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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Identity Tracking of a Disease as a Causal Chain</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Kouji Kozaki</string-name>
          <email>kozaki@ei.sanken.</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Riichiro Mizoguchi</string-name>
          <email>miz@ei.sanken.</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Takeshi Imai</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Kazuhiko Ohe</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Medical Informatics, Graduate School of Medicine, The University of Tokyo</institution>
          ,
          <addr-line>7-3-1, Hongo, Bunkyo-ku, Tokyo</addr-line>
          ,
          <country country="JP">Japan</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>ISIR, Osaka University</institution>
          ,
          <addr-line>8-1 Mihogaoka, Ibaraki, Osaka</addr-line>
          ,
          <country country="JP">Japan</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>This paper discusses the ontological treatment of identity of a disease based on an ontological model of diseases as causal chains. An individual causal chain changes through its processes such as extending, branching, fading, etc. When we suppose that an individual disease is constituted by such a causal chain, changes of the causal chain imply changes of the disease. Then, how should we deal with identity of a disease? To answer this, we consider identity of a disease as a causal chain based on some ontological theories. As a result, we propose an ontological model for identity tracking of a disease as a causal chain. This work should contribute to the ontological treatment of identity of diseases in medical information systems.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>INTRODUCTION</title>
      <p>
        Recently, many medical ontologies have been developed for
realizing sophisticated medical information systems, such as
OGMS
        <xref ref-type="bibr" rid="ref1 ref4">(Scheuermann et al., 2009)</xref>
        , DOID
        <xref ref-type="bibr" rid="ref4">(Osborne et al.,
2009)</xref>
        , and IDO
        <xref ref-type="bibr" rid="ref5">(Cowell et al., 2010)</xref>
        . They mainly focus on
the ontological definition of disease with related properties.
We proposed a definition of a disease involving capturing a
disease as a causal chain of clinical disorders
        <xref ref-type="bibr" rid="ref6">(Mizoguchi et
al., 2011)</xref>
        . This paper discusses the evolution of individual
diseases, whereas the main concern in our previous work
was capturing static characteristics of diseases. An
individual disease undergoes changes as it evolves, and some of
these changes may cause new diseases to appear as a result.
In some cases, some symptoms may appear as aftereffects
lingering beyond the point when the original disease was
cured. Even if the disease can be cured completely, it could
appear in the patient's anamnesis. Here, the problem is how
these changes should be dealt with based on our disease
ontology. We discuss it from the viewpoint of identity
tracking of a disease based on an ontological model of causal
chains and a theory of identity
        <xref ref-type="bibr" rid="ref7">(Kozaki et al., 2010)</xref>
        .
      </p>
      <p>This paper is organized as follows. The next section
outlines the definition of a disease in our previous work. In
Section 3, we describe an ontological theory of identity
tracking of a disease. In Section 4, we summarize some
related work. Finally, we present concluding remarks with a
discussion of future work.</p>
    </sec>
    <sec id="sec-2">
      <title>A MODEL OF DISEASES</title>
      <p>After it begins to exist, a typical disease, as a dependent
continuant, enacts extending, branching, and fading
processes before it disappears. Thanks to these processes, a
disease can be identified as a continuant that is an enactor of
those processes. Such an entity (a disease) can change
according to its phase while keeping its identity. On the basis
of this observation, we defined a disease as:
Definition 1: Disease (Mizoguchi et al., 2011)</p>
      <p>A disease is a dependent continuant constituted of one or
more causal chains of clinical disorders appearing in a
human body and initiated by at least one disorder.</p>
      <p>Note that, although any disease has dynamic flows of the
propagation of causality as its internal processes, it is the
enactor of its external processes, such as branching and
extending its causal chain of disorders.</p>
      <p>When we collect individual causal chains belonging to a
particular disease type (class), we are able to find a common
causal chain (partial chain) that appears in all of the instance
chains. By generalizing such a partial chain, we obtain the
notion of a core causal chain of a disease as follows:
Definition 2: Core causal chain of a disease1</p>
      <p>A sub-chain of the causal chain of a disease whose
