring of patients (hospital ward). Evaluation of usefulness is related to the probability of packet collisions radio information from each node. In the following sections we present a probabilistic model of WSN and set the relationship on the probability of collisions in a rate for the three groups of patients with regard to the percentage share of each group in the total number of patients. III.

NETWORK MODEL

The network consists of n sensors which are able to send information about the measured physical magnitude on one selected radio frequency to the receiving base, quite independently of each other. Duration of communication protocol is tp, the nodes send the information to the receiving point in randomly selected moments, every T s. at a average. Beginning and cessation of the transmission of a particular node takes place in random moments but these moments are relatively rare. It is a one-way transmission, i.e. from nodes to the receiving base. The nodes are completely independent of one another and their on or off state is of no influence on the operation of the network. All the nodes (sensor-senders) or a part of them may be mobile assuming that their senders have been left within the radio range of the receiving base. If one or more nodes start sending while protocol transmission of tp time is going on from another nodes then such a situation is called collision. The collision excludes the possibility of the correct receiving of information by the receiving base. Such a disturbed signal is ignored. The receiving base rejects the erroneous message and waits for a retransmission to be made after the average time T . We must

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accept a certain loss of information in exchange for simplicity in respect of both system and equipment.

Then the Poisson process N has the rate O = n / T. By (1) P ( N t = j ) = e −λ t

groups of nodes

1

5

5

NODE n2

1

NODE n1

1

5

Poisson process (Nt )

5

NODE 1

5

1 5

j-th protocol transmission

...

(i+1)-th protocol transmission

i-th protocol transmission

collision protocols

Theorem 1. Let n be the number of nodes and let T be the average time between transmissions of a node. Then the probability of collisions in the interval of s length (s > tp) is given by:

BASE STATION Information Management Center

SMS

n - nodes

(2)

In [18] we give the following theorem on the probability of collisions in the interval of s length in the case s > tp.

10%

1

NODE 1

NODE 1

1

30%

NODE n3

60%

[λt ] j ( j = 0,1, !). j!

GATE

P ( As ) =

∞

¦ e − λs

j =2

tp (λs ) j [1 − (1 − j ) j ], j! s

(5)

where O = n /T and tp is the duration time of a protocol. Moreover, in [18], the following theorem has been proved. Theorem 2. Let N(t) be a Poisson process with the rate

O >0, representing the time counter of transmissions of nodes.

MOBILE TELEPHONY GSM

Figure 1. Poisson modeling of network transmission protocols in WSN

IV.

Theorem 3. Assume that n is the number of nodes,

MATHEMATICAL MODEL

k

We model our wireless network using a Poisson process. Mathematically the process N is described by so called counter process Nt or N(t) (see [20], and [17], [18]) of rate O > 0. The counter tells the number of events that have occurred in the interval [0, t] (t • 0). N has independent increments (the number of occurrences counted in disjoint intervals are independent from each other), such that N(t) - N(s) has the Poisson O (t-s) distribution (mean O (t-s)), for t • s • 0, j = 0,1,2,…, j

(1)

[λ (t − s )] P{N (t ) − N ( s ) = j} = e − λ (t − s ) . j!

Let us state our main assumptions. There are n identical nodes observing a dynamical system and reporting to a central location over the wireless sensor network with one radio channel. For simplicity, we assume that our sensor network is a single-hop network with star topology. We also assume every node (sender-sensor) always has packet ready for transmission. We assume that nodes send probe packets at Poissonian times. The average time between sending (the wake-up times) of a node is T (the epoch period), and the duration of the on-time tp (the awake interval). Assume that the wake-up times corresponding to nodes are independent each of other. Let N be the Poisson process representing the time counter of sending nodes. We say that a collision occurs in the time interval of tp length, if at least two nodes start sending within this interval. We say that a collision occurs in time interval s , if there exist at least two nodes which start sending within this interval with the difference between the beginning of their sending time not exceeding the value of tp.

