# An Analogical Model to Design Time in Clinical Objects

Joël Colloc, Peter Summons

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Joël Colloc, Peter Summons. An Analogical Model to Design Time in Clinical Objects. Journées RITS 2015, Mar 2015, Dourdan, France. inserm-01154489

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# An Analogical Model to Design Time in Clinical Objects

Joël COLLOC<fnref n="1" />*, Peter SUMMONS<fnref n="2" />

**Abstract** - This paper proposes an object oriented model to implement medical Knowledge Base Systems (KBS). The model has two levels. The external level (type level) facilitates the implementation and the interoperability of the system. The internal level describes the objects which are combined with the composition (union) operator $\oplus$. A fuzzy vectorial space defines the evolution of the clinical objects involved in the system. Thus, the composition of the clinical picture objects is tuned by fuzzy functions whose values evolve with time. The model provides new tools to compare the evolution of objects and to implement analogical reasoning.

**Index Terms** - E-health, Medical Informatics, Modeling

## I. INTRODUCTION

Modeling time in the evolution of clinical pictures for diagnosis, prognosis and therapy remains a great challenge due to the need to express the emerging properties of the clinical pictures, syndromes and signs in interaction. To efficiently compare the evolution of the structure and state of these objects we propose distances that rely on a gradient computed from a fuzzy vectorial space Figure 2. Our object model integrates time fuzzy functions to express the composition evolution of a disease without the need for fuzzification and defuzzification stages. In a previous work, we summarized the complexity of disease modeling: every patient is unique; most diseases are multifocal and are dynamic linear or cyclic processes, such as with a duodenal ulcer and psoriasis [1]; and treatments may result in unusual clinical aspects or produce iatrogenic diseases.

## II. MATERIALS AND METHODS

Figure 1 shows the structure evolution of a disease and how an agent sorts the syndromes according to the gradient vector distances of their component signs and relevant attributes Figure 2. The attribute values (three to facilitate the representation) are normalized fuzzy functions on a [-1, 1] interval that allow us to build a vector which defines the state of each component object at each time t. In turn, the component objects create a composite object and its corresponding resultant vector in the same manner.

<figure><img src="image_2.png" /><figcaption>Figure 1: Evolution of a disease D composed of their clinical pictures CP, syndromes Sd and signs S</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: A fuzzy vectorial space defines a composition vector from its object components and their attributes</figcaption></figure>

For brevity, we illustrate our model with a simple example: the diagnosis and prognosis of acute diarrhea. A compulsory initial sign (CS1) in Figure 3 can lead to several diagnoses $\Delta_1$ to $\Delta_8$ and their corresponding prognoses $\Pi_1$ to $\Pi_8$ and therapies (Figures 4, 5), depending on the clinical signs $ES_1$ to $ES_6$, the history of risk (HR) and the signs of severity (SS) shown by the patient. The time evolution of the disease is compared according to the transitions of the

<footnote n="1">¹ UMR CNRS IDEES 6266, The University of Le Havre.</footnote>

<footnote n="2">² The University of Newcastle, University Drive, Callaghan, NSW 2308, Australia</footnote>

<footnote>* joel.colloc@univ-lehavre.fr, Peter.Summons@newcastle.edu.au</footnote>
<figure><img src="image_4.png" /></figure>

<table><caption>Figure 3: Automaton of acute diarrhea diagnosis ($\Delta_0$, $\Delta_2$ and $\Delta_4$ are intermediate states)</caption><thead><tr><th colspan="2">Compulsory Signs (CS), Evocative Signs (ES)</th></tr></thead><tbody><tr><td>CS<sub>1</sub></td><td>Recent frequent stool soft or liquid</td></tr><tr><td>ES<sub>1</sub></td><td>Nauseous state or vomiting, mucus, blood, abdominal pain (tenesmus) extracellular dehydration, fever, fatigue, muscle pain, infection, travel in tropical zone, recidivism, duration > 5 days</td></tr><tr><td>ES<sub>2</sub></td><td>Result of coproculture is positive et antibiogramme</td></tr><tr><td>ES<sub>3</sub></td><td>Result of Parasitology in stool +</td></tr><tr><td>ES<sub>4</sub></td><td>Colonic checkup: abdomen without preparation, colonoscopy</td></tr><tr><td>ES<sub>5</sub></td><td>Haemoculture</td></tr><tr><td>ES<sub>6</sub></td><td>Toxic Substances Research +</td></tr><tr><td>HR</td><td>History of risk: immunosuppression, Renal insufficiency, valvular disease, cirrhosis, diabetes, AIDS</td></tr><tr><td>SS</td><td>Severity of Signs: proctorrhagia, glairy mucus, temperature >= 38°5 C or hypothermia, bacteraemia, circulatory collapse</td></tr></tbody></table>