instances are included in all the individual chains of all
instances of a particular disease type. It corresponds to the
essential property of a disease type.</p>
      <p>Definition 2 provides a necessary and sufficient
condition for determining the disease type to which a given causal
chain of clinical disorders belongs. That is, when an
individual causal chain of clinical disorders includes instances
of the core causal chain of a particular disease type, it
belongs to the disease type. We can thus define such a disease
type that includes all possible variations of physical chains
of clinical disorders observed for patients who contract the
disease. According to a standard definition of subsumption,
we can introduce an is-a relation between diseases using the
chain-inclusion relationship between causal chains.</p>
      <sec id="sec-2-1">
        <title>Definition 3: Is-a relation between diseases</title>
        <p>Disease A is a supertype of disease B if the core causal
chain of disease A is included in that of disease B. The
inclusion of nodes (clinical disorders) is judged by taking an
is-a relation between the nodes into account, as well as
sameness of the nodes. (Mizoguchi et al., 2011)</p>
        <p>
          Assume, for example, that (non-latent) diabetes and
type-I diabetes are respectively defined as &lt;deficiency of
insulin  elevated level of glucose in the blood&gt; and
&lt;de1 This is a revised version of Definition 3 in
          <xref ref-type="bibr" rid="ref6">(Mizoguchi et al., 2011)</xref>
          .
struction of pancreatic beta cells  lack of insulin I in the
blood  deficiency of insulin  elevated level of glucose in
the blood&gt;. Then, we get &lt;type-I diabetes is-a (non-latent)
diabetes&gt; according to Definition 3.
        </p>
        <p>There is another way to define is-a relations among
disease types. Assume that the core causal chain of
arteriopathic disease is &lt;disorder of artery → disorder of heart
function&gt;. Then we can define a subtype disease of
arteriopathic disease which has the core chain &lt;disorder of aorta
→ disorder of heart function&gt; by specializing disorder of
artery to disorder of aorta. The specialization of disease
types in the latter way is always sound because the new
specialized types include only instances of the original types
via chain-inclusion (the former way). On the other hand,
generalization in the latter way does not always generate
sound results via chain-inclusion because what we get will
include causal chains that do not go through the core causal
chain of its supertype.</p>
        <p>We understand there is a difficulty in defining main
pathological/etiological condition(s) for each disease due to
the variety of disease manifestations. However, at least we
should be able to expect the existence of something
common to all instances of a disease type, otherwise we cannot
define the type. The core causal chain is such a common
thing that contains something corresponding to the main
pathological/etiological condition(s). That is, we would like
to claim that the right terminal end (the disorder located at
the most downstream position) of the core causal chain of a
disease defined in a bottom-up way from a collection of
individual causal chains should be understood as a kind of
main pathological/etiological condition(s). In an extreme
case, the core causal chain of the root disease of an is-a
hierarchy would consist of a single clinical disorder as a
special case of a causal chain, and this should correspond to the
main pathological/etiological condition(s) of the disease.
3</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>IDENTITY TRACKING OF A DISEASE</title>
      <p>
        A disease undergoes change during its course. The cause
may disappear, especially in its latter phase. Such
disappearance might have a negative influence on determination
of the disease of individual causal chains. Many other
fluctuations of disorders might influence the causal chains, too.
Ontology of diseases should address such issues. One of the
major issues related to such observations is identity tracking
of diseases. To tackle this identity problem, we need to
formulate the identity of a causal chain of clinical disorders.
Because the disease is a continuant, it can change while
maintaining its identity. The theory of processes and events
adopted in this paper is found in the literature
        <xref ref-type="bibr" rid="ref3">(Galton &amp;
Mizoguchi 2009)</xref>
        , in which the two key notions are (1)
processes are intrinsically ongoing/in-progress whereas events
are not, and (2) an event is constituted of processes.
3.1
      </p>
      <sec id="sec-3-1">
        <title>Classification of causal links</title>
        <p>
          There are two kinds of processes
          <xref ref-type="bibr" rid="ref6">(Mizoguchi et al., 2011)</xref>
          :
(1) Cumulative continuous process: a process that proceeds
without completing the current process at every instant
in time.
