Visualizing the indefinable: three-dimensional complexity of 'infectious diseases'

Abstract

Background: The words 'infection' and 'inflammation' lack specific definitions. Here, such words are not defined. Instead, the ability to visualize host-microbial interactions was explored.

Methods: Leukocyte differential counts and four bacterial species (Staphylococcus aureus, Streptococcus dysgalactiae, Staphylococcus chromogenes, and Escherichia coli) were determined or isolated in a cross-sectional and randomized study conducted with 611 bovine milk samples. Two paradigms were evaluated: (i) the classic one, which measures non-structured (count or percent) data; and (ii) a method that, using complex data structures, detects and differentiates three-dimensional (3D) interactions among lymphocytes (L), macrophages (M), and neutrophils (N).

Results: Classic analyses failed to differentiate bacterial-positive (B+) from -negative (B-) observations: B- and B+ data overlapped, even when statistical significance was achieved. In contrast, the alternative approach showed distinct patterns, such as perpendicular data inflections, which discriminated microbial-negative/mononuclear cell-predominating (MCP) from microbial-positive/phagocyte-predominating (PP) subsets. Two PP subcategories were distinguished, as well as PP/culture-negative (false-negative) and MCP/culture-positive (false-positive) observations. In 3D space, MCP and PP subsets were perpendicular to one another, displaying ≥ 91% specificity or sensitivity. Findings supported five inferences: (i) disease is not always ruled out by negative bacterial tests; (ii) low total cell counts can coexist with high phagocyte percents; (iii) neither positive bacterial isolation nor high cell counts always coincide with PP profiles; (iv) statistical significance is not synonymous with discrimination; and (v) hidden relationships cannot be detected when simple (non-structured) data formats are used and statistical analyses are performed before data subsets are identified, but can be uncovered when complexity is investigated.

Conclusions: Pattern recognition-based assessments can detect host-microbial interactions usually unobserved. Such cutoff-free, confidence interval-free, gold standard-free approaches provide interpretable information on complex entities, such as 'infection' and 'inflammation', even without definitions. To investigate disease dynamics, combinations of observational and experimental longitudinal studies, on human and non-human infections, are recommended.

Fig 1. Discriminant diagnostic ability of cell counts.

Cell counts collected from 611bovine milk samples are reported. When CD18+ and neutrophil (N) counts were assessed and cultures were conducted, culture-negative observations predominated below (log) 5 CD18+ counts/ml; however, numerous culture-negative data points were also observed above such threshold (A). Culture-negative observations above (log) 5 (CD18+ 1000 counts/ml) corresponded to animals previously E. coli-positive. If prior information were considered, most observations above (log) 5 CD18 would become positive (B). Because animals previously E. coli-positive were treated with antibiotics and anti-inflammatory drugs (one month before the leukocyte profile was conducted) and in both instances the same bacteriological procedures were implemented, the discrepancy observed (high total cell counts, predominantly explained by high neutrophil counts, in 61 culture-negative samples of the later assessment) cannot be attributed to either the bacteriological procedures (the same, in both instances) or to the absence of antibiotic and anti-inflammatory treatment. When prior information was considered, CD18+ counts discriminated better that the SCC: CD18+ counts did not overlap between culture-negative and—positive observations but revealed a substantial overlapping when SCC were utilized (red box, C). Therefore, the use of counts, if considered alone (without considering prior information on culture results and treatments), is not diagnostic: counts would display the pattern shown in A.

Fig 2. Discriminant diagnostic ability of simple or low-complexity indicators.

Neither molecular (cell-surface marker-related) nor cellular indicators (expressed as leukocyte percentages) distinguished culture-negative from-positive observations (A, B). While median values reached statistical significance (blue circles, P<0.03, Mann-Whitney test, A, B), overlapping leukocyte data distributions were observed between the culture-negative and -positive groups (blue boxes, A, B). Such lack of discrimination remained when low-complexity indicators (ratios that measured interactions involving two or more cell types) were considered, regardless of current information on bacterial status (C) or prior information (i.e., assuming as culture-positive all previously E. coli-positive animals, D).

Fig 3. Discriminant diagnostic ability of simple or low-complexity indicators measured in 3D space.

Cell count-based analyses, even when 3D patterns were considered, did not discriminate: CD18+ counts, together with the N/L and MC/N ratios, failed to distinguish immuno-microbial subsets when prior (A) or current (B) information was considered.

Fig 4. Discriminant diagnostic ability of complex, 3D data structures (emergence I).

When dimensionless indicators were built and explored in three-dimensional (3D) space, distinct (perpendicular) data inflections (not previously observed) distinguished several subsets, demonstrating emergence (A). Emergent patterns were also found when prior information was considered (animals previously E. coli—positive were regarded to be positive, B). When prior information was considered, four perpendicular data inflections differentiated four subsets, characterized by: (i) culture-negative only, (ii) predominantly culture-negative, (iii) culture-positive only, and (iv) predominantly culture-positive observations (C).

Fig 5. Data subset-validation, based on microbial-immunological data.

