automated medical diagnosis with fuzzy stochastc models- monitoring chronic diseses

8/18/2019 Automated Medical Diagnosis With Fuzzy Stochastc Models- Monitoring Chronic Diseses

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AUTOMATED MEDICAL DIAGNOSIS WITH FUZZYSTOCHASTIC MODELS:

MONITORING CHRONIC DISEASES

Laurent Jeanpierre and François Charpillet

LORIA, MAIA INRIA Team, Campus Scientifique, 54506 Vandoeuvre-lès-Nancy,France.Email: [email protected]

ABSTRACT

As the world population ages, the patients per physician ratio keeps on increasing. This iseven more important in the domain of chronic pathologies where people are usually monitored for years and need regular consultations.

To address this problem, we propose an automated system to monitor a patient population,detecting anomalies in instantaneous data and in their temporal evolution, so that it could alert physicians. By handling the population of healthy patients autonomously and by drawing the physicians’ attention to the patients-at-risk, the system allows physicians to spend comparatively more time with patients who need their services. In such a system, the interaction between the patients, the diagnosis module, and the physicians is very important. We have based this system on a combination of stochastic models, fuzzy filters, and strong medical semantics.

We particularly focused on a particular tele-medicine application: the Diatelic Project. Itsobjective is to monitor chronic kidney-insufficient patients and to detect hydration troubles.During two years, physicians from the ALTIR have conducted a prospective randomized studyof the system. This experiment clearly shows that the proposed system is really beneficial to the patients’ health.

Keywords: Stochastic processes, diagnosis, fuzzy filters, medical monitoring.

1. INTRODUCTION

The DIATELIC project

The automated monitoring of chronic renal diseases is an interesting application of artificial intelligence techniques to the medical field. Actually, as modern treatmentsenhance the medical care for kidney troubles, dialysed patients’ expected lifetimeincreases dramatically. Combined with the global aging of the population, thisworsens an already important shortage of nephrologists. Therefore, typically patientsare having to wait their turn before they can be healed.

In order to enhance this situation, in France, the LORIA (research laboratory incomputer science) and the ALTIR (Lorraine’s association for the treatment of renalinsufficiency) have funded the Diatelic project. With this system, patients are able tosend their medical data through the Internet on a daily basis. Then, a dedicated computer can analyse these data in real time and compare their evolution with the

c2004 Kluwer Academic Publishers. Printed in the Netherlands. Acta Biotheoretica 52: 291–311, 2004.


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292 JEANPIERRE AND CHARPILLET

patient’s profile. Finally, when an abnormal situation is detected, the system sends analert to the nephrologists of the ALTIR.

At this moment, physicians are able to consult all the archived data, the diagnosed evolution of the patient, and messages from the patient. From this point, they canmake their own diagnosis, convoke the patient for further analyses, or adapt the modelto this particular patient to conform to particularities and evolutions.

Tele-medicine, a transversal approach

Currently, there are four main approaches studied in the context of computer-aided medicine: remote consultations (Chen et al., 2001) which enables a physician to makea diagnosis on a patient without being physically present, itinerant medical profiles

(Shortliffe, 1998; Kosh and Slota, 1999) which enables specialists to access data theyneed from anywhere, the automated diagnosis or monitoring of patients (Huang, 1999;Chen et al., 2002a), and knowledge discovery in databases (Keravnou et al., 2000;Chen et al., 2002b). We could also consider remote surgery, but its domain is differentfrom the others since the computer has no real influence on the patient.

Our approach of tele-medicine is slightly different since it combines some aspectsof all these branches: some simplified form of remote consultation, a patient profile,and an automated diagnosis module. The article by Bellazzi and Magni (2001) shows asystem that is very close to ours, but it seems to be some very preliminary work.

Network aspects of the Diatelic project have been studied by Bellot et al. (2001).In the current article, we will focus on the diagnosis module which could be classified in the third branch: intelligent analysis of medical data. However, the fact that our

patients stay at home implies variations to other approaches. In particular, data are

available only once a day; moreover, they are far less reliable, since the patientmeasures all his signals himself. Additionally, no stepwise diagnosis (Groselj and Kukar, 1999) is possible because the patient is not at the hospital: since one of theobjectives is the cost reduction so that the system could be widely used, convoking the

patient for further analyses should be avoided as much as possible.The originality of our system resides in the way it is built. Usually, models are

based on the data they are to monitor. We have based our system on the medicalsituations the physicians want to detect, whatever the actual data might be. Moreover,since we only assist the nephrologists in their work, a black-box approach is not asolution. In order to provide them with a meaningful tool, they must be able tointegrate the system in their daily practice. This dictates several limitations uponavailable models. The complete description of this work is available in Jeanpierre(2002).

Since the year 2000, nephrologists from the ALTIR have used this system everyday with some of their patients. First, they conducted a prospective randomised studywith 30 patients for two years. Since the results are really encouraging, this will beextended to a greater population containing up to 150 patients.

Firstly, we will describe the diagnosis objectives, focusing more precisely on themedical implications of our choices. Next, we will explain the nature of the availablesignals, and their relationship with the situations we are to diagnose. This leadsnaturally to the patient model we implemented, along with its presentation to themedical team. The following section will focus on the diagnosing algorithm which


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AUTOMATED MEDICAL DIAGNOSIS WITH FUZZY STOCHASTIC MODELS 293

allows for computing the medical state of the patient from the daily data he sends.Finally, we will show the prospective experiment’s conditions, its results, and somefeedback we obtained from the physicians and their patients. We will conclude withconsiderations for developing the system in order to provide patients and nephrologistswith an even better tool.

2. DIAGNOSIS CONSIDERATIONS

The medical situation

The Diatelic project aims at monitoring chronic renal insufficient patients treated through continuous ambulatory peritoneal dialysis (CAPD). This treatment allows the

patients to operate their dialysis at home; this way, they can keep a normal life despitetheir illness. To achieve their treatment, they only have to fill their peritoneum with adialysis solution three to four times a day through a catheter, surgically-added at thelowest end of the peritoneum.