(2) Non-cumulative process: a process that proceeds by
completing the current process at every instant in time.
A causal chain is composed of one or more pairs of entities
such as a causal event/process and an effect event/process,
where the latter has been caused by the former. The effect
becomes another cause that causes another effect in the case
of multi-pair chains. We define three kinds of causal links
from the perspective of “ongoingness”.
        </p>
        <sec id="sec-3-1-1">
          <title>Definition 4: Ongoing causal link</title>
          <p>This is a link that shows that the propagation of causality
from the cause to the effect is ongoing.</p>
          <p>Definition 5: Historical causal link</p>
          <p>This is a link that shows that the propagation of causality
from the cause to the effect has terminated.</p>
          <p>Definition 6: Pseudo-simultaneous causal link</p>
          <p>This is a link that shows only a pseudo-simultaneous
relation between cause and effect, excluding the temporal
information. It is used mainly for causal events that can be
viewed as having happened at the same time.</p>
          <p>Continuous propagation of causal effect requires that
both causal and effect processes are ongoing. Therefore,
ongoing links can appear only between ongoing processes,
and they correspond to causal relations found in cumulative
continuous processes; &lt;braking → decelerating&gt; is a good
example of this type of causal link. We believe that many of
the causal links found in diseases are also of this type. For
example, in the chain &lt;deficiency of insulin → elevated
level of glucose in the blood&gt;, both processes are definitely
ongoing. The same applies to &lt;angiostenosis → lack of
oxygen in myocardial cells → necrosis of myocardial cells&gt;
which is a causal chain in myocardial infarction. On the
other hand, &lt;loss of kidney function → increase of waste in
the blood&gt; might be problematic, since “loss of kidney
function” is a past event and hence not ongoing. It is true
that “loss of kidney function” is an event, but after the event,
a new process or state “kidney is not functioning” is
ongoing, and this causes “increase of waste in the blood”. In
reality, a historical causal link appears between “loss of
kidney function” and “kidney is not functioning”, and an
ongoing link appears between “kidney is not functioning”
and “increase of waste in the blood”. The same applies to
“virus invasion”, “steroid treatment”, etc.</p>
          <p>Readers might suspect that we have to write unnecessary
processes as follows: “finish traveling” and then “not
traveling”. Of course, this is not the case. We are describing
causal chains of clinical disorders which we believe explain a
disease under consideration, and hence we can select what
to write as a disorder. Thus, we do not have to write
processes that are not necessary for explaining diseases.</p>
          <p>Although many of the causal links appearing in diseases
are ongoing, historical causal links also should appear in
such cases where the causal events have terminated and the
causality does not flow currently. A typical example is the
event of a virus invasion that had caused an infection.
Another case is a cured disease consisting of a causal chain of
past events, which will be discussed in Section 3.2 in detail.</p>
          <p>Transition from an ongoing process to a terminated
event can be explained in terms of the change from ongoing
causal link to historical causal link as follows: when the
causing process has terminated, the process constitutes a
new event as a past event of the causation, together with a
change of the ongoing causal link to a historical causal link.</p>
          <p>A pseudo-simultaneous causal link is special. Let us
assume a series of events associated with a vase, such as “fall
onto the floor, collision with the floor, break, and spill
water”. It is a common phenomenon and corresponds to a
noncumulative process. We take two events from it: collision
and breakage events. It seems like the two events happened
at the same instant in time. Precisely speaking, however,
these two events need non-zero time intervals, and the
collision happened before the breakage. In spite of this reality,
people tend to see that they happened at the same time with
the understanding that the collision caused the breakage. A
pseudo-simultaneous causal link is introduced to represent
such a causal relation. It does not include a non-zero
temporal interval but deals with the two events as if they
happen at the same time while keeping the causal order. It also
can be interpreted as a degenerated causal link that includes
the change of an ongoing causal link to a historical causal
link and is useful for representing causal events composed
of non-cumulative processes.
