Artificial Ventilation Modeling using Neuro-Fuzzy ...

2006 International Joint Conference on Neural Networks Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada July 16-21, 2006

Artificial Ventilation Modeling using Neuro-Fuzzy Hybrid System F. Liu, G. S. Ng, Senior Member, IEEE, C. Quek, Member, IEEE, and T. F. Loh

Abstract—Artificial ventilation is a crucial treatment to the patients in Intensive Care Unit. However, as the ventilator increasingly becomes more complex, it is not easy for less experienced clinicians to control the settings. The objective of the paper is to model the FiO2 settings by clinician, using a neuro-fuzzy hybrid system. Two important issues, the interpretability and accuracy are balanced through an iterative reduction and tuning process. Fuzzy sets are merged according to their Hebbian importance, while membership functions are tuned through the Least-Mean-Square (LMS) algorithm. Effective, compact and interpretable fuzzy rules are generated and tested on real ventilation data, benchmarked with other neuro-fuzzy systems.

A

I. INTRODUCTION

rtificial ventilation is essential treatment for patients who require breathing assistance in Intensive Care Unit (ICU). It is used to maintain the arterial oxygen and carbon dioxide levels of the patients. At hospitals, the settings of ventilator are manually adjusted by clinician, based on the patient’s physiological status. The adjustment is dependant on their clinical experience and expert knowledge. However, as new technologies develop, ventilators are increasingly more and more complex and it is not easy for clinicians with experience to use them effectively. Thus there is a need for the automation of the specific decision-making process to assist the clinicians. Artificial Intelligence (AI) is a study to emulate human intelligence using computational technology. It has been successfully applied to various medical applications [1]. Many artificial ventilation system based on AI techniques have been proposed, including VM [2], ESTER [3], KUSIVAR [4], VentEx [5], VentPlan [6], NeoGanesh [7]. As one of the AI techniques, fuzzy system has been widely used in biomedical applications in recent years. In fuzzy modeling, the numerical data can be interpreted in terms of linguistic concept, which are understandable to human user. The knowledge, in the form of fuzzy rules, can be extracted from the system, and provides assistance to the clinicians in practical use. Expert’s knowledge can also be incorporated into the system. In addition, fuzzy systems are more tolerant to the noise thus making them more robust. These advantages make the fuzzy system (FS) suited in medical decision-making. Some ventilator control systems based on

F. Liu, G. S. Ng, and C. Quek are with Centre for Computational Intelligence, Nanyang Technological University, School of Computer Engineering, 639798, Singapore. (e-mail: [email protected]; [email protected], [email protected];) T. F. Loh is with KK Women’s and Children’s Hospital, 229899, Singapore. He is with the Department of Paediatric Medicine. (e-mail: [email protected])

0-7803-9490-9/06/$20.00/©2006 IEEE

fuzzy logic have been proposed, including FuzzyKBWean [8], FAVeM [9], and SIVA [10]. An effective and compact rule set does not only reduce the modeling error, but also increase the system’s interpretability. The rules derived from experts and defined manually have been used to control ventilator [11][12]. However, as the system becomes more complex, it is difficult to manually define and tune the rules. The rules derived from the interview with experts are usually inaccurate and biased the expert. Thus it is desirable to find a way to automatically formulate and tune the rule base. Neural network (NN) [13][14][15] is a learning machine designed to model the brain function and imitate the human learning capabilities. It has good adaptivity where their synaptic weights can change with the surrounding environment. However, as it is a black box model, common knowledge is not easy to be extracted and interpreted from a trained neural network. The hybrid of FS and NN can effectively integrate the high-level inference ability of FS and the low-level learning capability of NN. The fuzzy rules can be tuned through the learning algorithm of NN, and knowledge can be derived from the system. Accuracy and interpretability are two issues in neuro-fuzzy system. They are important in artificial ventilation modeling. Firstly, the modeling accuracy reflects its ability to set the variables, which influence the treatment of the patient. Secondly, the derived rules should be understandable and interpretable to the user, so as to assist the ventilation. However, these two requirements usually cannot be satisfied simultaneously. There is a need to strike a balance between them. The objective of the paper is to model the setting of the FiO2 performed by a clinician in the artificial ventilation using a neuro-fuzzy hybrid system. The modeling accuracy and interpretability are compromised through an iterative tuning and reduction process. The fuzzy rules are merged and reduced according to their Hebbian importance, which reflects the coverage of the data by the rule. Interpretable rules are derived from the system and can be used to assist clinician to set the variables. II. EXPERIMENT DESIGN A. Data The data employed in the paper is collected from the KK Women’s and Children’s Hospital of Singapore. They represent a 20 day’s records for a patient in the hospital under the BIPAP ventilation mode. The sampling time of the record is about an hour. It consists of measured patient-status

