=Paper=
{{Paper
|id=Vol-2711/paper20
|storemode=property
|title=Computational Intelligence for Digital Healthcare
|pdfUrl=https://ceur-ws.org/Vol-2711/paper20.pdf
|volume=Vol-2711
|authors=Abdel-Badeeh M. Salem
|dblpUrl=https://dblp.org/rec/conf/icst2/Salem20
}}
==Computational Intelligence for Digital Healthcare==
https://ceur-ws.org/Vol-2711/paper20.pdf
Computational Intelligence for Digital Healthcare
Abdel-Badeeh M. Salem[0000-0001-5013-4339]
Faculty of Computer and Information Sciences, Ain Shams University, Cairo, Egypt
absalem@cis.asu.edu.eg, abmsalem@yahoo.com
Abstract. Digital healthcare (DH) is a multidisciplinary field of research, at the
intersection of medical sciences, biology sciences, biochemistry neurosciences,
cognitive sciences and informatics. In the last years, various computational in-
telligence (CI) techniques and methodologies have been proposed by the re-
searchers in order to develop digital knowledge-based systems (DKBS) for dif-
ferent medical and healthcare tasks. These systems are based on artificial intel-
ligence (AI) concepts and theories. Many types of DKBS are in existence today
and are applies to different healthcare domains and tasks. The objective of the
paper is to presents a comprehensive and up-to-date research in the area of DHI
covering a wide spectrum of CI methodological and intelligent algorithmic is-
sues, discussing implementations and case studies, identifying the best design
practices, assessing implementation models and practices of AI paradigms in
digital healthcare systems .This paper presents some of the CI techniques for
managing and engineering knowledge in digital healthcare systems(DHS).
Some of the research results and applications of the author and his colleagues
that have been carried out in last years are discussed.
Keywords: machine learning, computational intelligence, Artificial Intelli-
gence, knowledge engineering, digital healthcare informatics.
1. Introduction
Computational intelligence (CI) is the study of intelligent computer algorithms that
improve automatically through experience. CI aims to enable computers to learn
from data and make improvements without any dependence on commands in a pro-
gram.CI is an inherently interdisciplinary, includes; neurobiology, information theory,
probability, statistics, AI, control theory, Bayesian methods, physiology and philoso-
phy [1,2].
In the recent years, various AI paradigms and CI techniques have been proposed
by the researchers in order to develop efficient and smart systems in the areas of
health informatics and health monitoring systems.AI and CI offers robust, intelligent
algorithms and smart methods that can help to solve problems in a variety of health
and life sciences areas [3, 4, 5, 6].
There are numerous examples of successful applications of CI in areas of diagnosis
and prevention, prognosis and therapeutic decision making.
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0). ICST-2020
CI algorithms are used for the following tasks; (a) discovering new diseases, (b)
finding predictive and therapeutic biomarkers, and(c) detecting relationships and
structure among the clinical. CI contributes to the enhancement of management and
information retrieval processes leading to development of intelligent (involving on-
tologies and natural language processing) and integrated literature searches.
Moreover, applications of CI in bioinformatics include the following areas of re-
search ;(a) microarray analysis, chromosome and proteome databases, modeling of
inhibition of metabolic networks(b) signal analysis (echocardiograph images and
electroencephalograph time series). and (c) drug delivery and software for pattern
recognition in biomedical data [7,8,9,10].
This paper discusses the potential role of the AI and CI approaches, techniques,
which are used in developing the intelligent health informatics and health monitoring
systems.
The paper discusses the following CI paradigms: (a) bio-inspired computing, (b)
analogical reasoning computing, (c) vagueness and fuzzy computing, and (d) deep
learning.
Also, the paper presents the challenges as well as the current research directions in
the areas of digital health informatics.
Examples of the research performed by the author and his associates at Artificial
Intelligence and Knowledge Engineering Research Labs, (ASU-AIKE labs) are also
included.
The following cases and diseases are presented; cancer, heart, brain tumor, throm-
bosis diseases, Pandemic Influenza, Diabetics type-2, and volume visualization of the
interior body.
The paper is organized as follows: Section 2 discusses the smart health monitoring
paradigms. Section 3 reviews the bio-inspired computing approaches. In section 4, we
discuss the analogical reasoning paradigms.