3.2</p>
        </sec>
      </sec>
      <sec id="sec-3-2">
        <title>Classification of causal chains</title>
        <p>We introduce three kinds of causal chains to capture the
change of diseases according to the causal links as follows:</p>
        <sec id="sec-3-2-1">
          <title>Definition 7: Strongly connected causal chain</title>
          <p>Any causal chain all of whose causal links are ongoing
causal links; that is, it is composed of only ongoing
processes. A causal chain composed of one ongoing process
is included as a special case.</p>
          <p>Definition 8: Weakly connected causal chain:</p>
          <p>Any causal chain that includes at least one historical or
pseudo-simultaneous causal link and at least one
ongoing process.</p>
          <p>Definition 9: Historical causal chain:</p>
          <p>Any causal chain all of whose causal links are historical
or pseudo-simultaneous causal links. That is, it is a
causal chain composed only of terminated events.
Definition 10: Ongoing causal chain:</p>
          <p>Any causal chain that has at least one ongoing process.
It subsumes the strongly connected and weakly
connected causal chains.</p>
          <p>When an ongoing process of a strongly connected causal
chain has terminated, the whole chain becomes a weakly
connected causal chain composed of two strongly connect
causal sub-chains. If all of the ongoing processes have
terminated, then the chain becomes a historical causal chain.
Note here that whatever change happens, the identity of a
causal chain remains the same as before it becomes a
historical causal chain. This topic will be discussed in Section 3.3.
3.3</p>
        </sec>
      </sec>
      <sec id="sec-3-3">
        <title>Identity of a causal chain</title>
        <p>
          We begin our discussion on identity of a causal chain by
talking about identity of entities
          <xref ref-type="bibr" rid="ref7">(Kozaki et al., 2010)</xref>
          . There
are two types of identity:
Instance identity: Identity for discussing the sameness of
instances.
        </p>
        <p>Class identity of a thing: Identity for discussing the
sameness of the class to which the entity belongs.</p>
        <p>In order to talk about identity of a disease instance, we
need to establish identity of a causal chain of clinical
disorders. So, what we should discuss is under what conditions
the instance of a causal chain loses identity.</p>
        <p>
          After it has been born, an individual causal chain of
clinical disorders grows, branches, etc. and it may reach another
disease. Thanks to appropriate remedies, its causal disorders
disappear, whereas some downstream disorders are still
ongoing. During such a change, the disease, that is, the causal
chain of clinical disorders, keeps its identity. For example,
even if diabetes in a patient causes a cerebral infarction, the
clinical causal chain remains the same; that is, no new
causal chain appears because of it. Furthermore, even if an
aftereffect remains after all of the main causes have disappeared,
we should be able to identify it as the same causal chain in a
different state. In order to deal with such changes properly,
we employ Identity for replacement (I-Rep) among the four
kinds of identity discussed in our previous work
          <xref ref-type="bibr" rid="ref7">(Kozaki et
al., 2010)</xref>
          . I-Rep is defined as:
Identity for replacement (denoted as I-Rep):
        </p>
        <p>Identity wherein an instance of the whole continues to be
itself without becoming another thing while its parts are
being replaced, independently of the kinds and number of
replaced parts.</p>
        <p>A typical example for the use of I-Rep is a bike whose
parts are replaced one by one. Whatever parts are replaced
and in whatever number, a bike whose parts are replaced
remains the same in terms of I-Rep. Exactly the same
applies to causal chains of clinical disorders. Some readers
might notice that we could use Identity for essentiality
(IEss for short) instead of I-Rep. I-Ess is defined as identity
determined by the essential property of an individual. If you
use I-Ess with, say, a saddle that you love as its essential
property and parts of your bike are being replaced as in the
case above, then you would say, “This is not my bike any
more,” when the saddle has been replaced with a new one.
