Longitudinal canine and human leukocyte and microbial data

Three sets of data on human infections were analyzed. The first set included seven septicpatients with no history of chronic non-infectious diseases, who were infected by various bacteria and met at least three systemic inflammatory response syndrome (SIRS) criteria [32]: body temperature > 38°C, heart rate > 90 beats/minute, tachypnea or hyperventilation (>20 breaths/minute or P_ACO2 < 32 mm Hg at sea level), and white blood cell count ≥ 12000 or ≤ 4000/μl. Blood leukocyte percentagess were determined, over three days, since hospital admission (Table A in S1 File).

Human blood leukocytes were also collected from two non-septic but infected patients (Tables B, C in S1 File). The first case was a 49-year old man previously diagnosed with human immunodeficiency virus (HIV), who presented with ~ 1% CD4+ T cells and, over four months, experienced methicillin-resistant and -sensitive Staphylococcus aureus (MRSA and MSSA, respectively) mediated infections. The second case was a 60-year old man that received a hip implant who, over seven months, had recurrent MSSA infections [33, 34].

To elucidate whether the 4D method could be applied to non-human species, blood leukocytes and bacteriological tests were explored in one dog (Table D in S1 File). Over 9 months, the animal was spontaneously infected, first, by the opportunistic Enterobacter cloacae [35] and, later, by Staphylococcus pseudointermedius (a common cause of skin infections [36]).

Laboratory methods

Identification and quantification of human leukocytes (lymphocytes [L], neutrophils [N] and monocytes [M]) were conducted with an automated hematology analyzer (Coulter LH 780 Analyzer, Beckman Coulter International SA, Nyon, Switzerland). Blood culture was performed with the automated Bactec 9249 instrument (Becton Dickinson, New Jersey, USA). The pathogens isolated from blood were identified and tested for their antimicrobial susceptibility with the automated microbiology system Phoenix 100 (Becton Dickinson, New Jersey, USA). Similar techniques were utilized to conduct canine studies in a veterinary hospital.

Methods

These studies were approved by the Scientific Committee of the Thriasio Hospital, Magoula, Greece (protocol 57/16-02-2015) and the Human Research Review and Institutional Animal Care and Use (IACUC) committees of the University of New Mexico (protocols numbers 13–463 and 13-101022-T-HSC). Informed consent was not provided because this study was conceived after patients were discharged or died. Patient records were de-identified prior to analysis.

To diminish data variability, a single (one data-point wide) line of observations was created–a structure that eliminates variability from all dimensions except the one defined by the single line. For example, a bi-dimensional plot that measures, in one axis, the phagocyte/ lymphocyte ratio (the sum of M and N percents divided over the L percentage) and, in the other axis, the L%, creates a single line of data points [37].

Three-dimensional (3D) plots were used to extract more information. The addition of depth, to height and width, may uncover data patterns that uni- or bi-dimensional plots cannot reveal.

To estimate complexity, dimensionless indicators were utilized [9, 10, 38, 39], consisting of combinations of counts, percentages, ratios, or products derived from primary variables. When the percents of L, M, and N are used in an equation that includes many interactions (e.g., the {[M/L * N/M] / [N/L * L/M]) over ([M+L/N] * [L+N/M] / [N+M]/L * [M/N]}), a dimensionless number is created: the number produced does not describe any known biological structure.

Dimensionless indicators (DI) can capture many levels of complexity. For instance, in the DI described above, one level of complexity (level I) is estimated by each ratio of the first element or ‘numerator’ (M/L, N/M, N/L, and L/M). Two more interactions (of level II complexity) are measured by each product (M/L * N/M, N/L * L/M). Complexity level III is evaluated by the composite ratio of the numerator ([M/L * N/M] / [N/L * L/M]). Because the second element (‘denominator’) has the same structure, the number of interactions doubles when the denominator is calculated. An additional interaction (complexity level IV) is generated when the numerator and the denominator are simultaneously analyzed. When three DIs are assessed in 3D space, the number of interactions increases three times and one more interaction (level V complexity) is produced when the overall (3D) relationship is plotted. Thus, the example shown above covers at least (4 x 2 +1 x 2 +1 x 3 +1) 58 interactions and five levels of complexity.