While section 5 discusses the vagueness and Fuzzy computing Section 6 presents
our cases and applications, section 7 presents our future research directions and then
we conclude in section 8.
2. Smart health monitoring systems (SHMS) models
SHMS involves deploying CI, information, and networking technologies to aid in
preventing disease, improving the quality of care and lowering overall cost [10,11].
Currently, we have the following SHMS models;
• Real-Time Monitoring Model. In this model, sophisticated sensors and mobile
devices can feed real-time medical data directly to patients and doctors via secure
computing networks.
• Computer-Aided Surgery Model. In this model, advanced robotic devices make
surgery more accurate and potentially less invasive
• Telemedicine Model. In which, automated tools in the home and on mobile devic-
es are able help patients interact with providers remotely, enabling the patients to
adjust their daily lives by better managing their own care.
• Population-Based Care Model. In which, monitoring devices enable collection
of data from large populations with lower administrative and research costs than
current method.
• Personalized Medicine Model. In this system, machine learning and predictive
modeling will identify trends and causal relationships in medical data – leading to
improved understanding of disease, development of new cures, and more accurate
treatments tailored to each patient’s specific needs
• Ubiquitous Computing Model. This model is characterized by improved security
and privacy ensure the integrity of data stored in the “cloud,” allowing stakehold-
ers – patients, providers, and relatives – to access the right information at the right
time from anywhere in the world
• Decision Support Model. In which, computer systems offer possible diagnoses
and recommend treatment approaches, allowing doctors to quickly assess situations
and viable options
• Health 2.0 Model. In which, Web-based tools such as wikis and social networks
connect patients and clinicians to shared experiences, symptoms and treatments.
3. Bio-inspired computing
Figure 1 shows the different biological techniques of the bio-inspired computing this
section presents a brief overview about the different bio-inspired techniques, namely;
artificial neural networks, support vector machines, deep learning, genetic algorithms,
evolutionary computing, and DNA computing.
3.1 Artificial Neural Networks (ANN)
ANN is a class of learning algorithm consisting of multiple nodes that communicate
through their connecting synapses. ANN are inspired in biological models of brain
functioning [10, 12].
They are capable of learning by examples and generalizing the acquired knowledge.
Due to these abilities the neural networks are widely used to find out nonlinear rela-
tions which otherwise could not be unveiled due to analytical constraints. The learned
knowledge is hidden in their structure thus it is not possibly to be easily extracted and
interpreted. ANN can be used in the following medical purposes:
1. Modelling: simulating the functions of the brain and neurosensory organs.
2. Signal processing: Bioelectric signal filtering and evaluation
3. System control and checking: Intelligent artificial machine control and checking
based on responses of biological or technical systems given to any signals.
4. Classification tasks: Interpretation of physical and instrumental findings to
achieve more accurate diagnosis.
5. Prediction: provide prognostic information based on retrospective parameter anal-
ysis.
Fig.1. Bio-inspired computing
3.2 Support Vector Machines (SVM)
SVM are new learning-by example paradigm for classification and regression
problems [10,13]. Their main advantage lies in the structure of the learning algorithm
which consists of a constrained quadratic optimization problem (QP), thus avoiding
the local minima drawback of NN. The approach has its roots in statistical learning
theory (SLT) and provides a way to build “optimum classifiers” according to some
optimality criterion that is referred to as the maximal margin criterion. An interesting
development in SLT is the introduction of the Vapnik-Chervonenkis (VC) dimension,
which is a measure of the complexity of the model. The trade-off between complexity
and accuracy led to a range of principles to find the optimal compromise. Vapnik and
co-authors' work have shown the generalization to be bounded by the sum of the
training error and a term depending on the Vapnik-Chervonenkis (VC) dimension of
the learning machine leading to the formulation of the structural risk minimization
(SRM) principle. By minimizing this upper bound, which typically depends on the
margin of the classifier, the resulting algorithms lead to high generalization in the
learning process [10].
3.3 Deep Learning (DL)
Deep learning is a branch of AI covering a spectrum of current exciting research
and industrial innovation that provides more efficient algorithms to deal with large-
scale data in healthcare, recommender systems, learning theory, robotics, games,
neurosciences, computer vision, speech recognition, language processing,human-
computer interaction, drug discovery, biomedical informatics, act [14,15,16]. DL
provides efficient algorithms to deal with large-scale data in many areas, see Figure
2.