5166

variables and the setting variables by clinician. The patient-status variables include HR (Heart Rate), RR (Respiratory Rate), SaO2 (Oxygen Saturation), MAP (Mean Airway Pressure) and ETV (Expiratory Tidal Volume). The setting variables include FiO2 (Fraction of Inspired Oxygen), IE (Inspiratory / Expiratory Ratio), PEEP (Positive End Expiratory Pressure), PIP (Peak Inspiratory Pressure), RRset (set Respiratory Rate) and TVset (set Tidal Volume). B. Method The key strength of the fuzzy system (FS) is its ability to model the dynamics of a problem using a set of high-level IF-THEN fuzzy rules, where the main merit of neural network (NN) is its low-level learning capability. In this paper, the Mandani-type fuzzy system [16], other than the Takagi-Sugeno-Kang (TSK) fuzzy system [17], is employed due to its ability to produce interpretable rules. The fuzzy rule in Mandani system has the form in (1). (1) IF x1 = A and x2 = B THEN y = C where x1 and x2 are input variables; y is output variable; A , B and C are fuzzy sets. The hybrid of the FS and NN is shown in Fig. 1. It is a 5-layer neural network, including input, condition, rule node, consequence, and output layers. Each input variable in the FS corresponds to one input node and each fuzzy set for the input variable corresponds to a neuron in the condition layer. Similarly, one output node for each output variable, and the consequence layer consists of the nodes for its fuzzy sets. In the rule node layer, each rule node is generated for a fuzzy rule. There are links for each input/output variable to each of their fuzzy sets. The fuzzy rules are represented in the network by linking the condition, rule node and consequence layers. x1 = A1

and

x2 = B1

THEN

y = C1

R2 : IF x1 = A2

and

x2 = B2

THEN

y = C2

R1 :

FS:

x1

IF

centroid and width of the j th labeled fuzzy set of the output is denoted as c IVj and δ jIV . Assuming the multiply and sum operator are used as the T-norm and S-norm operators, the output of the system can be written like in (2) and (3):  n IV   n IV IV IV  o =  ∑ coL δ f (2) × oL k   ∑ coLk δ oLk  k k  k =1   k =1  m

i =1

R1

) (δ 2

II i , iLk ( i )

)} 2

(3)

where o is the output; n is the number of rules; m is the input dimension; the input data is X = [ x1 , x2 ,… , xm ] ; f k is the firing strength of the k th rule for data. The interpretability and accuracy are two important issues in neuro-fuzzy modeling. Interpretability refers to the capability of the fuzzy model to express the behavior of the system in an understandable way, while the accuracy refers to the capability of the fuzzy model to faithfully represent the system [18]. However, interpretability and accuracy are usually pursued for contradictory purposes and sometimes are dipoles apart as the system complexity increases. When tuning the membership functions (MF) of the rules to diminish the modeling error, the interpretability of the rules may be degraded during the tuning process, where the fuzzy sets can drift closer to each other and may end up overlapping each others [19]. An iterative process is proposed in the paper to deal with the problem, shown in Fig. 2. Initial rule generation

MF tuning (lower learning rate)

Rank rule

Merge MF

Remove redundant and conflicting rules & reduce feature

A1 A2

{(

f k = ∏ exp − xi − ciII,iLk (i )

C1

Stop criteria

MF tuning

y

NN:

x2 Input layer

B1 B2

Condition layer

R2 Rule node layer

Fig. 2. Chart of iterative tuning and reduction process

C2 Consequence layer

Output layer

Fig. 1. The hybrid of fuzzy system and neural network.

