1 Introduction

This paper discusses the necessary properties of the model to describe Doctor–Patient–Machine system of systems, the attributes of the functional interactions amond doctors, patients and machines, and the design of functional interactions of such system of sytems.

The primary objective of the doctor–patient–machine modeling is to establish the analytical and prediction framework of the well being and health care of the patient, which is a person. More specifically, two functions are necessary. The first one is the curing mechanism when some disease emerges and intervene with control if some deviation occurs, and the second one is the mechanism to maintain the present status within a predefined range of deviations.

This paper introduces two concepts, which are the dynamism of the structure reflecting the time sequence or changes in the time domain, and the blackbox element whose internal mechanism is unknown but its existence is certain or can be assumed. The dynamic structure requires the description of addition and deletion of elements of the system. This paper discusses the incorporation of the dynamism related to the time-domain aspect and the blackbox elements into the systems model.

The presence of machine learning related techniques in clinical treatment environment is increasing with the advance of machine learning techniques, particularly after the development of the deep learning algorithm [1]. The use of machines in clinical environment will increase in the future and this direction is irreversible. Although the use of machines in today’s conditions is limited to assist doctors, the patients will also be exposed to the machines present in the medical examination room in future. In this paper, the machine denotes an algorithm or an application embedded in a physical computing machine. A more accurate expression would be a software system, usually based on machine learning algorithms, that provide any kind of medical information that is useful for either doctor or patient in order to reach decisions related to the treatment of the patient.

2 Representation of Doctor–Patient–Machine System of Systems

Today, direct and concurrent interaction between doctor and machine during medical consultation is rare. Figure 1(A) illustrates the current stage of interactions in medical examination rooms, which is gradually changing to interaction shown in Fig. 1(B). The links indicate the interactions between the connected elements. In Fig. 1(B), the machine is basically hidden from the patient, and naturally the interactions between the doctor and the machine are also masked from the patient. The next stage will be the interaction structure shown in Fig. 1(C), where the machine interacts with both doctor and patient, indicated as links \(\alpha \) and \(\beta \). The interactions \(\alpha \) and \(\beta \) are basically different. More advanced case will be Fig. 1(D), where the doctor and patient possess his own machine, possibly functioning constantly and not just during the medical consultation.

A typical conventional research project and system is IBM Watson [2], primarily targeting oncological treatments, mainly to suggest anticancer drugs. Other projects are similar. Conventional projects in machine assisted diagnoses and healthcare [3] rely on published trials and test results to match with the patient’s current conditions for selecting treatment strategies. However, this is simply a larger scale version of the treatment details described in treatment guidelines recommended by medical councils and societies. Although this method can be interpreted to be a “personalized” if the genomic data are used because genomic data is personal, no life background and history of the patient is considered. Therefore, conventional personalized medicine is only partially personalized, and the crucial defect is that the life history of the patient has equivalent or more importance than patient’s physical conditions when defining treatment strategy.

The interactions represented by links in Fig. 1 are different from conventional concept of interactions, which denote some kind of information or “matters” that are exchanged by the related entities. In this paper, the interaction denotes any kind of functional relationships necessary to implement the exchange of “matters” between the entities, besides the non-measureble “matters” and functional elements necessary for functional relationship between the entities. Furthermore, we also differentiate the combination of binary interactions from N-ary interactions. This is another difference from conventional studies, partially due to the limited description capability of employed models, where any interaction is decomposed into a set of binary interactions.

Fig. 1.
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Change of doctor–patient–machine interaction structure

Figure 2 illustrates the description of the integrated system of two systems, which are the doctor (human) described as a system and the machine described as a system. The thin circles represent the physical boundary (shape) of each system. Multiple viewpoints exist to describe and understand the integrated system. Figure 2 is an illustrative example of one of possible facets. It should be noted that the relationships between the human and the machine is directly connected to the components of the two systems (human and machine), and the set of these relationships constitute the integrated system of a given facet. Depending on the viewpoint, the thin circles become meaningless, as the integrated system is the result of often complex relationships between human and machine systems. The physical boundary is completely different from the boundary defined by functions, if such boundary can be defined.

Fig. 2.
figure 2

Description of functional relationship between doctor and machine. System of systems (SoS) of doctor and machine represented with their components illustrating interactions and functional relationships between doctor and machine. The graph representations inside thin circles denote the representations with activated rulesets. The description is similar for patient and machine SoS.