Furthermore, a sixth level of complexity was considered when dynamics were addressed [18]. Using non-numerical indicators (arrows that connected pairs of consecutive observations), temporal directionality was investigated. Such arrows detected multi-directional data flows.

This design revealed distinct 3D/4D patterns, which distinguished data subsets. The validity of each subset was determined by analyzing microbial test results and/or leukocyte data.

Data analysis

Because all DIs–except a few indicators (N/L, M/N, M/L, N*L, M*N and M*L)–, included the same data contents, DI were not described but identified with descriptors written in italics (e. g., AAR). Because DIs expressed hypothetical interactions, they were not biologically observable and, statistically, they were neither interpretable nor predictable [40]. However, after distinct spatial patterns (such as perpendicular data inflections) were detected, data subsets were differentiated and statistical comparisons among subsets were justified. Because differences among data subsets were based on their immune profiles, validations were biologically grounded. Dimensionless indicators were generated by a proprietary algorithm [9]. Leukocyte percents, products, or ratios were compared with the Mann-Whitney test, which tested whether medians differed across data subsets (Tables E-H in S1 File). Plots and statistical analyses were created or conducted with Minitab 17^® (State College, PA, USA). The data described in the Table I in S1 File can be analyzed statistically with the procedure reported in the footnote of Table J in S1 File.

Methodological considerations

The detection of hidden data interactions (i.e., emergent patterns) demonstrated that 4D approaches can extract more information than alternatives. Because validity is questionable when hidden information is not ruled out, findings supported the validity of the combinatorial approach [41, 42].

In addition, spatial-temporal relativity was documented [15]. Relativity was associated with ambiguous (non-interpretable) data. When ambiguity occurs, numerical procedures, such as statistical analyses and mathematical modeling, cannot be conducted [16]. Data ambiguity -here observed in infections- has also been reported in neurology [16].

To prevent ambiguity, a method was designed to reduce noise, detect complexity, and capture anti-microbial immune dynamics (temporal changes). To reduce variability, the data were structured as single (one data point-wide) lines of data points. This strategy was combined with the analysis of complexity and temporal data directionality. Because no uni- or bi-dimensional plot can reveal 3D/4D patterns, to detect complexity, the circularity of 3D data interactions was assessed [9, 10, 31]. Arrows that expressed where each data point came from/went to measured temporal data flows, even when they occurred within brief timeframes.

The use of arrows that connected pairs of consecutive observations met the definition proposed by Nielsen and Jorgensen: ‘orientors’ are indicators that identify short-term, immediate directionality (qualitative information) but lack long-term predictability [20]. Yet, the 4D method exceeded such criteria: it analyzed qualitative and quantitative data.

In agreement with earlier reports, distinct patterns emerged when, over time, one indicator changed in larger (or smaller) magnitudes than the remaining indicators [43]. Because the 4D method demonstrated multi-directional data flows, the central assumption of reductionist methods (the presence of only uni-directional flows) was rejected [22].

The impact of the 3D/4D combinatorial approach was summarized in the contrast shown by Figs 2d, 8a and 8b: while the same data were analyzed with the same variables (and 3D plots were used in both analyses), no discrimination (ambiguity) was revealed in Fig 2d, but distinct (and informative) patterns were conveyed by Fig 8a and 8b. The difference was due to a double strategy, implemented in Fig 8a and 8b: (i) the construction and measurement of interactions that involved two or more cell types (not isolated variables, such as the lymphocyte percent [measured in Fig 2d]), and (ii) the observation of perpendicular patterns–a procedure that separates subsets that differ in one or more immunological function(s) and, given their non-overlapping distributions, results in statistically significant differences (Fig 8b). This means that statistical analysis should be conducted after (not before) data subsets are distinguished [9].

Clinical applications and extraction of new information

The 4D approach partitioned the data into subsets [44]. Applications include: (i) earlier detection of infection, (ii) identification of subsets that differ in immune profiles (pathogenesis-based diagnostics), (iii) selection and evaluation of therapies, and (iv) prevention of ambiguity.

For instance, canine leukocyte patterns detected inflammation even when bacteriological tests were negative (open circle with a cross embedded, Fig 4d). Such information enables clinicians to intervene and/or prognosticate, earlier.