With this treatment, the patient can replace some of the kidney’s functions. In particular, the renal insufficient patient quickly loses the purification functions, alongwith hydration regulation capabilities. Since the peritoneum is very well irrigated bysmall blood vessels, osmosis and diffusion are able to occur between the blood streamand the peritoneum content. This natural phenomenon tries and equilibratesconcentrations on each side of a semi-permeable membrane like the peritoneum.Hence, toxins progressively leave the patient’s blood to fill his peritoneum.Simultaneously, water will be drained at a rate depending on the dialysis solution’sconcentration.

CAPD generally is a good replacement for haemodialysis, because it allows patients to keep their autonomy and does not require them to spend three days a week in a dialysis centre. Additionally, it requires fewer medical staff to achieve a similar result. This point is, from a purely medical point of view, the advantage and thedrawback of this method. Actually, as the population ages, the number of patients per

physician rapidly increases. This is even more critical if we consider specialists whoare nephrologists. Moreover, as medicine enhances the quality of treatments, patientslive longer. Thus, CAPD is a real improvement over haemodialysis, since more

patients can be healed with the same number of nephrologists and nurses.In France, approximately 10% of chronic renal insufficient patients use peritoneal

dialysis techniques, i.e. at least up to 2000 patients. Moreover, this number increases by 7% each year.

However, since patients operate their dialysis on their own, their situation isriskier. The classical approach states that each patient has to come and see his physician once a month. Between two visits, each patient regulates his treatmentthanks to simple rules given by the nephrologists: “if your weight exceeds 70 kg, use aHYPER night bag.” Obviously, if the patient feels bad, he can phone to have histreatment adapted. In addition, nurses come and see some of the patients from time totime. Obviously, the patients are more at risk than those treated by haemodialysis,since their treatment does not take place at the hospital.

In particular, patients’ troubles are principally related to hydration problems: if thedialysis is too weak, the amount of water in the patient’s body keeps on increasing and


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he quickly enters hyperhydration. This pathology is insidious, because the patientshows few external signs of illness; he seems healthy to anyone except to physiciansand nurses. Internally, hyperhydration has catastrophic consequences: the blood

pressure (BP) quickly increases and begins damaging all the vital organs, and especially the kidneys. In this case, renal insufficiency quickly worsens to a statewhere no residual function exists. The kidneys just stop working. Ultimately,hyperhydration leads to the formation of edemas, which are usually deadly if nothealed in time.

Alternatively, when the dialysis is too strong, the patient simply dehydrateshimself. Ultimately, this may lead to coma and death, because the organism has notenough water left to enable the simplest vital operations. This is not so dramatic, sincea dehydrated person feels and looks bad: the patient knows he needs some healing.

Other troubles exist. In particular, the risk of infections is rather important sincethe catheter directly links the peritoneum’s content with the exterior. Normally, thecatheter’s sterility is ensured by the cautious use of adapted tools. However,manipulation errors often induce bacterial or viral infections, directly into the

peritoneum. This may lead to serious complications like peritonitis. However, even if this kind of accident is frequent, complications are usually avoided thanks to anadapted medical treatment.

The system’s objectives

The Diatelic system aims at improving this problematic situation by providing adaily analysis of each patient’s data. The objective of the module is to alert themedical team when a patient shows an abnormal behaviour. Since the major risk for

CAPD patients is related to hydration troubles, we have focused on the evaluation of this variable. Thus, the main objective of the system will be to ensure that each patientkeeps his hydration normal. The trouble is that normal is a subjective interpretation.Even more important, this value is not measurable directly. We will have to deduce itfrom the evolution of the available medical signals.

To regulate the patients’ treatment, nephrologists compute an ideal value for the patient’s weight. This value represents a standard condition, the patient showing agood equilibrium of bones, muscles, fats and water. Obviously, this is very dependenton the patient morphology. If he loses weight or if he grows fat, his ideal value must

be adapted to cope with this evolution. If the ideal weight of the patient is perfectlyknown, evaluating his hydration is easy: if his weight is over his ideal weight, the

patient tends to a hyperhydrated state. This is also true with a lower weight and adehydrated condition.

Finally, the problem can be summarized by these two questions: Is the ideal weightcorrectly set? What is the patient’s weight with respect to its ideal value? To answer these questions, we only have a set of medical signals the patient sends every day.Each signal is related to both questions.

The available medical signals

Each day, a CAPD patient completes a form with medical data. Within Diatelic,the paper sheet is replaced by a computer form, but the requested data are exactly the


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same. The only difference is that the entered values are transmitted directly to the physician’s office instead of waiting for the next consultation.

These data include the patient’s weight, his temperature, some blood pressuremeasures, and dialysis configuration. In this section, we will detail each signal, alongwith its relationship with our goal and the way it is acquired.

Weight

The patient’s weight is measured by simple domestic weighing-scales every day.This value depends on several parameters, since every part of the organism adds to thetotal weight. Major contributions are linked to bones, muscles, fats and water. Theinfluence of the first three is obvious; however, we are really interested in the

influence of the last one: water. Simple physics tells us that one litre of water weighsone kilogram. This implies that hydration has a direct impact on the weight.However, except for bones, the contribution of the patient morphology may vary

through time, since patients are monitored for very long periods. To isolate the water contribution to the global weight, nephrologists use the ideal weight as a referencevalue. Compared to this value, any weight evolution is directly related to variations of the patient’s hydration.

When the patient’s morphology evolves, so do his ideal weight and our reference.Hence, this signal is not sufficient to determine if the observed variations are related tohydration troubles or morphology modifications.

Blood Pressure

Blood Pressure (BP) is measured by the patient himself or by nurses if the patient

is not able to achieve a proper measure. Since the patient population is relatively old,this measure is somewhat biased because of the progressive deafening that generallyoccurs with ageing. However, we are more interested in BP variations than in its rawvalues. Therefore, a fixed bias is not a real trouble in this case; we simply observehigher values when they are measured by the patients.

