Multi-directional data ambiguity.

<p>Ambiguity was also expressed when temporal data directionality was evaluated: arrows that connected pairs of consecutive observations displayed different temporal directionality even when they exhibited similar numerical information (boxes, <b>a-d</b>). Such pattern indicated that some dynamic changes took place at temporal scales smaller than the one utilized. Therefore, the 3D, single line of data points defined by the L%, the phagocyte/lymphocyte (P/L) and the mononuclear cell/neutrophil (MC/N) ratios failed to discriminate dynamics: some observations with similar numerical values, which expressed different biological conditions, were not distinguished.</p

Longitudinal relationships in septic humans.

<p>Spatial patterns differentiated three data subsets among 7 septic patients analyzed with dimensionless indicators: (i) a vertical subset, (ii) a right subset, and (iii) the remaining observation, or ‘left’ subset (<b>a</b>). Higher M% and M/N ratio values distinguished the ‘right’ subset from the remaining data points, while higher L% and lower N/L ratio values differentiated the ‘left’ data point from the remaining observations (horizontal lines, <b>b</b>). Discrimination further improved when temporal and multidirectional data flows were assessed: several numerically similar observations displayed different directionalities (<b>c</b>). While not all observations could be analyzed statistically because some patterns included only one or two data point(s), the spatial-temporal analysis detected non-overlapping M% and M/N ratio distributions that differentiated by the ‘right’ subset with a left-to-right directional flow from the ‘right’ subset with a right-to-left flow (boxes, <b>d</b>). Non-numerical information (arrows) also distinguished ‘bottom/right-to-left’ from ‘bottom/left-to-right’ observations (boxes, <b>d</b>).</p

Canine leukocyte spatial-temporal relationships.

<p>When dimensionless indicators (DIs) were utilized and three-dimensional (3D) patterns were considered, canine data revealed two (‘left’ and ‘right’) subsets (<b>a, b</b>). Spatial data subsets exhibited non-overlapping lymphocyte percentages and N/L and M/L ratios (<b>c</b>). When temporal data directionality was considered, arrows expressing different directionality (<b>d</b>) increased discrimination: 4D (spatial-temporal) patterns distinguished five subsets (in addition to the first observation) and non-overlapping N% differentiated the ‘right side/left-to-right flow’ observations from the first one (horizontal lines indicate non-overlapping data subsets, <b>e</b>).</p

Classic analysis of immuno-microbial data.

<p>The classic method did not discriminate: leukocyte data distributions overlapped among different biological conditions, such as fever-positive and fever-negative individuals or individuals that recovered or did not recover from infections (blue boxes, <b>a-d</b>). The analysis of temporal data did not improve discrimination (<b>e-h</b>). Four studies were evaluated, including: (i) one dog [<b>a, e</b>], (ii) one human infected by MSSA [<b>b, f</b>]; (iii) one human HIV case, with a secondary MRSA infection [<b>c, g</b>]), and (iv) seven humans presenting with sepsis [<b>d, h</b>]).</p

Human leukocyte spatial-temporal (MSSA/hip implant-related) relationships.

<p>Three data subsets were identified when the MSSA/hip implant human case was explored with dimensionless indicators (<b>a</b>). All data points associated with antibiotic therapy were clustered within one subset (green polygon, <b>b</b>), even though antibiotics were administered in two non-consecutive periods (green boxes, <b>b</b>). The ‘vertical’ subset exhibited statistically significantly higher M/L values than the ‘bottom, left’ subset (<b>c</b>). When arrows that connected pairs of consecutive observations were assessed, three ‘bottom-up’ and two ‘top-down’ observations were detected (red and blue arrows, respectively, <b>d</b>). Changes in directionality were detected within one day: at days 159/160, one ‘bottom-up’ data point was followed by one ‘top-down’ observation (<b>d</b>). Spatial-temporal patterns (temporal data flows) differentiated four data subsets (<b>e</b>). The use of arrows distinguished ‘vertical, bottom-up’ from ‘vertical, top-down’ observations (horizontal line, <b>e</b>).</p

Human leukocyte spatial-temporal (HIV/MRSA-related) relationships.