For the k th rule, the label of the fuzzy set of the i th input variable is denoted as iLk ( i ) , and the label of the fuzzy set of the output variable as oLk . Gaussian membership function is used in each fuzzy set. For the condition layer, the centroid and width of the j th labeled fuzzy set of the input i is denoted as ciII, j and δ iII, j . For the consequence layer, the

1) Initial rule generation At the beginning of the iterative process, initial rules are generated to cover all the training data samples. That is, whenever a new data sample is presented, if there is no rule in the rule base, or if the strength of the rule with the largest firing strength is below a specified threshold, a new rule node will be created with the centroid of the sample. The initial width of each fuzzy set is proportion to the range of the variable. This threshold controls the coverage of data space by the rules and affects the number of initial rules. The larger the threshold the less number of the rules will be generated, and vice versa.

5167

2) Rule ranking via Hebbian importance For the i th data sample ( X i , yi ) and the k th rule, define the degree of the rule to cover the sample in (4)

{(

Ck ,i = f k × exp − yi − c

IV oLk

) (δ ) } 2

IV oLk

2

(4)

The Hebbian importance of the k th rule is defined in (5). n

I k = ∑ ck ,i

(5)

i =1

This is based on the Hebbian learning rule [21]. If all the input-output samples repeatedly fire a rule by the product of their firing strength and the membership values, and the accumulated strength surpasses that of other rules, it indicates the existence of such a rule. In another view, the accumulated strength exerted by the sample pairs reflects the degree of coverage of them by the rule. The rule that covers the samples to a higher degree will have greater influence on the modeling accuracy. This is due to the fact that when the MFs of the rule or the rule itself are merged or deleted respectively, it will result in a larger change in the fuzzy inference results and significantly affect the modeling accuracy. Thus such a rule is of greater importance. At the step, all of the rules are sorted in a decreasing order of their Hebbian importance. 3) Membership function merge A temporary rule set pool is created and initialized as null. The ordered rules in the original rule set are presented sequentially. The fuzzy set of the current presented rule in each dimension is added into the rule set pool, or merged with that of the previously presented rules, based on the degree of overlap of the fuzzy sets. Subsequently the newly added or merged fuzzy sets will be linked together to formulate a new rule in the rule set pool. For two fuzzy sets A and B , the degree of overlap is defined in (6). S ( A, B ) = max { A ∩ B A , A ∩ B B } (6) The A , B and A ∩ B can be computed using the centroid and width of the two fuzzy sets [21]. During the merging process, some fuzzy sets may be shared by several rules. Changing a shared fuzzy set is equivalent to modifying some rules simultaneously, which will exert much influence on the performance of system. Thus, the fuzzy sets within a rule may have different importance too. Denote the importance of a fuzzy set F as IˆF . The IˆF is initialized with the value of importance of its associated rule and changed during the merging process. Given two fuzzy sets A and B with the centroid, width and importance of c A , δ A , IˆA and cB , δ B , IˆB respectively, the merged fuzzy set C is calculated using (7)-(9). c = Iˆ c + Iˆ c Iˆ + Iˆ (7) C

δC

( = ( Iˆ δ

A A

A

A

B B

+ IˆBδ B

)( ) ( Iˆ

A

A

) + Iˆ ) B

B

(8)

IˆC = IˆA + IˆB

(9)

4) Reduce rules and features In the temporary rule set pool, if there is only one membership function within one dimension, this dimension (feature) will be removed; if there is any rule that has the same conditions and consequences with others, it is removed; if there are any conflicting rules that have equivalent conditions but different consequences, the one with the higher degree of importance is preserved and others are deleted. Finally, the original rule set is replaced by the temporary rule set pool. 5) Membership function tuning The least-mean-square (LMS) algorithm is used in the paper for the tuning of membership functions. Assuming the error function is 1 n 2 E = ∑ ( oi − yi ) (10) 2 i =1 the error at i th sample is ei = oi − yi