BP is directly related to hydration, since the blood volume depends on the amountof water it contains. Hyperhydration implies some blood volume increase, whichimplies a BP augmentation. The opposite is true also for dehydration and BP decrease.For this reason, monitoring the BP variations gives very reliable clues about hydrationvariations. This explains also why raw values have little importance.

Moreover, BP evolves as the patient’s position changes. In particular, when the patient stands up, BP normally increases slightly to cope with gravity, in order toirrigate the upper part of the body. However, when the patient dehydrates himself, this

phenomenon disappears. At this time, the upper body’s BP decreases quickly and maylead to losses of consciousness. This is why each patient measures his BP when he islying down and a second time just after standing up. The difference of these values isknown as orthostatic blood pressure. Orthostatic hypotension is a very strongdehydration indication. It is quite reliable, since it does not depend on variations of theraw BP values. There is no need for a reference value to evaluate it. However,hyperhydration has no influence on this.

The trouble with BP is that it does not depend on the hydration level only. The BPregulation is ensured by the heart and by muscles positioned around blood vessels.


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Any modification of these systems may modify the way BP evolves. In particular, patients suffering from heart diseases or insufficiencies show different schemas of BPevolutions with respect to their hydration. The good point is that these parametersrarely evolve. However, in our clinical experiment, we have observed at least one

patient who needed a profile modification because of a heart disease recovery.

Temperature

Temperature is measured by a simple medical thermometer. This signal isrelatively worthless for diagnosing hydration troubles, since we know no relationshiplinking its value to the amount of water the patient’s body contains. At most, we could use it as a witness of some infection. Even then, its utility would need to be proven.

Ultrafiltration

Peritoneal dialysis is achieved by filling the patient’s peritoneum with somedialysis solution, keeping it in stasis for several hours, and then flushing it beforestarting a new cycle. Before its injection, the dialysis solution is weighed. After beingflushed, it is weighed again, so that we can compute the weight difference, named Ultrafiltration.

This difference represents the throughput of the dialysis. During the stasis, the process equilibrates progressively the concentrations of the peritoneum’s dialysissolution and the blood contained in the vessels which irrigate its membrane. Even if the process is complex and several materials are exchanged during this period, theglobal weight difference is relatively predictable for a given patient. In fact, the

principal contribution to this value is the drained water. Toxins extracted from the

blood typically are negligible, compared with the amount of water containing them.Therefore, this value can be seen as an indicator of the amount of water contained

in the blood stream. Actually, the more water the blood will contain, the lessconcentrated the blood will be, and the more water the dialysis will drain.

However, the clinical study seems to indicate that this value is not reliable. In fact,it would be an interesting indicator of the quality of the peritoneum membrane, whichis progressively damaged as time passes. According to nephrologists from the ALTIR,the relationship between hydration and ultrafiltration is really thin, and should not betaken into account.

Automated measures

The question of acquiring these data automatically has been discussed, sinceseveral existing technologies allow for such an acquisition. However, physicians

prefer avoiding this solution, because of the psychological effect on the patients: Theythink that since measuring their physiological signals involves the patients in their treatment, they will better obey their physician’s directives.

3. THE COMPUTER MODEL

Several ways of modelling such a problem within a computer exist. In particular,we tried two approaches: a rule-based expert system (Buchanan and Duda, 1982) and aHidden Markov Model (HMM). These two modules are based on the nephrologists’


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knowledge of the hydration influence on the different medical signals available. Their objectives are to identify patients’ troubles before they become life-threatening, and tofigure out if the observed deviations are related to hydration evolution or to somemodification of the patient morphology. The principles of these two models aredifferent, but they are based on the same observations.

Therefore, we will describe firstly the observations of the diagnosing modules;then, we will briefly describe the rule-based system along with its drawbacks beforeshowing the HMM which has been used for several years in Diatelic.

Fuzzy observations

The observation function is based on a computer’s design limitation: computers are

discrete, i.e. any symbol a computer manipulates can have a finite number of values.There is no possibility of creating really continuous values. The trouble is that almostall we observe has a continuous value. For example, weight, BP, and so on.

There exist two main approaches to this problem. The first one uses a set of discrete values to represent a continuous one. In most cases, it is a valid approach,since it needs only an adapted set of symbols. For example, we could discretise theweight by using a symbol for each integer value: 60, 61, 62 kilograms. Within thismodel, 60.3 kg is not a valid weight; it will be rounded to 60 kg. The error amplitudeis inversely proportional to the number of the available symbols: if more precision isneeded, using a symbol for each 100 gram slice will be sufficient. The trouble is thatthe model should express the relationship between these symbols and the underlyingstate the system is to diagnose. This implies that the nephrologist who is responsiblefor introducing a new patient in the system is to state this relationship for all the

possible sensors’ values. This quickly becomes impossible as the symbols set grows bigger.

The second approach consists of using parametric curves to model the influence.This kind of model is very useful where the influence we are to model has a knownstructure. For example, in speech recognition, the classically used pattern is a mixtureof Gaussian probability distributions. However, this typically leads to huge parameter lists, and their precise influence is difficult to describe. Hence, this approach is hardlycompatible with a full-scale interaction with physicians.

To resolve this problem, we chose a hybrid approach through the fuzzy filtering of the medical signals as suggested in Steinmann (2001). To be precise, we decided tomodel each sensor as a fuzzy value that can have few symbolic values. Since weconsider long-term monitoring of chronic diseases, there exists a central condition thatrepresents a healthy situation. Therefore, in order to closely map the model with the

physicians’ way of describing their diagnosis rules, we chose a set of three values for each sensor: ‘low’, ‘normal’, and ‘high’.

For example, since nephrologists usually give rules such as “if your weight is high(> ideal weight + 1.5 kg), use a HYPER dialysis bag”, our weight sensor will be based on the ideal weight value. If it is lower (respectively higher) by at least 1.5 kilograms,the patient’s weight will be considered as low (resp. high).