Fig.2. Deep learning applications
3.4 Genetic Algorithms (GA)
GA follows the lead of genetics, reproduction, evolution and the survival for the
fittest theory by Darwin. GA is a class of machine learning algorithm that is based on
the theory of evolution [10, 17]. Genetic Algorithms (GA) provide an approach to
learning that based loosely on simulated evolution. The GA methodology hinges on a
population of potential solutions, and as such exploits the mechanisms of natural
selection well known in evolution. Rather than searching from general to specific
hypothesis or from simple to complex GA generates successive hypotheses by
repeatedly mutating and recombining parts of the best currently known hypotheses.
The GA algorithm operates by iteratively updating a poll of hypotheses (population).
One each iteration, old members of the population are evaluated according a fitness
function. A new generation is then generated by probabilistically selecting the fittest
individuals form the current population. Some of these selected individuals are carried
forward into the next generation population others are used as the bases for creating
new offspring individuals by applying genetic operations such as crossover and
mutation.
3.5 Evolutionary Computing (EC)
EC is an approach to the design of learning algorithms that is structured along the
lines of the theory of evolution. A collection of potential solutions for a problem
compete with each other. The best solutions are selected and combined with each
other according to a kind of ‘survival of the fittest’ strategy. GA are a well-known
variant of evolutionary computation [10, 17].
3.6 DNA Computing
DNA computing is essential computation using biological molecules rather than
traditional silicon chips. In recent years, DNA computing has been a research tool for
solving complex problems. Despite this, it is still not easy to understand. The main
idea behind DNA (Deoxyribo Nucleic Acid) computing is to adopt a biological (wet)
technique as an efficient computing vehicle, where data are represented using strands
of DNA. Even though a DNA reaction is much slower than the cycle time of a silicon-
based computer, the inherently parallel processing offered by the DNA process plays
an important role. This massive parallelism of DNA processing is of particular inter-
est in solving NP-complete or NP-hard problems [18,19].
It is not uncommon to encounter molecular biological experiments which involve 6
× 1016/ml of DNA molecules. This means that we can effectively realize 60,000 Tera
Bytes of memory, assuming that each string of a DNA molecule expresses one char-
acter. The total execution speed of a DNA computer can outshine that of a conven-
tional electronic computer, even though the execution time of a single DNA molecule
reaction is relatively slow. A DNA computer is thus suited to problems such as the
analysis of genome information, and the functional design of molecules (where mole-
cules constitute the input data) [20].
DNA computing will solve that problem and serve as an alternative technology.
DNA computing is also known as molecular computing. It is computing using the
processing power of molecular information instead the conventional digital compo-
nents. It is one of the non-silicon-based computing approaches. DNA has been shown
to have massive processing capabilities that might allow a DNA-based computer to
solve complex problems in a reasonable amount of time [20].
4. Analogical reasoning computing (ARC)
ARC provides both a methodology for problem solving and a cognitive model of
people [21, 22, 23, 24]. Case-Based Reasoning (CBR) is the most common technique
of the ARC oaradigms.CBR means reasoning from experiences or “old cases” in an
effort to solve problems, critique solutions and explain anomalous situations. The case
is a list of features that lead to a particular outcome; e.g. The information on a patient
history and the associated diagnosis. We feel more comfortable with older doctors
because they have seen and treated more patients who have had illnesses similar to
our own. CBR is an analogical reasoning method provides both: a methodology for
building efficient knowledge-based reasoning systems (CBRS), and a cognitive model
for People. CBR is a preferred method of reasoning in dynamically changing situa-
tions and other situations where solutions are not clear cut [22].
Most commonly application of CBR used in developing expert systems technolo-
gy. In CBR expert systems, the system can reason from analogy from the past cases.
This system contains what is called “case-memory” which contains the knowledge in
the form of old cases (experiences). CES solves new problems by adapting solutions
that were used for previous and similar problems [22]. The methodology of CBR
directly addresses the problems found in rule-based technology, namely: knowledge
acquisition, performance, adaptive solution, maintenance.