The interactions \(\alpha \) and \(\beta \) of Fig. 1(C) are different, as the doctor and patient not only requires different kinds of information, but even for the same data, information presentation or visualization are different for the doctor and the patient, as these two have different basic knowledge. In the more advanced case described in Fig. 1(D), the machine interacting with the doctor and the machine interacting with the patient can communicate directly without the intermediation of either doctor or patient. This type of communication is completely different from previous communications (Fig. 1), because although the machine communicates with human in Fig. 1(B) and (C), the communication of the machine is always with a human. On the other hand, the communication in Fig. 1(D) is more precisely an information exchange and functional interactions among machines without involving humans in the process. Therefore, all limitations imposed by human intervention is cleared, which is basically the (1) size limit, (2) speed limit and (3) functional merger. The first two are simple. The data size becomes limited by the storage capacity of the machines involved in the communication, so the primary data of images and structures that have considerable data size can be exchanged. In medical examinations, multiple images or structural data are generated, so the data size is high. The speed limit is similar, as the amount of transmitted data per unit time is order of magnitudes faster in computer only communication, limited only by the data transmission speed and read and write speed limit of storage devices. The third limitation is particular to computer-computer communication, currently impossible if human is involved. It is technically possible for the machines to provide a kind of API (application programming interface) to enable access of internal functionalities to allowed parties. In a illustrative situation, a patient with his machine (M\(_p\) in Fig. 1(D)) in a examination room is connected with the doctor’s machine (M\(_d\) in Fig. 1(D)), and these two machine exploit the functionality of the other machine for necessary tasks. The doctor’s machine (M\(_d\)) can provide functions to visualize the patient’s test results and analyses of prognostics. On the other hand, the patient’s machine (M\(_p\)) may offer mainly access means to patient’s past data. Other functions are possible, and the point is that the machines constitute an temporary integrated system of machines M\(_d\) and M\(_p\).

The hypernetwork model [4] is used to describe the SoS of doctor, patient and machine (Fig. 1). Each hypernode is a collection of rulesets, which is a superimposed representation of multiple descriptions that the hypernode is used to describe. One description is activated at a time, invoked by the activated rulesets of other hypernodes. Therefore, the selection of the activated ruleset is governed by the ruleset of the hypernode that is connected with direction to the hypernode.

Fig. 3.
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The ruleset Ax is activated from the set of rulesets in hypernode A, which defines the activated ruleset By in hypernode B

Fig. 4.
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The ruleset Ax is activated from the set of rulesets in hypernode A, which defines the activated ruleset By in hypernode B

Figure 4 illustrates the basic mechanism of description activation or visualization of a given perspective. Suppose the hypernode A is connected to the hypernode B. This is the simplest case, two hypernodes and unidirectional connection from one hypernode to the other hypernode. The hypernodes A and B are instances in the pool of hypernodes, and are not directly visualized, as multiple perspectives are superimposed and meaningless for direct interpretations. In Fig. 4, the hypernodes A and B contain \(N_A\) and \(N_B\) rulesets, respectively. Following the rule activation pattern defined in the hypernode A, suppose the ruleset A\(_X\) is activated among \(N_A\) rulesets. Note that only one ruleset is activated at a time. Then if the destination hypernode of the activated ruleset A\(_X\) is the hypernode B, the role of the hypernode B is also specified in the ruleset A\(_X\). Another possible description is the ruleset ID to be activated in the hypernode B directly specified in the ruleset A\(_X\).

The visualized hypernodes A and B (Fig. 3) are actually the rulesets A\(_X\) and B\(_Y\) activated from the sets of rulesets in hypernodes A and B. In more realistic descriptions, multiple hypernodes connect to both hypernodes A and B, and both hypernodes connect to multiple hypernodes. Thus the connection of a hypernode is multiple inputs and multiple outputs, and the link is either unidirectional or bidirectional. When visualized, a hypernode has one of three roles: concept (CPT), attribute (ATT) or relationship (REL).

When describing SoS of doctor–patient–machine, the viewpoint (or facet or perspective) to capture the system is closely associated with hierarchical levels defined in each system (doctor, patient and machine) and boundaries that separates the systems. multiple hierarchical levels, multiple entities separated by boundaries, and multiple facets are equivalent, and are represented with relationships in hypernetwork model. They are functionally equivalent, differing in interpretation defined by the viewpoint. In the case of hierarchy, phenomena associated with each hierarchical level is treated as an independent phenomenon and consequently interpreted as a different viewpoint to represent the target system. In the case of boundaries, the association is more indirect, where the entities that the boundary separates correspond to the perspectives. The boundaries function as relationships among involved entities. The sequenced activation of rulesets defines the viewpoint.