The trouble is that this implies an annoying threshold effect: if we consider anideal weight of 60 kg, 61.4 kg is normal, but 61.5 kg is high. In turn, this impliesstrong variations in the diagnosis because of brutal variations of the available data. To


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prevent this threshold effect, we used fuzzy filtering: the system will map a givensensor value to a confidence distribution over the symbols instead of returning a singlesymbol. In the previous example, 61.4 kg will be 8% normal and 92% high. Thissmoothes the diagnosis rules and almost removes the threshold effect. In particular, itenables the system to compensate for the influence of several sensors. For example, if the weight is 60% high, but other sensors have normal values, it will be less importantthan a situation where BP would be high also, even by a mere 30%.

We tried and compared the two approaches, i.e. with fuzzy filters and withoutthem; the results show a real enhancement with fuzzy filtering. Diagnoses aresmoother and they vary less when we add some noise to the system’s input values. Thelast question of importance is the way fuzzy filtering can be achieved. We worked from simple considerations to define the right parametric curves for each symbol.

First, this function must reach its boundaries. For example, a weight that is10 kilograms over its ideal value is clearly high. There is no chance it could beconsidered low or even normal. The next point is that the confidence is not linear. For a given increment, the influence will depend on the base value of the sensor. The ideais that the reference value is not perfectly known, so it is useful to have the smallest

possible variations around this value. With these constraints, the usual functions, i.e.exponential and linear functions, cannot be applied to our system.

Thus we decided to define the relevant function from its constraints by using amere interpolation function on a given interval. The ‘low’ symbol (resp. ‘high’) isdefined by four constraints: it is 100% at its lower (resp. higher) boundary, 0% at itsupper (resp. lower) boundary, and it has a zero derivative in these points. The simplestformula that allows such constraints is a polynomial with four degrees of liberty:

Low ( x) = 3 x

2

+ 2 x

3

∀ ∈ − x [ ; ]1 0 (1)High ( x) = 3 x2 – 2 x3 ∀ ∈ x [ ; ]0 1 (2)

Normal ( x) = 1 – (Low ( x) +High ( x)) ∀ ∈ − x [ ; ]1 1 . (3)

For the sake of simplicity, these formulas have been computed with a referencevalue of 0 and interval amplitude of 1; however, we can transpose them to any other values thanks to equation (4). Outside of their definition interval, each symbol has afixed probability equal to its value at the corresponding terminal. ‘Normal’ is simplydefined as the complement of the two other symbols.

x sensor reference

amplitude =

−. (4)

Figure 1. Graphic representation of our fuzzy symbols.


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For example, if 60 kg is a normal weight, 60.1 kg will be 97% normal withstandard amplitude of 1.5 kg. 60.2 kg will be 90% normal, and 60.3 kg will be 78%normal only.

The fuzzy filters actually enables the model to express the relationship between themedical state of the patient and the sensors’ values with relatively few parameters.Moreover, the physicians can easily interpret each parameter, because their values aredirectly expressed in a human-readable form. The clinical experiment we conducted clearly shows that nephrologists from the ALTIR are able to work with this modelwith a very short adaptation period. After a few days they are able to tune a model for any patient and they can interpret a patient’s profile with little effort.

A rule-based expertSince the MYCIN system showed good results (Buchanan and Shortliffe, 1984),the first module we built was based on a rule-based expert system. Actually, this kind of computer module is able to select and apply rules from a set of predefined ones to aset of fac ts. In our problem, we used CLIPS, a generic rule-based system initiallydeveloped by the NASA since 1984.

More precisely, we used Fuzzy CLIPS, which is a newer version that permits theuse of fuzzy logics. Therefore, it is clearly well adapted to our perception model. Thesystem will work from the insertion of a daily fact that includes all the medical signalsof a given patient. At this moment, rules are gradually applied to process these rawdata, and produce high-level knowledge: the desired diagnosis.

After some tuning, the system was able to produce very good diagnoses for a given patient. However, it required that we set the proper values for thresholds, rule

priorities, and influences. Therefore, we could not apply this system to a whole population of patients. In fact, there were so many parameters to set for each patientthat several days of trials were necessary before obtaining the proper parameter combination. Additionally, no one was able to understand the exact implication of asingle parameter value anymore. Therefore, the system became a “black box” thatsometimes produced relevant diagnoses. Obviously, it was not compatible with a dailyinteraction with the physicians anymore.

The stochastic model

As stated in Horn (2001), it is necessary to evolve from a knowledge-based to adata-based system to achieve a good medical diagnosis. In fact, this amounts toadmitting that our knowledge is neither complete nor perfect. By focusing on the rawdata, we try and deduce relations on observed facts rather than to explain how theseobservations are produced by the organism.

Regarding the definition of the module, this approach is totally different. In Rule-Based systems, we have to formally express diagnosis rules. With a Data-Based system, we state the influence the diagnosis has on the sensors; this declarativeknowledge is far easier to gather and formalize.

In the vast family of numerical models, we decided stochastic models should bethe best bet to cope with both the uncertainty of our knowledge and the noise that mayinfluence the system. More precisely, we chose Markov models, because of their ability to model temporal evolutions of dynamic systems. Moreover, these models


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have been studied for years, and we know very efficient algorithms to handle their usewithin a computer.

The Mathematical Formalism

A Markov model is a finite state automaton with probabilistic evolution which can be specialised into several models: Hidden Markov Models (HMM), Markov DecisionProcesses (MDP), and Partially Observable Markov Decision Processes (POMDP).We chose the last one, which is the more potent but also the more complex. However,we use only a small part of its possibilities; in particular, we may study the planningoperations in future extensions only.

A POMDP is a structure (S , I , O, A, B, R):

S

I

O

A A S I S

B B S O

R

::

:

: : ( ),

: : ( ),

:

a finite set of discrete sets, a finite set of discrete influences,

a finite set of observable symbols,

a transition function

an observation function

a reward function.

× →

→

Π

Π

(5)

In this structure, the set of states has a central role: it represents the hidden state of the modelled system, the state which dictates the system behaviour. The Markovhypothesis states that the knowledge of this state gives the knowledge of all the futuresystem evolutions and observations, with no additional information requirement.