According to Kolodner [21], CBR from the computational perspective refers to a
number of concepts and techniques (e.g. data structures and intelligent algorithms)
that can be used to perform the following operations; (a) record and index cases, (b)
search cases in the case-memory to identify the ones that might be useful in solving
new cases when they are presented, (c) modify earlier cases to better match new cas-
es, and (d) synthesize new cases when they are needed, see figure 3.
Fig. 3. Case-based reasoning methodology
5. Vagueness and fuzzy computing
5.1 Rough sets
Rough set theory was proposed as a new approach to vague concept description
from incomplete data. The rough set theory is one of the most useful techniques in
many real-life applications such as medicine, pharmacology, engineering, banking
and market analysis. This theory provides a powerful foundation to reveal and discov-
er important structures in data and to classify complex objects. The theory is very
useful in practice, e.g. in medicine, pharmacology, engineering, banking, financial
and market analysis [25]. In what follows, we can summarize the benefits and ad-
vantages of rough set theory:
1. Deals with vagueness data and uncertainty.
2. Deals with reasoning from imprecise data.
3. Used to develop a method for discovering relationships in data
4. Provides a powerful foundation to reveal and discover important structures in data
and to classify complex objects.
5. Do not need any preliminary or additional information about data.
6. Concerned with three basics: granularity of knowledge, approximation of sets and
data mining
5.2 Fuzzy Rules
Fuzzy logic allows one to express knowledge in a rule format that is close to a nat-
ural language expression. The difference between this fuzzy rule and the Boolean-
logic rules we used in our forward- and backward-chaining examples is that the claus-
es “temperature is hot” and “humidity is sticky” are not strictly true or false. Clauses
in fuzzy rules are real-valued functions called membership functions that map the
fuzzy set “hot” onto the domain of the fuzzy variable “temperature” and produce a
truth-value that ranges from 0.0 to 1.0 (a continuous output value, much like neural
networks).
Reasoning with fuzzy rule systems is a forward-chaining procedure. The initial
numeric data values are fuzzified, that is, turned into fuzzy values using the member-
ship functions. Instead of a match and conflict resolution phase where we select a
triggered rule to fire, in fuzzy systems, all rules are evaluated, because all fuzzy rules
can be true to some degree (ranging from 0.0 to 1.0). The antecedent clause truth
values are combined using fuzzy logic operators (a fuzzy conjunction or and opera-
tion takes the minimum value of the two fuzzy clauses).Next, the fuzzy sets specified
in the consequent clauses of all rules are combined, using the rule truth values as scal-
ing factors. The result is a single fuzzy set, which is then defuzzified to return a crisp
output value. More technical details and applications can be found in the recent book
of Voskuhl [26].
6 Case studies and applications
6.1 CI for Thyroid Cancer Diagnosis
Cancer is a group of more than 200 different diseases. From the medical point of
view, Cancer occurs when cells become abnormal and keep dividing and forming
either benign or malignant tumors. Cancer has initial signs or symptoms if any is ob-
served, the patient should perform complete blood count and other clinical examina-
tions. To specify cancer type, patient needs to perform special lab-tests. In our re-
search Labs, we have performed an interesting research for developing intelligent
systems for thyroid cancer diagnoses. .This research are based on using case-based
and rule-based reasoning, ontological engineering, and artificial neural networks [27,
28, 29].
Figure 4 shows an examples for the encoded rules for cancer diagnosis..
Fig. 4. Example for the encoded rules for cancer diagnosis.
6.2 Heart Disease Expert System
Heart disease is a vital health care problem affecting millions of people. Figure 5
shows Types of Heart Diseases. Expert system (ES) is a consultation intelligent sys-
tem that contains the knowledge and experience of one or more experts in a specific
domain that anyone can tap as an aid in solving problems.
At our research unit, we have developed two versions of expert systems for heart
diseases diagnosis.
The first one uses the rule-based reasoning while the second one uses case-based
reasoning. The first version is composed of three components: knowledge base, user
interface and computational model.
The knowledge was gathered from expert doctors in EL-Maadi Military Egyptian
hospital, Egyptian Health Insurance Institute and medical books. We have built the
system’s knowledge base for the 24 heart diseases and it is composed of 24 facts and
65 rules.
The system is implemented in Visual Prolog and has been tested for 13 real exper-
iments (patients). The experimental results have shown 76.9% accuracy in estimating
the right conclusion [30].
