gms | German Medical Science

Though being characterized by a high degree of domain heterogeneity controlled medical vocabularies (such as the UMLS, SNOMED, or FMA [Ref. 1]) use a bipartite hierarchical structure, with two kinds of partial orders, viz.taxonomies (characterized by the is-a relation, which associates specific with general concepts such as Femur is-a Bone), and partonomies (associating parts and wholes by mereological relations, such as part-of and has-part). While reasoning in taxonomic hierarchies is quite well understood, we lack an equal form of consensus for part/whole-related reasoning (cf. [Ref. 2] for a survey). For instance, it remains quite unclear how to interpret a mereological relation which holds between two concept classes, e.g., Neck-of-Femur part-of Femur, or Bone has-part Calcium (e.g., does part-of/has-part hold for all concrete instances of these concept classes, or not?). The embedding of part/whole-related reasoning into more general mereological reasoning, as well as the interactions between mereological and topological reasoning (so-called mereotopological reasoning), i.e., the relation between parts and wholes and the space they occupy, are pressing and difficult issues from the perspective of knowledge representation [Ref. 3]. Still the phenomenon of property inheritance can be found in mereotopological hierarchies as well. We naturally classify a "fracture of the neck of the femur'' as being a "fracture of the femur'', simply because the neck of the femur is a part of the femur.

Up until now, none of the present models of biological structure has been able to convey an ontologically founded, semantically precise and uncontroversial account of both taxonomy and partonomy [Ref. 4]. This poses severe problems for inference engines, in which both reasoning patterns have to be combined. In this paper, we sketch an approach to modeling parthood in biomedical structure in terms of spatial inclusion. As we subscribe to a completely topological account of mereology, it is likely to get a much better agreement, as topological inclusion is based upon strictly geometric criteria.

In our approach, we completely abandon the mereological relations has-part and part-of and rather treat parthood as spatial inclusion, using loc (has-location) and its inverse relation inc (includes), with loc and inc both being transitive and antisymmetric relations (in the same way as the relations has-part and part-of share these algebraic properties). Spatial inclusion has a strict point-set theoretic semantics, and we assume the extension of spatially relevant solid objects to include the objects' hollow spaces, i.e. those spaces within the convex hull of the object which can be considered a "fillable discontinuity of the object's surface'' [Ref. 3]. Otherwise, all space regions located, e.g., within the blood vessels of an organ, or within the bronchi of the lung would be located in the exterior space-a stipulation which fundamentally violates common conceptualizations in the biomedical domain. It is, however, not plausible to consider the complete convex hull of a biomedical object as spatially coinciding with this object. Under this assumption a whole body would nearly coincide with the circulatory system (since its capillaries permeate all body parts), which is not acceptable at all.

For a biomedical concept A, we introduce two reificator nodes, A _inc stands for the relation inc, while A _loc stands for the relation loc (τ stands for the relation instance-of which represents concept class membership):

We will now illustrate how the proposed formalism is capable of accounting for various forms of mereotopological inferences:

''A nephritis is an inflammation located at a kidney as a whole or at any of those objects which are necessarily located in the kidney.''

Since Kidney _loc subsumes, e.g., Glomerulum _loc (according to the encoding principles for compositional taxonomic hierarchies), Glomerulonephritis is correctly subsumed by Nephritis, given:

and Is-A(Glomerulum _loc , Kidney _loc ). The relation loc is used both for the spatial inclusion of Glomerulum into Kidney and for the relation between the process Glomerulonephritis and Glomerulum.

"Insulin production is located in the pancreatic beta cells. Beta cells are included in Langerhans Islets, which are included in the pancreas.''

From Is-A(InsulinProduction, BetaCells _loc ), Is-A(BetaCells _loc , LangerhansIslets _loc ) and Is-A(LangerhansIslets _loc , Pancreas _loc ), we infer that InsulinProduction is located at LangerhansIslets, as well as at the Pancreas.

"Amputation of a foot is an amputation which targets a foot and is located at a foot.''

"Amputation at a foot is an amputation which is located at a foot.''

The relation targets addresses a spatial structure, not in "neutral" terms of location where a process takes places, but rather as an object which is modified in the course of the process. Given Is-A(Toe _loc , Foot _loc ), as a consequence, AmputationAtToe is an AmputationAtFoot, but not an AmputationOfFoot, because the target role does not propagate. Note the subtle but important semantic distinction between "at'' (location) and "of'' (target).

The already discussed distinction in propagation patterns between Nephritis and Gastroenteritis can be explained by the same terms. Whilst Nephritis is an inflammation "at'', Gastroenteritis is not only an inflammation "at'' but also an inflammation "of''. Therefore, GlomerulonephritisIs-A Nephritis, whereas Gastroenteritis does not subsume Appendicitis. This way, specialized roles such as inflammation-of, fracture-of, or amputation-of can easily be reduced to a small set of universal thematic roles, such as targets and loc.

This paper covers two major issues. The first one is concerned with ontological considerations underlying part-whole relations. Substituting mereological relations by strict topological inclusion has the advantage of eliminating the difficult and controversial delimitation between the notions of spatial inclusion and generic part-hood. The second issue has to do with parsimony of the formalization of these locational relations. The relation loc is used not only to express the spatial relationships between physical objects and spaces, but also between processes and physically defined structures. In the same way, inc relates not only physical objects, but also physical objects with their inherent functions. Thus we do not need additional formal language devices in order to obtain the inferences (propagation of properties across compositional hierarchies) needed in such a reasoning framework. This way, we combine ontological clarity with formal simplicity. Reducing various types of inferences in compositional hierarchies to one single taxonomic subsumption computation step parallels-on the reasoning level-our claims for formal simplicity with respect to the definition of suitable relations. From a practical perspective, our reductionist approach allows us to reuse off-the-shelf terminological reasoning engines (such as LOOM, FaCT, and RACER). The capability of robust inference engines to deal with massive amounts of knowledge is a prerequisite for any serious application concern in the biomedical field, as we have demonstrated by assembling huge knowledge bases using description logics [Ref. 5], [Ref. 6].