The transition function is a probabilistic description of the system evolution: for a

given action used in a given state, it predicts the distribution of states the system willreach on the next step. The classical way to implement such a function consists of using a S S× probabilistic matrix for each possible action.

The reward function is a way of indicating the goal we would like the model toreach. Several forms of rewards exist, depending on the relative importance of states,actions and observations. As we focus on passive diagnosing (nephrologists areresponsible for the patient’s treatment), the system does not need to choose atherapeutic action. The computer’s role is limited to monitoring patients and alerting

physicians. Therefore, we will not detail the reward subtleties.The observation function is another probabilistic function which describes how the

model state is hidden by the observation process: The system’s state is not directlyobservable, but there exists a set of observable symbols which are influenced by thesystem’s state. The trouble is that this influence is not perfectly known and its

measurement may be spoilt by noise; this is why this function is probabilistic.Anyway, these symbols are the only available data.

Considering the observation model we described earlier, continuous medicalsignals are transformed into confidence distributions among sets of three fuzzy valuesnotated ‘-’, ‘=’ and ‘+’. Therefore, we decided to use the approach described in(Koenig and Simmons, 1996): considering a sensor c, its observed value c(O) is

projected onto its fuzzy symbols, and the resulting confidence vector is aggregated into a probability vector. Each component of this vector is the probability of observingthe continuous sensors from a specific state:


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P c O s P c O v P c v s

v

( ( ) | ) ( ( ) ) ( | ).

{ , , }

= = ⋅ =

∈ − = +

∑ (6)

This is possible only if each sensor is considered as statistically independent fromthe others, depending only on the model’s state. Next, we can aggregate the

probabilities for observing each sensor c in a single observation probability for eachstate to obtain our observation function:

P O s P c O s

c

( | ) ( ( ) | ).= ∏ (7)

Finally, the description of the influence of the model’s state on a given sensor willrequire only three probabilities per possible state. Once again, we can use a matrix per

sensor to store these probabilities.

Application to medical diagnosis

There are two principal applications for POMDP: localization and planning. Theformer consists in searching an optimal sequence of actions to reach a given goal.Since the goal is expressed through the reward function, this is equivalent to findingthe action sequence which maximizes the expected reward. Localization consists of trying and figuring out the hidden state of the system, using the available knowledge(the model) and the observed data.

Since we focused on the diagnosis problem, we obviously chose the localization problematics; the planning functions will be studied in future work. From thedictionary, diagnosing is “determining a disease from symptoms”. On the other hand,localization is defined as “to position in space”. Hence, these two notions are very

similar. To achieve medical diagnosis with localization algorithms, we simply defined an ad hoc space: our POMDP state space is based on a map of pathologies. Therefore,

positioning the patient on this map is equivalent to determining the pathologies itsuffers from.

Considering our particular problem, the long-term monitoring of patients, we havea special state that plays a central role in the system: the healthy condition. Normally,any patient should be in this state, where all is right and there is no particular risk.From this point, we can derive variations, based on the possible appearance of some

pathology. We decided to focus on hydration troubles, since they represent the principal risk for CAPD patients. As we stated in the observation-related section, thesetting for the ideal weight has a crucial role in the regulation of the dialysis strength.Since one of the main hydration indicators is the weight and this sensor is evaluated with respect to its ideal value, the evaluation of the pertinence of this setting has been

elected as an interesting point to diagnose also.Finally, our model states will spread across two axes: hydration and ideal weight.

Considering our problem, we chose to model these variations in the same fashion assensors: hydration may be normal (‘=’), low (‘-’) or high (‘+’). Therefore, the healthystate will be notated (‘=, =’): normal hydration with a correctly set ideal weight.

From the analysis of the available medical signals, we can isolate four usefulindependent sensors: Weight, Blood Pressure, Orthostatic Blood Pressure (OBP) and Ultrafiltration (UF). Each one is related to hydration troubles in a known way.Obviously, Ideal Weight is only related to the weight sensor. Other sensors may be


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influenced by the couple Weight/Ideal Weight, but we assumed our sensors areindependent of one another. Therefore, this relationship will be modelled through themodel state: hydration and Ideal Weight influence the perception of the weight, BP,OBP and UF. Table 1 shows the direct relationship between the fuzzy perceptions and each possible disorder, considered as the only influence.

Table 1. Disorders’ influence on sensors.

Sensor Disorder Weight BP OBP UF

+ / = High High Normal + High

- / = Low Low Low Low= / + Low Normal Normal Normal= / - High Normal Normal Normal

Table 2 shows the resulting influence of the combination of both disorders;obviously, we can see that some combinations are difficult to diagnose. These arereferred as “High&Low” since one disorder usually comes with a high sensor reading,whereas the other one implies a low sensor reading. The actual value can be almostanything since it depends on the relative strength of both disorders. One of them candominate the other one, or both influences can bring an artificially normal reading. For this reason, we decided not to include these two states into our state space. Finally, our model will use five states: ‘healthy’, ‘hyperhydration’, ‘dehydration’, ‘Ideal WeightHigh’ and ‘Ideal Weight Low”.

Table 2. Combined influences of two disorders.

Sensor Disorder

Weight BP OBP UF

+ / + High&Low Normal + Normal + Normal ++ / - High Normal + Normal + Normal +- / + Low Normal - Normal - Normal -- / - High&Low Normal - Normal - Normal -

In the current version of the Diatelic system, no action has been implemented.Actually, the actions represent the known influences a given patient will receiveduring the considered time lapse. Concerning CAPD patients, these influences contain

but are not limited to dialysis strength and drugs consumption. In general, to modifythe dialysis strength, a patient can use various concentrations of dialysis liquid.Usually, they use three kinds of standard bags: ISO, MEDIUM and HYPER. ISO bagshave a concentration which is comparable with the human blood; thus, they should drain almost no water at all. On the other side, HYPER bags are much moreconcentrated. Such a bag is used to drain much water. MEDIUM bags have anintermediate concentration and effects.