The Second version of the expert system uses CBR methodology. We have repre-
sented the knowledge in the form of frames and built the case memory for 4 heart
diseases namely; mistral stenosis, left-sided heart failure, left-sided heart failure, sta-
ble angina pectoris and essential hypertension.
The system has been implemented in visual prolog for Windows and has trained
set of 42 cases for Egyptian cardiac patients and has been tested by another 13 differ-
ent cases.
Each case contains 33 significant attributes resettled from the statistical analysis
performed to 110 cases.
The system has been tested for 13 real cases. The experimental results have shown
100% accuracy in estimating the correct results for using nearest neighbor algorithm
and this percentage is dropped to 53.8% in case of using the induction algorithm. The
systems are able to give an appropriate diagnosis for the presented symptoms, signs
and investigations done to a cardiac patient with
Fig. 5. Types of heart diseases
the corresponding certainty factors. It aims to serve as doctor diagnostic assistant
and support the education for the undergraduate and postgraduate young physicians.
6.3 Mining Patient Date for Determining Thrombosis Disease using Rough Sets
At our research unit, ASU-AIKE labs, a rough set-based medical system for min-
ing patient data for predictive rules to determine thrombosis disease was developed
[31,32] this system aims to search for patterns specific/sensitive to thrombosis dis-
ease. This system reduced the number of attributes that describe the thrombosis dis-
ease from 60 to 16 significant attribute in addition to extracting some decision rules,
through decision applying decision algorithms, which can help young physicians to
predict the thrombosis disease.
6.4 Genetic Algorithms Approach for Mining Medical Data
In our research group we developed a hybrid classifier that integrates the strengths
of genetic algorithms and decision trees. The algorithm was applied on a medical
database of 20 MB size for predicting thrombosis disease [33]. The results show that
our classifier is a very promising tool for thrombosis disease prediction in terms of
predictive accuracy.
6.5 An Agent-Based Modeling for Pandemic Influenza in Egypt
Pandemic influenza has great potential to cause large and rapid increases in deaths
and serious illness. The first major pandemic influenza H1N1 is recorded in 1918-
1919, which killed 20-40 million people and is thought to be one of the most deadly
pandemics in human history. In 1957, a H2N2 virus originated in China, quickly
spread throughout the world and caused 1-4 million deaths worldwide. In 1968, an
H3N2 virus emerged in Hong Kong for which the fatalities were 1-4 million [34]. In
recent years, novel H1N1 influenza has appeared. Novel H1N1 influenza is a swine-
origin flue and is often called swine flu by the public media.
In the absence of reliable pandemic detection systems, computational intelligence
techniques and paradigms have become an important smart software tools for both
policymakers and the general public [35, 36,27]. In our application, we propose a
stochastic multi-agent model to mimic the daily person-to-person contact of people in
a large-scale community affected by a pandemic influenza (novel H1N1) in Egypt.
The developed multi-agent model is based on the modeling of individuals' interactions
in a space time context. The model involves different types of parameters such as:
social agent attributes, distribution of Egypt population, and patterns of agents' inter-
actions. Analysis of the results leads to understanding the characteristics of the mod-
eled pandemic, transmission patterns, and the conditions under which an outbreak
might occur. In addition, model is used to measure the effectiveness of different con-
trol strategies to intervene the pandemic spread. More technical and computing as-
pects can be found in reference [36, 37]
6.6 Daily Meal Planner Expert System for Diabetics Type-2 in Sudan
Actually, recent estimates place the diabetes population in Sudan at around one
million – around 95% of whom have type 2 diabetes and patients with diabetes make
up around 10% of all hospital admissions in Sudan [38,39]. Mostly, Type 2 diabetes is
strongly connected with obesity, age, and physical inactivity [39]. Most medical re-
sources reported that 90 to 95% of diabetic is diagnosed as type 2. So, a successful
intelligent control of patient food for treatment purpose must combines patient inter-
esting food list and doctors’ efficient treatment food list. In addition, many rural
communities in Sudan have extremely limited access to diabetic diet centers. People
travel long distances to clinics or medical facilities, and there is a shortage of medical
experts in most of these facilities. This results in slow service, and patients end up
waiting long hours without receiving any attention. Hence the expert systems para-
digm can play a very important role in such cases where medical experts are not
readily available. At our research ASU-AIKE labs, Ain Shams University, Egypt, we
design and implement of an intelligent medical expert system for diabetes diet that
intended to be used in Sudan [38,39]. The expert system provides the patients with
medical advices and basic knowledge on diabetes diet. The development of such sys-
tem went through a number of technical stages, namely; requirements analysis, food
knowledge acquisition, formalization, design and implementation. Visual prolog was
used for designing the graphical user interface and the implementation of the system.