Higher M/L values were observed in the MSSA recurrent infection, after antibiotics were prescribed for the first time (Fig 5c). Such profile was consistent with reports that indicate monocytes increase earlier (approximately 3 days after initiation of an immune response) than lymphocytes [45]. However, because high M/L values were also observed after cessation of antibiotic treatments (in recurrent infections), the 4D method may also be used to explore topics of major medical interest: antibiotic-immunological-bacterial-temporal interactions [46].

New (and in vivo) methods are needed to reduce lengthy procedures and other limitations associated with in vitro perspectives. For example, antibiotic susceptibility tests cannot measure tissue environmental conditions, such as hypoxia [47]. While classic methods have focused on the microbe and used in vitro (or, when animal models are used, in vivo) approaches, such methods are error-prone because they (i) do not assess poly-microbial infections, (ii) ignore the fact that animal models do not truly represent human infection conditions, (iii) do not account for differences across individuals, and (iv) do not measure immune dynamics [48–52].

Earlier and more informative methods are also needed to evaluate antibiotics [53, 54]. Such new methods could consider (i) the predominant cell type(s) involved in some infections and (ii) the fact that some antibiotics synergize with (or inhibit) specific cell types [55–58]. For instance, immune responses against Salmonella species differ: those against typhoid fever-causing agents are monocyte-mediated, while responses against gastroenteritis-causing serovars are neutrophil-mediated [58]. In Pseudomonas aeruginosa-related infections, amikacin is synergistic with neutrophils but ciprofloxacin is not [59]. In spite of such reports, no method is available to explore antibiotic-immunologic-microbial-temporal relationships with earlier, in vivo inputs.

Changes in directional flows (observed even within a few hours) demonstrated earlier evaluations of antibiotic therapy are feasible and data ambiguity may be prevented. For example, the temporal flows of human leukocyte data demonstrated (three times) that antimicrobial interventions may interact not only with the microbe but also with the immune system (days 160–161 [hip implant/MSSA case, Fig 5d], and days 119–120 and 135–146 [HIV case, Fig 6e and 6f]).

This evaluation–conducted as a part of a process aimed at exploring the properties of infectious disease data–may, later, be implemented by clinicians that use a clinician-friendly software package. While such a package has not yet been developed (and, therefore, this approach is not ready for application in clinical settings), a simpler but informative approximation is already feasible: when data points are located within the range characterized by high P/L and N/L, as well as low MC/N values, an infection cannot be ruled out (red symbols, Fig 8a); in contrast, when observations exhibit high MC/N and low P/L and N/L values, recovery is likely (blue symbols, Fig 8a). When such data subsets are perpendicular to one another, they tend to differ at statistical significant levels, as shown here (Tables I, J in S1 File). When personalized data are considered, the presence or absence of data inflections may support or modify earlier decisions. For instance, when a data inflection is observed within one day, it may be suspected that such change is not a random effect and, consequently, earlier (diagnostic- and/or treatment-related) decisions may be defensible (Fig 9a). In contrast, when temporal data flows do not change in directionality, it may be suspected that earlier decisions were not effective and, consequently, they might be reevaluated (Fig 9e). When only a minor change in the data flow is observed (Fig 9b), an additional test (conducted a few hours later) and/or pattern amplification strategies (e.g., reducing the scale of the axis of interest) may improve data visualization.

While no data representation can replace clinical expertise, data visualizations that integrate several leukocyte data combinations may facilitate earlier interpretations. When–after a therapy is prescribed in response to a neutrophil-predominant profile, i. e., one characterized by a high N/L value–a shift toward a mononuclear cell-predominant profile is observed, the hypothesis that the infection is progressing toward recovery is supported. In contrast, when a neutrophil-predominant profile remains even after therapy, a revision of the earlier decision may be considered. Because directionality-based analyses do not require population-based metrics, 4D methods may apply to personalized medicine–where new methods are needed [18, 44].

The 4D analysis of infectious disease-related data properties–including dynamics and complexity–can prevent ambiguity and foster data partitioning into subsets, facilitating earlier, personalized, explanatory (immunology-based) inferences. To further explore such properties, prospective studies are recommended.