A given patient uses 3 bags a day, each bag staying in stasis for 4 hours in the peritoneum. Some patients use an additional bag during the night. Hence, we can have


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at most (3^3)x4 = 108 different dialyses. Moreover, each patient reacts to a particular treatment differently from the other patients. Finally, there are several noise sourcesthat perturb the standard evolution of the patient: stress, ambient temperature, and meals are common sources which are totally uncontrolled since the patient is at home.All these facts made it impossible to learn a complete set of actions for each patient.Finally, we chose to implement a generic action which includes no influence, butensures the temporal coherence of the diagnosis: for example, a patient’s hydrationwill rarely evolve from a leakage to an excess in a single night. The action wemodelled will make such an evolution very improbable.

Currently, a patient profile will contain only 60 probabilities, along with a fewcomputed tendencies like the average BP measured during a few days. These

probabilities are the parameters of the observation function: we have four sensors with

three fuzzy values influenced by five states. Since the fuzzy values are used throughconfidence distributions, one third of these probabilities can be deduced. Finally, a

patient profile will contain 40 independent parameters.

Figure 2. Diatelic’s observation function.

Since our sensors are independent, it is possible to plot the probability of theobservation of each sensor within each state of the model. The resulting graphs,represented in Figure 2, show intuitively the influence of each state on the various

sensors. Physicians can dynamically interact with this representation by dragging thecurves with their mouse. At this time, the program automatically computes the newmodel, and displays the updated diagnosis. This way, nephrologists can adapt the

profile to their patient.Considering our model definition, the semantics of each parameter is obvious. In

the same fashion, anyone could interpret the diagnosis without difficulty: Thelocalization algorithm (Forney, 1997) computes a probability distribution over thestates for each time data have been received. Since we fixed the medical semantics of each state, imposing a strong relationship with the possible occurrence of troubles, we

UF

Healthy Dehydration Hyperhydration I.W. Low I.W. High

Weight

BP

OBP


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can interpret these distributions directly as the probability of the correspondingtroubles. We tried several ways of displaying these voluminous data (five daily

probabilities), but we finally elected the simplest one: for each patient, a graphicsdisplays a set of five plots, one per state. Each plot has a specific colour whichidentifies it from the others. The nearer from the top of the display a plot is, the more

probable the associated state is.

Figure 3. Sample diagnosis from Diatelic.

Figure 3 shows a sample diagnosis computed during a dehydration incident. At the

beginning of this period, the patient was healthy. After a few days, some gradualdehydration (plotted in black) appears. When the black plot becomes dominant, analert is sent to the physician who adapts the patient’s treatment. In the few followingdays, the ‘healthy’ state becomes dominant again, we certainly avoided an accident.Shortly after the dehydration peak, we can observe a small increase of the ‘IdealWeight High’ plot. This is due to the patient’s BP which returned to its normal value.At this time, the weight is over its ideal value, and other sensors are almost normal.This situation is characteristic of bad ideal weight setting. However, as theseconditions are transient, and since the other sensors are slightly over their normalvalue (in their tolerance interval), this state never becomes a real hazard. It remains amere possibility.

4. THE DIAGNOSING ALGORITHM

As we showed in the previous section, computing the patient’s diagnosis isequivalent to determining the probability of each model state at each time step. Thiscan be efficiently computed thanks to the application of Bayes’ rule for conditional

probabilities (equation (8)) and dynamic programming principles (Puterman, 1994).The resulting algorithm, Forward-Backward, has been published in Forney (1997):

P ( )A.B = P ( )A | B . P ( )B = P ( )B | A . P ( )A . (8)

At the time t , the patient’s diagnosis is the vector γ which contains the probabilityof each state st , knowing the observation sequence O and the model λ :


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γ λ t t q P s q O( ) ( | , )= = . (9)

The application of Bayes’ rule allows for isolating the observations from themodel:

γ λ

λ t t q

P s q O

P O ( )

( , | ).=

=

( | )(10)

The observation sequence can be split at time t :

γ λ λ

λ t t t T t q

P s q O P O s q

P O ( )

( , | ) ( | , ).

...=

= =+

( | )1 (11)

The introduction of the parameters α and β will simplify the equation:

α λ t t t q P O s q( ) ( , | )...= =1 (12)

β λ t t T t q P O S s( ) ( | , )...= =+1 (13)

γ α β

α β t t t

t t q S

q q q

q q ( )

( ) ( )

( ' ) ( ' ).

'

= ⋅

⋅∈

∑(14)

The computation of α is known as the forward procedure, while computing β relies on the backward procedure. The first step of the forward computation relies onthe application of Bayes’ rule once again:

α λ λ t t t t t t q P O O s q P O s q( ) ( | , , ) ( , | ).... ...= = =− − 1 1 1 1 (15)

The first term is the simple application of the observation function B to the state q,

since the Markov hypothesis allows us to drop all the previous observations. The lastterm can be detailed, depending of the state at the time t – 1:

α λ t t t t t

q S

q B O q P O s q s q ( ) ( , ) ( , , ' | )...

'

= = =− −

∈

∑ 1 1 1 . (16)

A new application of Bayes’ rule will enable the summed term to be split:

α λ λ t t t t t t

q S

q B O q P s q s q P O s q ( ) ( , ) ( | , ' ) ( , ' | ).....

'

= = = =− − −

∈

∑ 1 1 1 1 (17)

The first term in the sum is the mere application of our transition function to thestates q and q’, and to the action at - 1. The last term is simply the expansion of α at thetime t – 1, in the state q’:

α α t t t t

q S

q B O q A q a q q ( ) ( , ) ( , , ' ) ( ' ).'

= − −

∈

∑ 1 1 (18)

This expression is simple enough to be computed with a complexity linear in timeand in the cardinality of S S× . We will have to work similarly with equation (13):

β λ t t T t q P O S s( ) ( | , )...= =+1 . (13)

In order to allow for the appearance of a recursive form, we will expand thisexpression, depending on the state at time t + 1:

β λ λ t t t t T t

q P s q s q P O S q ( ) ( ' | , ) ( | , ' )....