2.1 Unknown Elements

When describing the doctor–patient model with attached machines, the health related aspects are mainly treated. The problem is the existence of many unknown elements that constitute a system of the doctor and patient. The number of unknowns are particularly large for elements directly related to the disease in question. Therefore, in the SoS in Figs. 1(C) and (D), not every elements of doctor and patient are elucidated, thus no accurate representation is possible. Naturally the machine is completely describable, as it is designed by human. We represent the unknown elements as blackbox elements that presumably exist. The following cases of unknown are possible: (1) unknown existence and unknown relationship existence; (2) known or existence possible, but unknown relationship with other elements; (3) known or existence possible, relationship with other elements known or existence possible. The term “existence possible” means that the existence can be assumed based on a hypothesis, but the existence is not certain or confirmed. The relationship with other elements denotes any kind of interaction or functional interdependence among the element and other relevent elements.

2.2 Dynamic Structure and Time Sequence

The time domain information is important in health-care because the treatment should be adapted to individual patient conditions, and patient’s personal conditions are the results of the patient’s life history. Therefore, all personal background data are relevant and should be taken into account when generating treatment strategy for the patient.

Conventional personalized medicine usually refers to the personal conditions of the current status, or of the conditions at the instant of the treatment start or of the diagnosis. Commonly the genomic data are used as the indicator of personal characteristics. It is true that DNA sequence is highly variable among individuals, and although only a fraction is elucidated, SNPs and other variations are associated with drug effectiveness and likeliness of onset of diseases. However, genome data is biological, and phenomena associated with genomic data contains only natural or hereditary facts, and information related to the current conditions of the patient are absent. Medical treatment of patients, on the other hand, involves social aspects, such as family composition, social status, job, daily activity patterns, food preferences, body activity patterns, among others. These aspects should be considered when determining treatment strategy, which results in personalized treatment. Perhaps these aspects have higher weight than genome related biological aspects when elaborating treatment strategy, although no sufficient foundation is available.

The personalized medicine investigated in this paper is fundamentally different from conventional concepts and topics discussed in conventional research which have narrow meaning limited to biological data.

Then the life history of the patient should be modeled, which implies that a model with description capability of the time domain structural change is necessary.

Figure 5 is a conceptual illustration, where the time axis is added to the N-dimensional space to represent system structures. Basically the \(\Delta T\) between adjecent times is a constant value, although not a requisite. The structures of adjacent times \(N-1\), N and \(N+1\) are visualized independently, but these are internally described independent of the value of \(\Delta T\).

Fig. 5.
figure 5

Sequence of structures on time domain. “structure T[1]” denotes the structure at the instant T[1], and so on.

Elements belonging to two structures of adjacent time instances are related based on relationships among them. Basically, two types of representation are possible when time domain description is used. One is to connect individual hypernodes and links with relationship hypernodes, and the other one is to introduce a single REL hypernode with details of differences as ATT hypernodes connected to this REL hypernode. Both represent the differences between two structures as a relationship, differing on the description detail level. To simplify the description, the time domain differences are described only between the adjacent structures, although the differences can be described by introducing REL hypernode that connects structures of arbitrary time instances. Figure 6 illustrates the description of relationships between two structures of adjacent times, where the differences are represented by REL hypernodes that connect to the relevant hypernodes in either or both structures of time T[N] and \(T[N+1]\). The primary role of gray hypernodes is REL, as they define the relationships between the hypernodes and links that are different in two structures.

Fig. 6.
figure 6

Describing relationship between structures of adjacent times.

The integrated system is represented according to the perspective to visualize the system, which is closely related to the function of the interest. The system is not a simple collection of entities, as the hypernodes connected by links, but it is a representation that combines the elements.

2.3 Wave Propagation Analysis

The structural properties of the represented SoS is analyzed using the wave propagation patterns. The main purpose of the wave propagation analysis is the prediction of phenomena associated with the health status of the patient. The method is basically to inject a fictional pulse to multiple elements in the description, and to analyze the propagation pattern over the whole system. The analysis is possible in two directions, one for structural analysis with fixed time, and the other one form time domain analysis, where the pulse propagates on time dimension of the described system with adjacent times.