(11)

th

For the j input dimension of the k c

II j , iLk ( j )

and the width δ

II j , iLk ( j )

th

rule, the centroid

are updated using (12) and

(13). ∆c IIj ,iLk ( j ) = −γ ∆δ jII,iLk ( j ) = −γ

∂ei2 ∂c IIj,iLk ( j ) ∂ei2 ∂δ jII,iLk ( j )

(12) (13)

where γ is the learning rate. The updating formula for centroid and width of the output dimension is similar to that in the input dimensions. 6) Stop criteria If the training error after one reduction and tuning cycle, is much larger than that after the previous cycle, the system will stop and the rule set after the previous cycle is restored as the final rule set. That is to say, denote the training error after the i . If i exceeds the maximum iteration imax , i th cycle as Etrain i +1 i or Etrain > η Etrain , the iterative reduction and tuning process stops. The η is a human defined parameter that controls the reduction of the system complexity, based on the fact that if the number of rule is less than what that is necessary, the training error will become much larger than before. The proposed system reduces the fuzzy rules through the Hebbian ordering of the rules, thus is named a Hebbian-Rule-Reduct system.

C. Experiment setup It is crucial to provide adequate oxygenation of the arterial blood for the maintenance of life. Thus the arterial oxygen tension should be maintained of a proper level. The arterial oxygen tension is controlled by adjusting the FiO2. The

5168

objective of the experiment is to model the manual setting of FiO2 by clinician using a neuro-fuzzy hybrid system. Among all of the variables in the medical records, the SaO2, FiO2, RR, PEEP, set or measured at current time step, are used to predict the value of FiO2 at next time step. To model the FiO2, the use of SaO2, FiO2 (old) and PEEP has been suggested [22]. The variable RR is advised by clinician. There are a total of 408 data samples, divided into 3 cross-validation groups to evaluate the performance of the system. Within one cross-validation group, the first 60% data is used as training set and the following 40% data is used as testing set, shown in Fig. 3.

in the CV1 and CV2. In CV3, only the RSPOP produce less number of rules than the Hebb-Rule-Reduct. From the average number of rules in the last column, the proposed system produces the least among all these Mandani systems. Fig. 4 – 6 show the target and predicted values of FiO2 in testing set of the 3 cross-validation groups. In CV1, small deviations appear only when the amount of FiO2 becomes higher or lower abruptly. In CV2 and CV3, the output of the proposed system is nearly perfect-match to the target setting of FiO2. The membership functions and some sample rules are extracted to show the interpretability of the proposed system. The membership functions for the 4 input variables and 1 output variable are shown in Fig. 7 – 11. The overlap between the fuzzy sets is low for all the variables. Each fuzzy set has a clear semantic meaning. Three samples fuzzy rules are shown in Fig 12. These rules are the acquired knowledge from the data by the proposed system. They can be understood by human user and used to assist the clinicians. TABLE I. COMPARISON OF RMSE RMSE Model CV1 CV2 CV3 Hebb-Rule-Reduct 2.085 0.753 0.536 POPFNN 13.776 6.031 2.375 RSPOP 13.841 6.031 2.166 EFuNN 3.417 2.908 1.219 DENFIS 3.045 2.243 1.045 ANFIS 2.409 1.863 0.560

Fig. 3. The FiO2 serious and the division of 3 cross-validation groups

III. EXPERIMENTAL RESULTS AND ANALYSIS In this experiment, the Root Mean Squared Error (RMSE) between the advised value of FiO2 by neuro-fuzzy hybrid systems and the setting of the clinician is used to measure the performance.. Some other neuro-fuzzy systems are employed for benchmark comparison. They are namely, EFUNN [23], POPFNN [24], RSPOP [25], DENFIS [26] and ANFIS [27]. The former 3 models are Mandani-type systems, while the latter 2 are TSK models. The experimental results are shown in Tables I and II. Table I shows the comparison of RMSE between these neuro-fuzzy models. In both the CV1 and CV2, the proposed Hebb-Rule-Reduct system performs much better than other systems. In CV3, the ANFIS is slightly worse than the proposed system. The last column of Table I shows the average RMSE of the 3 cross-validation groups. The proposed system is the best among all of these neuro-fuzzy systems. Table II shows the comparison of the number of the derived fuzzy rules. As the form of the TSK-style rule is different from the Mandani-style rule, these two kinds of rules are not comparable. Thus, the comparison is only made among the Mandani systems. The number of derived rules reflects the interpretability of the system. The more there are the rules, the more complex and the more uninterpretable the system is and vice versa. In Table II, the proposed Hebb-Rule-Reduct system produces the least number of rules 5169