= = = =+ + +∑ 1 1 1 (19)

Once again, the first term is the application of the transition function to the states qand q’, and to the action at .


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β λ t t

q S t T t

q A q a q P O S q ( ) ( ' , , ) ( | , ' ).'

...= =

∈+ +∑ 1 1 (20)

From this point, we can split the observation sequence again, so that the time t + 1is separated from the others:

β λ λ t t

q S t t t T t

q A q a q P O S q P O s q ( ) ( ' , , ) ( | , ' ) ( | , ' ).'

...= = =

∈

+ + + +∑ 1 1 2 1 (21)

The last term is merely the expansion of β , applied at the time t + 1 and the stateq’ . The central term is simply the application of the observation function B to thesymbol observed at time t + 1 and to the state q’:

β β t t

q S t t

q A q a q B O q q ( ) ( ' , , ) ( , ' ) ( ' ).'

=∈

+ +∑ 1 1 (22)

Since this function’s complexity is also linear in time and inS S

× , so is thecomplexity of our diagnosis computation, γ . Finally, since our state space is relativelysmall, this complexity is acceptable and allows for a real-time analysis of data.Obviously, computing the diagnosis of a given patient for several months has littleinterest and becomes costly concerning the necessary computing time. Hence, welimited the computation to the latest 60 days: at any time, physicians can have a look at the computed diagnoses for the last two months.

5. THE PROSPECTIVE EXPERIMENT

Conditions

The Diatelic analysis module has been studied in a monocentric prospective

randomised experiment which lasted two years. This study included 30 voluntary patients who were suffering from terminal chronic renal insufficiency. The objectivesand the conditions of the experiment have been explained to all patients, who accepted them. All these patients have been treated through standard CAPD for one month athome after being equipped and trained by nephrologists from the ALTIR.

After this month of formation, patients were randomly distributed across two populations: the Diatelic and the Reference groups. The first group has beenmonitored with the module this article describes while the other one was monitored the classical way. The first patient entered the experiment on 6 th June 1999. The latestentered on 8th August 2000. The global study ended in August 2002, two years later.The objectives of the study were to find out the impact Diatelic has on the patients’life quality, their morbidity, and the global treatment cost.

Table 3. Group characteristics.

Group Diatelic ReferenceSex (Men / Women) 8 / 7 9 / 6Average age (standard deviation) 69.8 (±14.8) 70.7 (±12.4)Diabetic patients 5 4Comorbidy (Charlson Index) 5.7 4.8Distance from the ALTIR in km 52 52.5


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Gladly, the two groups are statistically comparable. Significance is evaluated through a standard ANOVA (analysis of variance) statistical test. Table 3 shows their compared characteristics. The Charlson Index is an evaluation of the illness severity

based on the age and pathologies, ranked with respect to their mortality. Thesecharacteristics show no significant difference between the two groups. More than thesenumerical values, medical causes for the renal insufficiency and residual kidneyfunctions are also statistically comparable across the two groups.

Results

At the end of the experiment, results have been gathered and new data will not beincluded. However, since the intuitive evaluation of the system by the patients and

their nephrologists was very positive, the experiment continued from then. All theresults are not known yet. In particular, the study of the life quality’s forms is notcomplete. However, the results we expose here are really positive. After six months,the first medical enhancements were already discernible by the medical team(Chanliau et al., 2000).

To begin, we will consider the compared mortality: the study included 30 patients;on 8 th August 2002, 12 patients were still in the groups. Table 4 shows the reasons for the departure of the 18 other CAPD patients, but none of these causes are statisticallysignificant. In particular, the number of deceased patients seems prohibitive. However,none of these deaths is related to dialysis troubles, and this should not be counted against our system. Moreover, the average Charlson index is very high in both groupsand patients are quite old; since these two factors amount to a low survival rate(Charlson et al., 1987), this high death percentage is not really surprising.

Table 4. Reasons for patients’ departure from the experiment.

Number of patientsReason for departure

Diatelic ReferenceDeceased 8 4Transferred to haemodialysis 3 1Geographic movement 0 1Kidney transplant 0 1

The first significant factor the study reveals deals with the number of visits each patient pays to his nephrologist. The normal frequency of a patient’s visits is once amonth, i.e. 12 in a year. However, the delay between two visits is decided by the

physician, depending on the health level of the patient. Table 6 shows the comparisonof the visits frequency with respect to the fact of whether the patient died or not, whichis a crude but objective indicator of the patients’ health level. As expected, unhealthy

patients come and visit their physician more often. On the other hand, Table 5 showsthe compared value of the two groups, indicating both the average value and standard deviation of consultations and hospitalizations. The number of normal visits is almostthe same for both groups, but spontaneous visits show a very significant( P ANOVA < 0.0066) drop in the Diatelic group with respect to the Reference group.


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Table 5. Yearly medical interventions for CAPD patients. An ANOVA test shows that thedecrease of spontaneous visits are significant ( P < 0.0066).

Yearly medical actions per Year Diatelic ReferenceProgrammed visits 10.6±2.3 11.0±2.3Spontaneous visits 2.8±2.1 5.3±2.7Total number of visits 13.4±3.4 16.3±2.4Days at the hospital 11±14.5 20.5±36.1

Table 6. Comparison of the frequency of patients visits with respect to their death. A Wilcoxontest shows that deceased patients have more predicted visits ( P < 0.019).

Visits per Year Deceased Patient Surviving PatientProgrammed Visits 12.5±3.72 10.9±1.9Spontaneous Visits 3.5±3.8 2.16±3.36

Therefore, we could say that the use of Diatelic contributes to a globalenhancement of the patients’ health level which amounts to a global diminution of theneed for consultations. Similarly, the length of treatments at the hospital per year,regardless of the hospitalization reason, shows a diminution of 46% in the Diatelicgroup; however the very large standard deviation in both groups implies this loss is notsignificant. There are too many in-group variations.