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Then the probability of collisions in the interval of s length (s >tp ) is given by the formula (5). In this paper we study the case, when the average times between transmissions are not necessarily the same. In the following theorem we give the formula for the probability of collisions in this case. n = ¦ ni , (1 ” k ” n) and ni is the number of nodes such that Ti i =1

is the average time between transmissions of a node (1 ” i ” k). Then the probability of collisions in the interval of s length (s >tp ) is given by

P( As ) =

∞

¦

e − λs

j =2

k

where

λ =

n

¦ Tii

tp ( λs ) j [1 − (1 − j ) j ], j! s

(6)

and tp is the duration time of a protocol.

i =1

Proof. Let N(t) be the Poisson process representing the time counter of n sensors, such, that: n =

k

¦ ni

(1 ≤ k ≤ n) , and ni is

i =1

the number of transmissions of nodes for which Ti is the average time between transmissions of a node (i = 1,…,k). Let N(i)(t) (i = 1,…,k) be the Poisson process representing the time counter of sending nodes for which Ti is an average time between transmissions of a node and that all N(i)(t) (i = 1,…,k) are independent random variables. Then N(i)(t) has the rate ni / Ti (i = 1,…,k) and N(t) can be k

written in the form N (t ) = ¦ N (i ) (t ) . i =1

2013 IEEE Symposium on Computational Intelligence in Healthcare and e-health (CICARE)

Consequently we obtain that the Poisson process N(t) has the k

ni rate λ = . Then, applying Theorem 2 with λ = i =1 Ti

¦

k

ni , i =1 Ti

¦

Discussion on determining the usable radio spectrum that is in effect for the duration of the individual bits of the communication protocol is beyond the scope of this article and is the subject of further research using WSN.

we obtain the formula (6). The theorem has been proved. V.

SIMULARIONS RESULTS AND DISCUSSION OF THE RESULTS

The following figures (Fig. 2 and Fig. 3) presents the results of theoretical calculations and simulation results of a wireless network. It was assumed that a measure of the accuracy of the network is the probability of a collision WSN (packets) radio, labeled P(As). Probability of a collision is based on the (6) and is dependent on WSN network parameters: the number of nodes in the network, (which corresponds with the number of hospital beds) and radio traffic generated, the frequency of the announcement. Message transmission parameters were chosen according to the assumptions presented in Table 1. The first simulation (shown in Fig. 2) was performed for the assumptions of Table 1. In Fig. 2, the solid line shows the probability of collision P(As) theoretically calculated for the conditions given in Table 1. The dashed lines are the results of three simulations, for T1 = 5s, T2 = 10s, T3 = 3600 s. The duration of the simulations were Simulations were different duration. For relatively short simulation time we see a greater divergence in relation to the theoretical performance. The simulation time is longer, the better approximates the probability determined theoretically as a result of confirming the results expected. Similarly to the results shown in Fig. 3.

Figure 2. Collision probability depending on the number of nodes determined in accordance with the assumptions in Table 1 (T1 =5s.).

The second simulation (shown in Fig. 3) were performed for less critical assumptions means that the group of patients whose state of health requires increased supervision (represent 10% of all patients) radio communications transmission takes place every 10 seconds. This assumption is also acceptable from the point of view of hospital staff to monitor patients. Particularly noteworthy is the analysis of the obtained values of P(As) as a key answer to the question of the justification for the use of such a network solution for monitoring hospital. Figures 2 and 3 shows that the values of P(As) are small enough, even for a large number of nodes (hospital beds). Extending the time of 5s to 10s for the transmission of signals for the group of patients with the worst health status gives significant improvement in quality of radio communication. The results in Fig. 3 underestimate the criteria established with the medical staff (Table 1), however, are acceptable. There is another much better opportunity to improve the transmission quality by reducing the probability P(As) by shortening the duration of the communication protocols. The duration of the protocol adopted tp = 3,2×10-5 s. a long time and he was taken for comparison with previous studies presented in the bibliography. A detailed analysis of the requirements for the communication protocol allows for prominent shortening it for at least a whole order of magnitude. The adoption of such conditions for the transmission protocol gives excellent qualitative improvement of the transmission, but it will be at the expense of the radio spectrum needed for expansion.

Figure 3. Collision probability depending on the number of nodes designated to the mild requirements for monitoring (T1 =10s.).

VI. CONCLUSIONS AND FUTURE WORK In this paper we presented the model of the wireless sensor network in application to monitoring patients in the hospital. We presented the network model, the mathematical model and numerical simulation (verification of the presented mathematical model). The mathematical model was based on Poisson Arrivals See Time Averages (PASTA). In computational experiments we used the Python programming language together with NumPy and Matplotlib libraries. The presented mathematical model has been positively verified by performed numerical simulations. In our future work on application WSN networks to healthcare we can see two main goals. We will work out new mathematical models of the wireless random access networks.

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The models will be based on randomization of selected parameters of wireless sensor networks. This will let investigate other applications of the WSN in the healthcare. The second goal will be using wireless sensor network, based on presented models, integrated with information system. This will allow to use different kinds of computational intelligence methods to optimize performance of the wireless healthcare monitoring systems. REFERENCES. [1]

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