<p>Viral load values of the HIV+ patient were not informative: they exhibited more than 1000-fold changes among clinically stable observations (arrows indicating green symbols, <b>a</b>). In contrast, dimensionless indicators (DIs) differentiated two spatial (‘vertical’ and ‘horizontal’) subsets, which included two MRSA isolations within the vertical subset (set I, <b>b</b>), while all bacteria-negative data points were horizontally located (set II, <b>b</b>). A second set of DIs separated the ‘vertical’ data points into two sub-subsets: (i) the ‘top vertical’ and (ii) the ‘left horizontal’ groups, which did not overlap with the remaining (‘right horizontal’) data points (<b>c</b>). At least the L% and the M/N ratio distinguished the three spatial data subsets (<b>d</b>). More information was extracted when arrows that connected pairs of consecutive observations were measured (<b>e, f</b>). The assessment of <i>spatial</i>-<i>temporal data directionality</i> differentiated, twice, changes that took place within one day (days 118–119; and 135–136; arrows, <b>e, f</b>). While the spatial (3D) analysis detected only two or three data subsets (<b>b, c</b>), the spatial-temporal (4D) assessment distinguished five data subsets (<b>g</b>). For instance, the L%, M%, N/L, and M/N ratios differentiated ‘top vertical’ from the remaining observations (blue horizontal lines, <b>g</b>). The L% and N/L ratio also distinguished the ‘left/top-down’ observation from the ‘left/bottom-up’ observations (green horizontal lines, <b>g</b>). Furthermore, the N/L ratio discriminated the ‘right horizontal’ from the remaining subsets (red horizontal line, <b>g</b>). Some leukocyte profiles were associated with antibiotic therapy, for instance, higher M/L values were observed after antibiotics were prescribed, even after antibiotic therapy was discontinued (<b>h</b>).</p

Spatial-temporal and personalized data analysis.

<p>When the leukocyte data of five septic patients tested daily over three days were analyzed on personalized bases, several <i>temporal patterns</i> were observed (the data of the two remaining septic patients were not analyzed because they were tested only two days). At least <i>two directionalities</i> were differentiated: (i) data flows that came from the center or left and, over time, moved to the right (‘from left-to-right’, <b>a, b</b>); and (ii) responses that followed the opposite directionality (<b>c-e)</b>. These responses were induced by: <i>A</i>. <i>baumannii</i> (<b>a</b>), <i>E</i>. <i>faecalis</i> (<b>b</b>), <i>S</i>. <i>liquefaciens</i> (<b>c</b>), and <i>E</i>. <i>coli</i> (<b>d, e</b>).</p

Spatial analysis of low-complexity indicators.

<p>Even in its simplest version–which did not utilize dimensionless indicators–, the 4D method was more informative than the non-structured analysis reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159001#pone.0159001.g001" target="_blank">Fig 1</a>. When low-complexity indicators that measured interactions involving two or more cell types were spatially analyzed (the phagocyte/lymphocyte [P/L], the mononuclear cell/neutrophil [MC/N], and the neutrophil/lymphocyte [N/L] ratios), two subsets of septic patients-related data, perpendicular to one another, were detected (<b>a</b>). The spatial analysis exhibited a single (one data point-wide) line of observations (<b>a</b>). When leukocyte data were partitioned according to the spatial patterns, several comparisons reached statistical significance ((<b>b)</b> and Table J in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159001#pone.0159001.s001" target="_blank">S1 File</a>).</p

Spatial-temporal data ambiguity.

<p>Ambiguity (numerically similar observations that expressed different biological conditions) was also documented when three-dimensional (3D) relationships were explored and single (one data point-wide) lines of observations were utilized to explore longitudinal data. <i>Ambiguity</i> exhibited <i>spatial-temporal relativity</i>: data points that corresponded to recent infections occupied more space and/or exhibited broader data ranges than observations not associated with recent infections and/or recorded over longer periods (<b>a-d</b>). For instance, observations recorded within three days (red arrow, <b>a</b>) displayed a broader data range than observations collected over the following four months (blue oval, <b>a</b>). Consequently, no numerical value of leukocyte data, per se, could distinguish recent from older or protracted responses.</p