Average 1.125 7.394 7.346 2.515 2.111 1.611

TABLE II. COMPARISION OF THE NUMBER OF RULES Number of Mandani-type rules Model Average CV1 CV2 CV3 Hebb-Rule-Reduct 12 3 26 13.7 POPFNN 48 28 53 43.0 RSPOP 29 9 11 16.3 EFuNN 32 57 109 66.0

Fig. 4. Target and predicted values of FiO2 in CV1

Fig. 9. MFs for PEEP

Fig. 5. Target and predicted values of FiO2 in CV2

Fig. 10. MFs for RR

Fig. 6. Target and predicted values of FiO2 in CV3

Fig. 11. MFs for FiO2

Rule 1:

IF SaO2 is Normal(2) and FiO2 is Medium and PEEP is High and RR is Medium, THEN the new FiO2 is High.

Rule 2:

IF SaO2 is Low and FiO2 is High and PEEP is Medium and RR is High, THEN the new FiO2 is High.

Rule 3:

IF SaO2 is Normal(1) and FiO2 is High and PEEP is Medium and RR is Low, THEN the new FiO2 is Medium.

Fig. 7. MFs for SaO2

Fig. 12. Three sample fuzzy rule derived from the proposed system.

IV. CONCLUSION Fig. 8. MFs for FiO2 (old)

In this paper, the setting of FiO2 in artificial ventilation is modeled by a neuro-fuzzy hybrid system. An iterative rule reduction and tuning process is proposed to produce interpretable fuzzy rules while still maintaining low modeling error. Fuzzy sets are merged through their Hebbian importance and the redundant rules and features are removed. 5170

An effective, compact rule set is obtained after learning. The proposed system is tested on the real ventilation data. The overall modeling error is lower than the other comparable neuro-fuzzy system, while the extracted fuzzy rules can be understood by human user and used to assist clinicians.

[18]

[19]

[20]

REFERENCES [1] [2] [3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13] [14]

[15] [16] [17]