Data subsets identified on the bases of dimensionless indicators (hypothetical indices of unknown biological validity) were evaluated with biologically explicit data. When prior information was considered, the culture-negative subsets showed the highest L %, while the culture-positive subset exhibited the lowest L%, and the highest N% (A). A similar pattern was observed when relationships involving monocytes and lymphocytes were analyzed; for instance, (i) the monocyte/lymphocyte (M/L) ratio distinguished the culture-negative, high L% subset from all other subsets; (ii) a composite index that included a product and a ratio (the [M*N]/ L) differentiated both culture-negative from both culture-positive subsets, and (iii) a double interaction (the [M/N] / [N]L] ratio) separated the low L%/high N%/culture-positive from all other subsets (lines, B).

Fig 6. Detection and evaluation of observations suspected to be false (emergence II)

Emergence was also expressed as observations suspected to be false. Such detection was elicited by dimensionless indicators (hypothetical indices derived from products or ratios of leukocyte data, which assess numerous relationships, e.g., BAS, AM, BAP). Dimensionless indicators detected two subsets of culture-negative data (A). Because culture-negative data subsets were separated by the culture-positive cluster, one subset was suspected to be false-negative (FN culture results, B). A similar contrast led to suspect that one culture-positive observation was a false-positive (FP): it was located within the culture-negative cluster but far from the location of culture-positives (B). Such inferences did not depend on the set of dimensionless indicators analyzed or whether current or prior information was considered: when a separate set of indicators was analyzed, it showed similar patterns (C) and, when only current information was considered, patterns remained, differing only in the number of FNs observed, which increased (red polygon, D).

Fig 7. Pattern recognition-based differentiation.

When hypothetical patterns were evaluated, four biologically different data subsets emerged when prior information was considered (A), which were characterized as: (i) culture-negative/phagocyte predominant (a subset displaying the lowest L% and high N%, i.e., the FN subset); (ii) culture-positive/mononuclear cell-predominant (a subset composed of only one observation, displaying high L% and low N%, i.e., the FP subset); (iii) culture-negative/mononuclear cell-predominant (which displayed high L% and low N%); and (iv) culture-positive/phagocyte predominant (which displayed low L% and high N%). Similar biological patterns were observed when only current information was analyzed (B).

Fig 8. Detection and evaluation of microbial subsets (emergence III).

When only culture-positive data were analyzed (including observations collected from cows previously E. coli-positive), dimensionless indicators distinguished, with perpendicular data inflections, three non-overlapping subsets (A). One of such subsets was devoid of S. aureus+ observations, but predominantly composed of observations collected from previously E. coli-positive animals. When validated, such subset revealed higher M/L ratio values than the remaining subsets (B). The two other subsets differed in their L % values (B).

Fig 9. Detection of immuno-microbial subsets (emergence IV).

When both culture-negative and -positive patterns were explored with dimensionless indicators, a perpendicular data inflection distinguished two subsets predominantly composed of either culture-positive or—negative observations (vertical and horizontal subsets, respectively A). When only the data symbols corresponding to S. chromogenes and (previously) E. coli-positive observations were emphasized, most S. chromogenes-positive observations were found within the horizontal subset—the same subset otherwise revealing culture-negative data points (B), while most observations corresponding to animals previously E. coli-positive were located within the vertical subset (B).

Fig 10. Evaluation of immuno-microbial subsets.

When the subsets reported in Fig 9 were explored with leukocyte data, the horizontal subset revealed significantly higher L%, regardless of whether S. chromogenes-positive only, (previously) E. coli-positive only, or culture-negative only data were assessed (A-C). Similarly, the vertical subset displayed significantly higher N % and phagocyte (P or N+M) percentages than the horizontal subset (P<0.001, Mann-Whitney test). Yet, statistical significance did not result in discrimination: overlapping data distributions were found between subsets, in all assessments (A-C).

Fig 11. Detection and evaluation of new inflammatory responses (emergence V).

Robustness and redundancy were documented: patterns similar to those reported in Fig 9 were obtained when different indicators were utilized, which detected one horizontal subset (mainly composed of culture-negative observations) and one vertical subset (mainly composed of culture-positive observations, A, B). The median L, N, and phagocyte percents of such subsets differed, reaching statistical significance (blue circles, P<0.001, Mann-Whiney test, C).

Fig 12. Additional demonstrations of emergence.

Non-overlapping leukocyte data distributions differentiated a third (‘other’) subset from the ‘horizontal’ and ‘vertical’ subsets reported in Fig 11 (broken lines, A). However, when the leukocyte variables were assessed with a 3D plot, observations of the ‘other’ subset overlapped with the remaining subsets (B). That limitation, however, could be overcome if the data were structured as a single line of observations (as shown by an additional set of dimensionless indicators, C) and temporal data were available. When two or more longitudinal observations from the same individual are analyzed within a single (on data point-wide) line, prognosis (and, therefore, diagnosis) can be unambiguously determined, even in the absence of distinct patterns: regardless of any numerical value, arrows connecting pairs of data points can indicate where the most recent data point is coming from/going to, indicating whether such observation approaches the disease-negative or—positive pole of the line.