of high validity; the tracking trustworthiness of the validated complete paths exceeds 95%. A second important measure for cell tracking algorithms are mitosis detection rates. The initial adjacency matrix (path fragments) contains 865 correct mitoses (43%). This number can be increased to 1114 (55%) using our dedicated mitosis detector in conjunction with the validation algorithm (table 2). The trustworthiness of the validated mitosis detection amounts to 86.8% (calculated analogous to tracking trustworthiness as #correct mitoses ). Errors occur to a large part due to complex #detected mitoses scenarios of simultaneously occurring merged cell events / mitoses. Naive tracking, i.e. tracking without validation, yields large numbers of false mitotic events (mainly merged cells, which depart later, thereby producing a false Y-shape); the trustworthi- ness of these unvalidated mitoses lies below 50%. Evaluation of cell tracking (III): Genealogical assignments. The degree of relation between cells also turns out to be a rigorous parameter to evaluate tracking algorithms. If two cells are related to one another, they share a common ancestor at some point; the degree of relation can then be defined as the number of mitoses, by which the two cells are connected (see figure 8). If two cells are not related at all, their degree of relation is zero. This definition can be used to evaluate the fraction of correct genealogical trees. False rejection errors are those relations, which have not been detected (i.e. got erroneously the degree zero assigned to); false acceptance errors are those relations to which a wrong degree of relation (.0) has been assigned. Both errors are expressed as a fraction of the total number of relations found in reference data set A. Figure 8 displays the false rejection rate and false acceptance rate for the genealogical assignments in each frame. Since the validation algorithm rejects a high number of paths, the number of cells that could be automatically related to one another is rather small: the last frame of reference dataset A contains 2343 cells which are related through 7828 genealogical assignments, where our automated algorithm detects 600 assignments only (7.7% of all possible relations in the last frame). However, the trustworthiness of these genealogic relations is extremely high (96.3%). The low number of correct detected assignments is a result of the exponential error propagation within the binary lineage tree structures (cf. fig. 8c). Automated Tracking Turns Cell Culture into Numbers IV) A parameterized cell culture: Automated extraction of biological parameters from cell tracking data In this section we demonstrate how validated cell tracking can be used to automatically derive a multitude of biologically important measures, some of which are not obtainable by other methods. Apart from conventional characteristics, like growth curves and confluency, we also introduce more complex figures, like life time distributions, and the distribution of symmetric and asymmetric cell divisions. Still, we only present a fraction of the information about cell behaviour, which can be gained from validated cell tracking; for instance, we will not touch upon the large field of migration analysis or conditional measures (e.g. life times as a function of local cell densities etc.). Proliferation curve. Frequently required characteristics of in vitro cell cultures are proliferation curves, i.e. the progression of the overall cell number. This measure can be easily calculated from time lapse data, provided the observed area is representative for the whole growth area (culture dish). Figure 9 displays the proliferation curve for the adult stem cell population of reference set A. The typical sigmoidal shape has been recorded almost completely; parts of the initial lag phase and the final contact inhibition phase can be seen. Automatic cell detection yields growth curves with an overall error below 5%, a precision, which is currently unattainable with any other non-invasive method (e.g. impedance based measurements as described by Ke et. al [31]). The exponential part of the proliferation curve has been recorded en detail; it corresponds well with the number of detected mitoses (bar graph in figure 9). From these data, the probability for each cell to divide within a given time span can be calculated as #Mitoses (red curve in fig. 9, time span has been chosen as #Cell 2hours); it is not evenly distributed over time and spans from less than 0.4 to more than 1.6 percent. Cell area/confluency. Another basic cell culture charac- teristics which can be readily extracted from cell detection data, is the mean cell area as a function of cell density. Figure 10 shows that in case of contact inhibited adult stem cells, the average cell area scales inversely linear with the cell density. Such curves are particularly useful for impedance based observation systems in automated cell cultures for e.g. cell based screening systems [32,33]. The confluency (red curve) is calculated as the sum of all cell mask areas divided by the total observed area. Note, that this measure will always be significantly smaller than the really occupied fraction of Figure 8. Genealogical assignments. (A) shows a cell mask and its genealogical tree with an example for the degree of relationship. (B) displays the trustworthiness of the genealogic assignments for each frame as false acceptance (FAR) and false rejection rate (FRR). (C)illustrates the exponential error propagation within binary tree structures. It is apparent that a very small number of errors can lead to a large number of false/ unsure genealogical assignments doi:10.1371/journal.pone.0027315.g008 PLoS ONE | www.plosone.org 9 November 2011 | Volume 6 | Issue 11 | e27315