The numerical evaluation of the health level of patients is difficult to achieve, sinceit is not directly measurable. However, we compared the evolution of three interestingvalues: the weight, the average blood pressure, and the amount of drugs a patient uses

to regulate their blood pressure. Table 7 summarizes all these values, along with their standard deviations. The first point of interest is that the weight increase of the patientsseems better controlled in the Diatelic group; however, the in-group deviations are solarge that this variation is not significant. Blood pressure shows a significant( p < 0.03%) drop in the Diatelic group with respect to the Reference group. This iseven more important if we consider the raw values of the blood pressure presented inTable 8. With these data, we can note that patients were globally in a hypertensionsituation in both groups at the beginning of the experiment. After two years, theDiatelic group returned to normal blood pressure values. Correlated with the weightevolution and the almost significant ( P < 0.0614%) drug consumption decrease, itseems probable that these evolutions are due to a better hydration regulation.

Finally, the last objective of the Diatelic Project was to reduce the treatment costsof CAPD patients, so that it could be applied to large populations. The trouble is that

these costs are difficult to evaluate. Actually, they include costs for treatments(equipment, drugs and dialysis bags), hospitalizations, and transports. Since theaverage distance from patients’ home to the ALTIR is statistically comparable in bothgroups, our first costs estimates are strongly correlated to visits evolution and bring nonew information.

However, the ARH (Regional hospitalization agency) and the URCAM (Regionalunion of medical insurance funds) are very interested in this system; they funded anexperiment extension for three more years and 150 patients. Therefore, Lorraine will

become a pilot site for evaluating the Diatelic system on a regional scale. The


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objective will be to cross-check the prospective study’s conclusions and to evaluatethe impact of the equipment on a whole region on the medical costs of dialysis. In fact,renal insufficiency is a public sanitary problem since 6,000 new patients are to betreated in France every year. This amounts to 2% of the global cost of the Frenchsanitary system.

Table 7. Global evolution of medical signals over a two year period.

Variations of Diatelic ReferenceWeight +0.413kg (±4.3kg) +2.631kg (±3.9kg)Blood Pressure -1.177mm Hg (±1.133mm Hg) -0.023mm Hg (±1.582mm Hg)Drugs -0.2 (±0.561) +0.333 (±0.9)

Table 8. Blood Pressure evolution over a two year period.

Blood Pressures (mm Hg) Diatelic ReferenceInitial Systolic 13.73±1.6 13.33±2Initial Diastolic 7.87±1.2 8±1.1Final Systolic 11.53±1.6 13.9±1.5Final Diastolic 7.1±1.1 7.9±0.8

6. CONCLUSION AND PERSPECTIVES

This article describes diagnosing software architecture which enables a simpleinteraction with human specialists while maintaining a low computing complexity. We

ensured this intuitive interaction process by enforcing very strong medical semanticsin every part of the model. This way, without requiring special abilities in computer science, it allows physicians to understand the actual influence of each model

parameter with respect to the diagnosis.The low computing complexity is the consequence of the use of a classical

Partially Observable Markov Decision Process. This model combines a strongmathematical background which makes coping with uncertainty and noise with provenresults possible, and very efficient algorithms like the Forward-Backward procedurewhich makes computing of the patient diagnosis in real time possible.

We tested this system through a prospective randomized study in which 30 patientswere monitored for two years. The analysis of several parameters from the Diatelicgroup, and their comparison with the Reference group suggests that our system was

beneficent to the patient’s health. From an economical point of view, this better health

condition implies fewer consultations and a large drop in the related costs. From amedical point of view, patients seem to control their hydration-level better whileconsuming fewer drugs. Several other parameters, like the hospitalization duration,show an interesting influence, but the gathered data show too much in-groupvariations to permit statistically significant conclusions.

This experiment has been elected to a duration extension by French sanitaryassociations which offered financing for a three-year study on a regional scale: 150

patients will be monitored from several medical centres in Lorraine. To ensure the bestquality of services, a new enterprise has been funded: Diatelic S.A. which will ensure


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the installation and the maintenance of the computer systems at the patients’ home aswell as on the server side. It will also ensure software maintenance as well asextensions and upgrades. Additionally, several dialysis centres in France, are startingand using the system for their own patients’ monitoring.

There are several perspectives for enhancing the data analysis. We think the most promising would regard continuous aspects. In particular, two particular points seemimportant: smoothing the diagnosis and isolating proper actions to model. Thediagnosis may be smoothed by working from stereotyped situations to progressiveones: currently, a given patient may be totally hyperhydrated, without any problem or completely dehydrated. States probabilities should not be interpreted as intermediatesituations. For example, a patient who is diagnosed as 50% healthy and 50%dehydrated is not really half-dehydrated. In fact, he may be totally dehydrated or

healthy, but the system is unable to decide. Using a state space that gradually evolvesfrom a healthy to a dehydrated condition would be more accurate. Moreover, the

patient dynamics could be better modelled with such a continuous state space since thesystem would know how much a patient is dehydrated. Obviously, strong dehydrationis longer to heal than a light one.

The second major improvement would be to integrate dialysis options as actions inthe model. It seems obvious that it will be impossible to define more than one hundred actions for each patient. To cope with this situation, we think we could use continuous

parametric actions. The idea is that the modelled phenomenon is physical; with few parameters, we may be able to express the water amount a given bag will drain withrespect to the stasis duration. From this point, computing the right transition matrixshould be easy.

As a long-term improvement, we could imagine a system that would check the

appropriateness of the patient’s treatment, and propose modifications when useful.This behaviour would be based on the planning functions of the POMDP. The troubleis that these functions are very complex and computing intensive. The addition of continuous elements would even worsen this situation. This is why we consider this

possibility for long term evolutions only.

ACKNOWLEDGMENTS

We would like to particular ly thank Doctor Pierre-Yves Durand and Professor Jacques Chanliau for their invaluable collaboration. From the ALTIR, theytried and commented on several versions of the Diatelic system. Their feedback contributed to most enhancements we have incorporated. Without their help, the

project certainly would not have achieved such results.

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automated medical diagnosis with fuzzy stochastc models- monitoring chronic diseses

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