In the case of diseases, for example, an individual causal
chain of diabetes has the essential property of an elevated
level of glucose in the blood. If its identity is defined in
terms of I-Ess for that property, then it would become
another causal chain when the glucose level becomes normal
because it loses its identity. However, this is not appropriate
because identity of the causal chain itself should be kept
unchanged as long as some disorders caused by the diabetes
remain. Furthermore, even if only an aftereffect is left, it
should be identified as the same causal chain in a different
state. This is why we employ I-Rep instead of I-Ess.</p>
        <p>Class identity, on the other hand, is used to talk about to
what type an individual causal chain belongs. As stated in
Definitions 1 and 2, an individual causal chain of clinical
disorders Ci is identified as belonging to a disease type DA
when it includes an instance of the core causal chain of DA
as a part, and then, it gains class identity for DA. This Ci is
said to be an ongoing disease DA if it is an ongoing causal
chain. Ci can get another identity for a different disease
when it also includes an individual core causal chain of
another disease, say, DB. Class identity is kept until the
ongoing causal chain becomes a historical causal chain.
Therefore, the extinction condition of causal chains in terms of
IRep and I-Ess is the same.</p>
        <p>
          Let us discuss conditions for extinction of a causal chain
in terms of I-Rep. Any individual causal chain, Ci, is born as
a single ongoing process, that is, as a strongly connected
causal chain. It never changes its I-Rep identity by
replacement of its parts. Neither growth nor branching can change
its identity. When an intermediate disorder terminates to
become an event, it becomes a weakly connected causal
chain, keeping its I-Rep identity. In other words, it does not
change its I-Rep identity if it has at least one ongoing
disorder. Now, we discuss what happens when all the ongoing
processes have terminated and hence all the links have
become historical causal links. According to previous work
          <xref ref-type="bibr" rid="ref3">(Galton and Mizoguchi, 2009)</xref>
          , an event is constituted of
processes, and when all associated processes have
terminated, it finally appears as a whole as the result of constitution
of past (terminated) processes. Because processes and
events are different categories, the newly created event
should have different identity from that of the processes.
When all the links have become historical causal links,
therefore, the resulting historical causal chain must be a
different instance (chain) from the ongoing causal chain
because all of its nodes and links are different from the
original chain (chain before the change). That is, when all
disorders included in an ongoing causal chain have gone (been
successfully treated), the chain loses its identity and
becomes a historical causal chain of different identity, which
corresponds to curing the disease, and the resulting
historical causal chain represents the anamnesis of the patient.
Those past processes constituting the events represent how
the previous disease appeared in the patient's anamnesis
and how the disease was cured.
        </p>
        <p>Note here that a change of part of the ongoing causal
chain does not influence the identity of the whole chain
thanks to the I-Rep identity; that is, an ongoing causal chain
remains the same chain after curing a few disorders in the
chain before all of the disorders have been cured.</p>
        <p>We associate two kinds of identity with each individual
causal chain of disorders, namely, instance identity and
class identity. At first glance, class identity seems to be
useful to talk about when a disease is cured. However, this is
not the case, because a causal chain keeps the same instance
identity and remains being the same disease as long as there
are still ongoing downstream disorders/symptoms even
when all the disorders included in its core causal chain have
been cured. When all disorders included in a causal chain
are cured, the ongoing causal chain disappears and a new
historical causal chain is born. As discussed already,
because the newly born historical causal chain is a different
individual from the corresponding ongoing causal chain, it
should have a different instance identity. However, its class
identity should be the same as that of the original causal
chain, since a previous disease that appeared in the patient's
anamnesis must be the same as the disease of the
corresponding ongoing one. In summary, the historical causal
chain should have the same class identity as the original
disease. Considering various cases concerning
ongoing/historical states, there can be several states for a causal
chain. We can identify the following three major states:
1) Ongoing: an individual causal chain Ci of disease DA
whose core causal chain is still ongoing.
2) Curing: Ci as a whole is ongoing but the core causal
chain of disease DA of Ci is inactive (has become a
historical causal chain).
2.1 A few partial causal chains in the downstream
are still ongoing.
2.2 No ongoing causal chains but a few long-term
remaining disorders that have no influence on
others (aftereffects).
2.3 Although disease DA seems to have been cured
at a certain time, it might recur in the future.
2.4 In a case of cancer, it might metastasize to other
regions, etc.</p>
        <p>3) Cured: Ci as a whole is a historical causal chain.