The system is a promising helpful smart tool that reduces the workload for physicians
and provides a more comfort for diabetic patients.
6.7 CI in Medical Volume Visualization (MVV)
MVV brings profound changes to personal health programs and clinical healthcare
delivery. It’s seeks to reveal internal structures hidden by the skin and bones, as well
as to diagnose and treat disease. Visual representation of the interior body is a key
element in medicine. There are many techniques for creating it; such as magnetic
resonance imaging, computed tomography, and ultra-sound [40]. The past few dec-
ades have witnessed an increasing number of new techniques being developed for
practical clinical image display. One approach is to render the data interactively using
a specialized multi-processor hardware support. Since these devices are not cheap,
they are not widely used in practice. Another alternative is to use volume visualiza-
tion [41]. In our research labs, we performed a comprehensive study for the recent
intelligent techniques and algorithms used for medical data visualization [41]. These
techniques cover filtering, segmentation, classification and visualization as well as the
intelligent software supporting medical volume visualization. The study reveals hy-
brid techniques are the best approach for medical image segmentation is the best. In
our future, work we are looking to develop mobile based intelligent system using
direct volume rendering texture mapping technique with bones data sets.
7. Future research directions
Currently, we are working on the following applications;
(a) Determining the appropriate computational intelligent paradigm and model ca-
pable to classify Alzheimer disease and to build computer aided diagnostic sys-
tem capable of detecting Alzheimer's at any stage [42.43].
(b) Big medical data analytics of intensive care unit data using machine learning
and computational intelligence techniques [44,45].
(c) Developing an intelligent medical imaging evaluation system to help doctors
diagnose pneumonia caused by the novel corona virus. The system capable of
detecting corona at any stage.
8. Conclusions
The development of robust intelligent medical decision support systems is a very
difficult and complex process that raises a lot of technological and research challeng-
es that have to be addressed in an interdisciplinary way. The development of robust
intelligent healthcare systems is a very difficult and complex process that raises a lot
of technological and research challenges that have to be addressed in an interdiscipli-
nary way. This paper analyzes the main paradigms and applications of the computa-
tional intelligence (CI) in healthcare from the artificial intelligence perspective.
The main results based on our analysis. CI offer potentially powerful tools for the
development a novel digital healthcare system. The variety of such techniques ena-
bling the design of a robust and efficient IHS. The key to the success of such systems
is the selection of the CI technique that best fits the domain knowledge and the prob-
lem to be solved. That choice is depending on the experience of the knowledge engi-
neer. And, digital medical decision support systems can benefit from systematic
knowledge engineering and structure using techniques from the different disciplines
artificial intelligence. AI technologies and techniques play a key role in developing
intelligent tools for medical tasks and domains.CI Techniques (e.g. CBR, Data Min-
ing, Rough Set, Ontology) can cope with medical noisy data, sub symbolic data, and
complex structure data. In addition, CI offer intelligent computational methods for
accumulating, changing and updating medical knowledge in IHS, and in particular
learning mechanisms that will help us to induce knowledge from medical information
or data. From our comprehensive analysis, one can recommend the following recom-
mendations:
1. The cooperation between physicians and AI communities is essential to produce
efficient computing systems for medical purposes. The physicians will have more
information to deliver a better service and dynamic guidelines to improve quality
and reduce risks.
2. Mobile devices can feed real-time medical data directly to patients and doctors via
secure computing networks and IoT. The web based and IoT medical systems can
enhance the online education/ learning/training processes.
3. The use of ICT technologies also improves the quality of patient care and reduces
clinical risk. At the same time, the patient will be part of the healthcare process,
having more information about diseases and access to his/her electronic health rec-
ord.
4. Public health authorities can get more accurate information and develop dash-
boards to make better and fast decisions.
5. Hospital management benefits from a more updated meaningful data. This data is
used by management systems to delivery KPI (Key Performance Indicators).
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