The wave propagation analysis explores this property of the hypernetwork model, that the ruleset activation is controlled by the hypernode that connects to the hypernode in question.

The sequence of the ruleset activation pattern is analogous to wave propagation, where the rulesets of hypernodes are subsequently activated, and the activation pattern of the rulesets of all affected hypernodes defines the avtivation pattern of the whole description. If the avtivation is constrained to a single time, then the activation pattern of the structure is elucidated. On the other hand, when the propagation on time domain is enabled, it becomes the prediction when the ruleset activation is in future direction, and the retrospective analysis for past direction. In any wave propagation analysis, only a fraction of hypernodes in the pool is usually activated, implying that the number of hypernodes of visualized network is smaller than the number of hypernodes in the pool.

The time sequence description is particularly useful to predict the future prognosis, and to analyze the influences of changes in elements of the components of the system.

Two immediate applications of the system representations are: (i) analysis of the structure, by investigating the consequences/influences of the changes in system components (change, addition and deleteion); and (ii) prediction, particularly on time domain, i.e., prediction of the future conditions based on the past history and the present state.

The integrated system consisting of doctor, patient and machine (Fig. 1) is treated as a system of systems (SoS). Each of the three components (doctor, patient and machine) is a system of considerable complexity and can also be interpreted as a SoS.

Various failures of complex systems [5] suggest that complex systems cannot be represented as a pure aggregation of individual systems, where the interactions among component systems can be represented as a couple of relationships. Furthremore, it is assumed that functional boundaries can be clearly described. If these assumptions were valid, incidents of failures of complex systems should be minial, which is false. One method is to try to extract the interactions among component systems as simple as possible, Similar method is to design the integrated system (SoS) to contain only simple functional interactions among the component systems. However, both methods are ignoring the reality, where such extraction or design is not possible in real world. This is particularly true for the doctor-patient-machine SoS discussed in this paper.

Physical boundaries among the three entities, doctor, patient and machine, is easily characterized. However, the most important point is whether a boundary can be defined in the representation from the functional perspective, which is necessary for the wave propagation analysis. Our ongoing project on the description of doctor-patient-machine SoS suggests that any represenation of the functional aspect of arbitrary two entities, for instance doctor and machine, patient and machine or doctor and patient, requires the description of elements that belong to different hierarchical levels in both entities (Fig. 2). The hierarchical level refers to the conventional hierarchical levels in structural representations.

An important role of the machine M\(_d\) is to assist doctors (Fig. 1) to diagnose and to build treatment plan. These actions involve numerous decision makings by the doctors. Similarly, patients are also requested to make decisions regarding his own treatment. The decision making by doctors involve imaginations and predictions under insufficient information. The ability of this prediction differentiates the skill of experiment and novice doctors. On the other hand, no such differences exist among patients. The primary role of the machine M\(_d\) assisting doctors is to provide analytical results that can be deduced from data stored in the machine, which is information based on past data. For the prediction by skilled doctors, all relevant information is valuable.

For the prediction by skilled doctors, all relevant information is valuable. The prediction of future progress of patient conditions by machines are the results of calculations using past data and machine learning techniques, which are the replications of past accumulated cases.

Fig. 7.
figure 7

System representation of integrated human (doctor) and machine, each of which is also described as systems. The boundary between human and machine is also represented.

Fig. 8.
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Abstract level of descriptions of doctor-machine SoS.

Following the line of our previous works [4], we assume that the component systems cannot be extracted separately, implying that the boundary among the components cannot be defined.

Figure 8 illustrates the possibility to change the level of description details of human-machine SoS. The top description represents the most abstract level, and the bottom one a more detailed. Adequate level of details can be chosen for purposes. Each representation denotes a different viewpoint, impossible using conventional models.

3 Conclusions

The time domain is a requisite element when representing doctor patient machine as an integrated system. The conventional health care aid systems focus on the patient conditions that are measureble with medical exams, and the individual factors often mean gene level factors, also measureble with medical exams. However, no personal life history is considered, which plays an important role in planning personalized treatment strategy for the patient.

This paper presented the framework that enables the description of previously ignored aspects of patient’s personal data. Analyses are also possible using the gramework, and are particularly useful to estimate the future changes and to detect influences of changes in elements of the system.