<table><caption>Figure 4: Diagnoses $\Delta_0 - \Delta_8$ and Prognosis $\Pi_1 - \Pi_8$</caption><thead><tr><th colspan="2">Diagnosis</th><th>Prognosis</th></tr></thead><tbody><tr><td>$\Delta_0$</td><td>Acute diarrhea</td><td></td></tr><tr><td>$\Delta_1$</td><td>Viral diarrhea</td><td>$\Pi_1$ Mild</td></tr><tr><td>$\Delta_2$</td><td>Diarrhea with invasive germ</td><td></td></tr><tr><td>$\Delta_3$</td><td>Mild bacterial diarrhea</td><td>$\Pi_3$ Curable</td></tr><tr><td>$\Delta_4$</td><td>Bacterial or parasitic severe diarrhea</td><td></td></tr><tr><td>$\Delta_5$</td><td>Bacterial severe diarrhea</td><td></td></tr><tr><td>$\Delta_6$</td><td>Parasitic severe diarrhea</td><td>$\Pi_5$ to $\Pi_8$ Life-threatening</td></tr><tr><td>$\Delta_7$</td><td>Septicemia (Gram negative germs)</td><td></td></tr><tr><td>$\Delta_8$</td><td>Toxic diarrhea</td><td></td></tr></tbody></table>

automaton and the relevant signs that could occur as shown in Figure 3. The temporal analogical reasoning is implemented by computing a resulting gradient distance vector with the component objects as shown in Figures 1 and 2.

### III. DISCUSSION-CONCLUSION

Although rule-based models have been widely used to build diagnosis KBS in the medical domain, they failed to model deep knowledge [2], to represent causality, time, object structure evolution and threshold incertitude in evaluating attributes and some contradictory rules [3]. A fuzzy rule approach is not well suited to implement a clinical object model where semantic capability is required to consistently express the structure evolution of a disease as in Figure 1. Also, most fuzzy rule approaches need a fuzzification step to represent scattered chunks of knowledge and a defuzzification step to allow the rules to be triggered by an inference engine [4] [5]. Our object model provides disease representations which are very close to a practitioner's

<table><caption>Figure 5: Therapies $\Theta_1$, $\Theta_3$ and $\Theta_5 - \Theta_8$</caption><thead><tr><th colspan="2">Therapy</th></tr></thead><tbody><tr><td>$\Theta_1$</td><td>Oral hydration, antikinetics opiates (codeine, diphenoxylate, loperamide), smectite + diet</td></tr><tr><td>$\Theta_3$</td><td>$\Theta_3$ Oral or I.V. hydration, chelating agent of toxins (colestyramine), stool culture, antibiotic assay and targeted antibiotic treatment</td></tr><tr><td>$\Theta_5$</td><td>hospitalisation, $\Theta_5$ + correction of hypovolaemia (plasma+albumin), I.V., antibiotic treatment. Clostridium difficile (Vanomycine)</td></tr><tr><td>$\Theta_6$</td><td>idem as $\Theta_5$ + parasitic research, antiparasitic: metronidazole ou Tinidazole and then Tiliquinol</td></tr><tr><td>$\Theta_7$</td><td>idem as $\Theta_5$ + blood culture + I.V. antibiotic treatment</td></tr><tr><td>$\Theta_8$</td><td>Tox screen + chelating agent of the drug</td></tr></tbody></table>

way of thinking and to the medical semiology. This work is in progress and we are currently building a multi-agent platform to implement all the model features, with agents specialized in the different clinical steps: diagnosis, prognosis and therapy inspired by our previous works [1, 6].

### ACKNOWLEDGMENTS

**Warning**: This material is protected by the "Agence des dépôts numériques", all rights are reserved.

### REFERENCES

[1] J. Colloc and P. Summons, "An object oriented time model of a decision support system for intoxication diagnoses," in *Proceedings of Industrial Simulation Conference, Palerme*, 2006, pp. 387-392.

[2] E. Turban, J. Aronson, and T. Liang, *Decision Support Systems and Intelligent Systems*, P. Education, Ed. Pearson Education, 2005.

[3] J. McCarthy, "Generality in artificial intelligence," in *ACM Turing Award Lectures, the First Twenty Years 1966-1985*, N. Y. ACM Press, Ed. Addison-Wesley Publishing Company, 1987, ch. 1971, pp. 257-267.

[4] E. Mamdani and S. Assilian, "An experiment in linguistic synthesis with fuzzy logic controller," *International Journal Man-Machine Studies*, vol. 7, pp. 1-13, 1975.

[5] I. Iancu, "A mamdani type fuzzy logic controller," in *Fuzzy Logic - Controls, Concepts, Theories and Applications*, P. E. Dadios, Ed. Intech, 2012, ch. 16, pp. 325-350.

[6] J. Colloc and C. Sybord, "A multi-agent approach to involve multiple knowledge models and the case base reasoning approach in decision support systems," in *proceedings of 35th IEEE Southeastern Symposium on System Theory SSST'03 WVU, Morgantown, USA*, 2003.

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