The first and last cases are obvious. The second case is
vague in its nature. It may not be clearly defined, especially
when doctors consider aftereffects, recurrence, metastasis
etc. We would like to cover such cases as states in which the
core causal chain becomes a historical causal chain while
the chain as a whole is ongoing. However, there is room to
investigate more-detailed classification of these cases.
3.4</p>
      </sec>
      <sec id="sec-3-4">
        <title>Identity tracking of a disease</title>
        <p>As a summary of the discussion made thus far, we discuss
examples of the life of an individual disease as a causal
chain of clinical disorders, as shown in Fig. 1. Note here
that we are not trying to predict the future state of a
particular disease of a particular patient, but to exemplify possible
changes of diseases in the real world represented as a causal
chain of clinical disorders in terms of its I-Rep identity and
type membership.</p>
        <p>We do not discuss cases where pseudo-simultaneous
causal links appear, since these should be dealt with in a
similar way to the case of historical causal links.
(1) A causal chain of clinical disorders, Ci, is born as a
strongly connected causal chain. At the same time, it
gains its instance identity (Iid_1). Ci can extend, branch,
etc. while keeping its identity. Before it establishes
itself as an instance of a particular disease type, its class
identity remains undetermined.
(2) When Ci extends and includes an instance of the core
causal chain of the disease diabetes as its partial chain,
it becomes an instance of diabetes and gets class
identity Cid_A for diabetes.
(3) Once Ci gets class identity for a disease type, it never
loses it until Ci disappears, and the class identity
remains unchanged independently of its extension and/or
branching because it still includes the instance of the
core causal chain of the disease.
(4) Ci can get more than one class identity, say, Cins_B for
diabetic retinopathy. Ci may extend further and cause
serious disorders/symptoms, which could lead to the
patient's death.
(5) After some changes of the disorders as well as the
termination of the ongoing process to become an event,
related causal links of Ci change from ongoing links to
historical links. Then, Ci changes from a strongly
connected causal chain to a weakly connected causal chain.
Nevertheless, Ci keeps its instance identity as an
ongoing causal chain.
(6) When a partial chain of Ci corresponding to the core
causal chain of diabetes and diabetic retinopathy
becomes a historical causal chain (the associated disorders
have disappeared), we might say that the patient is
cured of the disease. However, in some cases, a few
disorders/symptoms might still remain, and hence Ci
might still be ongoing. For example, some destroyed
nerve tissue might be left after that change.
(7) When all of the processes in Ci have terminated and
become events, and hence all of the causal links
become historical links, Ci becomes a historical causal
chain as a new individual causal chain, all of whose
nodes are events constituted of related past processes.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4 CONCLUSION</title>
      <p>
        We have discussed and proposed an ontological account of
the evolution of a disease as a causal chain of clinical
disorders. As far as the authors know, there is little activity
regarding ontology for the evolution of diseases in DOID and
OGMS, whose main focuses are definitions of related types.
Although OGMS defines “disease course”, it is dealt with as
a process, whereas we discussed it in terms of a causal chain
as a dependent continuant. We believe that, together with
our previous paper
        <xref ref-type="bibr" rid="ref6">(Mizoguchi et al., 2011)</xref>
        , we have made
a step toward a comprehensive ontological account of
diseases, covering their evolution. Other researchers
        <xref ref-type="bibr" rid="ref2">(Galton et
al., 2005)</xref>
        have discussed causal relations amongst events,
states, and process. Although our notions about the kinds of
causal links share some ideas with theirs, the definition of
identity of a causal chain is a unique feature of our theory.
      </p>
    </sec>
    <sec id="sec-5">
      <title>ACKNOWLEDGEMENTS</title>
      <p>A part of this research is supported by the Japan Society for
the Promotion of Science (JSPS) through its “Funding
Program for World-Leading Innovative R&amp;D on Science and
Technology (FIRST Program)."
(1)
(2)
(3)
(4)
(5)
(6)
(7)</p>
      <p>Historical causal chain</p>
      <p>Historical causal chain Iid_２</p>
      <p>…</p>
    </sec>
  </body>
  <back>
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