H. W. I. Wan and S. Fadzilah, "Artificial Intelligence in medical application: An exploration," Health Informatics Europe Journal. Available: http://www.hi-europe.info/files/2002/9980.htm, 2002. L. M. Fagan, "VM: Representing Time-Dependent Relations in a Medical Setting," in Dept. Computer Science: Stanford University, 1980. C. Hernandez-Sande, V. Moret-Bonillo, and A. Alonso-Betanzos, "ESTER: an expert system for management of respiratory Weaning Therapy," IEEE Transactions on Biomedical Engineering, vol. 36, pp. 551-564, 1989. R. Rudowski, C. Frostell, and H. Gill, "A knowledge-based support system for mechanical ventilation of lungs. The KUSIVAR concept and prototype," Computer Methods Programs Biomedicine, vol. 30, pp. 59-70, 1989. N. Shahsavar, H. Gill, U. Ludwigs, A. Carstensen, H. Larsson, O. Wigertz, and G. Matell, "VentEx: An on-line knowledge-based system to support ventilator management," Technology and Health Care, vol. 1, pp. 233-243, 1994. G. W. Rutledge, G. Thomsen, B. Farr, M. Tovar, L. Sheiner, and L. M. Fagan, "VentPlan: A ventilator-management advisor," presented at Proceedings of the Fifteenth Annual Symposium on Computer Applications in Medical care, 1991. M. Dojat, F. Pachet, Z. Guessoum, D. Touchard, A. Harf, and L. Brochard, "NeoGanesh: a working system for the automated control of assisted ventilation in ICUs," Artificial Intelligence in Medicine, vol. 11, pp. 97-117, 1997. C. Schuh, C. Zelenka, and M. Hiesmayr, "FuzzyKBWean: A computer program for fuzzy knowledge-based weaning of ICU patients," presented at Proceedings of the ERUDIT-Workshop, Austria, 2000. K. M. Goode, D. A. Linkens, P. R. Bourne, and J. G. Cundill, "Development of a fuzzy rule-based advisor for the maintenance of mechanically ventilated patients in ICU: a model-based approach," Biomedical Engineering: Applied Basis Communication, vol. 10, pp. 236-246, 1998. H. F. Kwok, D. A. Linkens, M. Mahfouf, and G. H. Mills, "SIVA: A hybrid knowledge-and-model-based advisory system for intensive care ventilators," IEEE Transactions on Information Technology in Biomedicine, vol. 8, pp. 161-172, 2004. Y. Sun, I. Kohane, and A. R. Stark, "Fuzzy logic assisted control of inspired oxygen in ventilated newborn infants," presented at Proceedings of Annual Symposium on Computer Applications in Medical Care, 1994. T. Nemoto, G. E. Hatzakis, C. W. Thorpe, R. Olivenstein, S. Dial, and J. H. T. Bates, "Automatic control of pressure support mechanical ventilation using fuzzy logic," American Journal of Respiratory and Critical Care Medicine, vol. 160, pp. 550-556, 1999. G. S. Ng, S.S. Erdogan and P. W. Ng, “Contender's network, a new competitive-learning scheme,” Pattern Recognition Letters, vol. 16, no. 11, pp. 1111-1118, 1995. G. S. Ng and H. C. Sim, “Recognition of partially occluded objects with back-propagation neural network,” International Journal of Pattern Recognition and Artificial Intelligence, vol. 12, no. 5, pp. 645-660, 1998. G. S. Ng and H. Singh, “Data equalisation with evidence combination for pattern recognition,” Pattern Recognition Letters, vol. 19, no. 3, pp. 227-235, 1998. E. H. Mandani and S. Assilian, "An experiment in linguistic synthesis with a fuzzy logic controller," International Jounal of Man-Machine Studies, vol. 7, pp. 1-13, 1975. M. Sugeno and G. T. Kang, "Structure identification of fuzzy model," Fuzzy Sets and Systems, vol. 28, pp. 15-33, 1988.

[21] [22]

[23]

[24]

[25] [26]

[27]

5171

J. Casillas, O. Cordon, F. Herrera, and L. Magdalena, "Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: an overview," in Interpretability issues in fuzzy modeling: Springer, 2003, pp. 3-22. M. Setnes, R. Babuska, U. Kaymak, and H. R. v. N. Lemke, "Similarity Measures in Fuzzy Rule Base Simplification," IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 28, pp. 376-386, 1998. D. O. Hebb, The organization of behavior. New York: John Wiley and Sons, 1949. C. F. Juang and C. T. Lin, "An online self-constructing neural fuzzy inference network and its applications," IEEE Transactions on Fuzzy Systems, vol. 6, pp. 12-32, 1998. H. F. Kwok, D. A. Linkens, M. Mahfouf, and G. H. Mills, "Rule-base derivation for intensive care ventilator control using ANFIS," Artificial Intelligence in Medicine, vol. 29, pp. 185-201, 2003. N. K. Kasabov, "Evolving fuzzy neural networks for supervised/unsupervised online knowledge-based learning," IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 31, pp. 902-918, 2001. K. K. Ang, C. Quek, and M. Pasquier, "POPFNN-CRI(S): Pseudo outer product-based fuzzy neural network using the compositional rule of inference and singleton fuzzifier," IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 33, pp. 838-849, 2003. K. K. Ang and C. Quek, "RSPOP: Rough set-based pseudo outer-product fuzzy rule identification algorithm," Neural Computation, vol. 17, pp. 205-243, 2005. N. K. Kasabov and Q. Song, "DENFIS: Dynamic evolving neural-fuzzy inference system and its application for time-series prediction," IEEE Transaction on Fuzzy Systems, vol. 10, pp. 144-154, 2002. J.-S. R. Jang, "ANFIS: Adaptive-network-based fuzzy inference system," IEEE Transactions on Systems, Man, and Cybernetics, vol. 23, pp. 665-685, 1993.