The results of this study are valid for the research period and the number of patients who fulfill the inclusion criteria. These inclusion criteria and low prevalence of cancer children in the province of Santiago de Cuba may explain why the sample size of this study is lower. In addition, the race of cancer children in this study is the same than the one reported in  because the ethnography of Santiago de Cuba population is characterized by a mixture of several race ethnicities (European whites, aboriginal Indians and African blacks). Nevertheless, the gender ratio of cancer children is different to that reported in . This difference may be explained because gender ratio can be controlled/fixed in a population study, but not in a study with cancer patients. Gender ratio of cancer patients depends on disease prevalence for gender and age group, and inclusion, exclusion and interruption criteria.
On the other hand, results of this study confirm that acute lymphoid leukemia, non-Hodgkin lymphoma and cancer of the central nervous system are most frequently observed in untreated pediatric patients, as in [2,3,4, 38,39,40,41]. Additionally, this study confirms that acute lymphoid leukemia is more frequent than acute myeloid leukemia, in agreement with [39, 41]. The predominance of the male gender of these patients confirms the result documented in  and contradicts that reported by Toquica et al. .
For both tumor types, p-values indicated that correlation between θp and (R/H)p was non-significant and therefore non-lineal. Nevertheless, significant, lineal and low correlations were reported for ((R/H)p and (Xc/H)p) and (θp and (Xc/H)p).
Several reasons can be attributed to nearly 10% of cancer patient not satisfying the criteria of phase angle, such as: the biological individuality, the phase angle does not have to change once the cancer patients is diagnosed for the first time, not all new diagnosed cancer children have the same performance status and detected at the same time and not all tumor type influences equally θp. These reasons justify why the individual analysis of the bioelectrical parameters is suggested in this study.
The finding that 90.70% of all cancer patients satisfy θp < θr confirms that the phase angle may be used as an indicator of disease severity and quality of life and loss of body homeostasis of the cancer patient, a matter that agrees with . These findings have been confirmed in adult patients with cancer [8, 42, 43] and in patients with other pathologies [8, 13, 15, 34, 44]. Gupta et al.  report an average survival less than 3 months in patients with lung cancer whose θp values are between 2 and 3°. This finding is confirmed in other studies [8, 13, 15, 34, 42,43,44]. Nevertheless, the effect of θp on the survival is not discussed in this work because no patient dies.
In this study, θp < θr may be explained because in the majority of cancer patients prevails that (Xc/H)p < (Xc/H)r for all value of (R/H)p, for each age group, gender and experimental group. This may suggest that component (Xc/H)p of the ordered pair ((R/H)p, (Xc/H)p) prevails in the body bioelectric state of the cancer patient. From the biophysical point of view, (Xc/H)p cannot decrease until zero because θp tends toward zero, which means the death of the cancer patients. This occur for all values of (R/H)p, confirming that (R/H)p and θp are not linearly correlated. This may suggest that (Xc/H)p decreases until its minimum value that brings about a quicker decrease of (R/H)p than (Xc/H)p so that θp stays in its normal range. From the thermodynamic point of view, a quick decrease of (R/H)p may mean the occurrence of different self-organized biophysical-chemical processes in the organism that reduce the body bioenergetics losses to guarantee its maximum survival and self-preservation as a living system. One of the main characteristics of the biological organisms, as open systems, is to tend toward its maximum survival.
If net inductive effects of the patient  are neglected, Xcp may be due to the different total capacitive electrical reactance contributions of the tumor (named Xct), healthy tissue (Xco) and tumor-surrounding healthy tissue interface (named Xco-t). This interface is the tumor micro-environment and constitutes by the mixture of cancer cells, normal cells and other components. Xcp may be expressed in a first approximation as Xcp ≅ Xct + Xcο + Xcο − t. As the capacitive contribution predominates in each tissue, Xc = 1/(2πfC), where C is the electrical capacity of the biological tissue under consideration and f is the working frequency (50 kHz). For this reason, Xcp, Xct, Xco and Xco-t may be substituted for their respective electrical capacities. Therefore, Cp may be calculated approximately as Cp ≅ CtCοCο − t/(CοCο − t + CtCο − t + CtCο), where Cp, Ct, Co and Co-t are the total electrical capacities of the entire patient, the tumor, the healthy tissue and the surrounding healthy tissue-tumor interface, respectively.
It has been experimentally documented that Cο > > Ct (e.g., Ct = 3.546 ± 1.931 pF for lung cancer and Co = 893 ± 572 pF for normal lung tissue) and the increase in capacitance of normal cells when cancer cells are added to them . The first finding is confirmed by other authors [47,48,49,50]. The second finding may mimic the mixture of cancer and normal cells in the tumor surrounding healthy tissue interface. These two findings may suggest that CοCο − t > > CtCο > CtCο − t and therefore Cp ≅ Ct.
In addition, Cp ≅ Ct may also be obtained if contributions of Xco-t to Xcp (Co-t to Cp) are neglected with respect to those of Xct and Xco (Ct and Co). In this case, (Xc)p ≅ (Xc)t + (Xc)ο and Cp ≅ CtCο/(Ct + Cο). Cp ≅ Ct is due to the fact as normal cells have dielectric constants and membrane electrical capacities greater than those of cancer cells [46,47,48,49,50]. In contrast, Frike and Morse  report that Ct > Co. The fundamental contributions of Xct and Xco to Xcp may be argued because electrical activities occur mainly in the tumor and in healthy tissue (distant from the tumor). This result is expected because normal and cancerous cells are mainly confined in these two tissues and not in the tumor-surrounding healthy tissue interface. This aspect may explain in part why there are differences in the electrical properties of the tumor and healthy tissue, in agreement with others studies [47, 48, 52, 53].
The finding Cp ≅ Ct confirms that electrical properties and biological characteristics of the cancer histological variety significantly influence the body homeostasis, quality of life, survival and body bioelectrical and physiological parameters of a patient with Ts/Tns. Nevertheless, the tumor-surrounding healthy tissue interface cannot be completely neglected because it influences the electrical-chemical microenvironment of the tumor, which is related to the aggressiveness and metastasis of it [54,55,56] and its protection against the attack of cellular and humoral elements of the immune system [57, 58].
Due to the close relationship between the electrical and physiological parameters of a biological tissue [8, 21, 22, 34, 44, 58, 59], changes of Ct and Xct may be related to those of the transmembrane potential and the membrane permeability of cancer cells . In turn, these changes have been related to other alterations observed in cancer cells as high mitotic activity, increase in the electronegativity of the extracellular surface, changes in intracellular and extracellular ionic concentrations, breakdown of homeostasis of electronic transport in the cell membrane, the depletion of adenosine triphosphate, the failure of the contact inhibition mechanism, morphological changes, aggressiveness, metastatic capacity, among others [47, 56, 59]. This leads to an alteration of the body homeostasis in cancer patients.
Loss of body homeostasis of a patient (child or adult) with cancer may lead to the decrease of the body cell mass and changes of its cell metabolism, body composition and distribution of total body water, as reported in [33, 60, 61]. This may explain the cachexia and modifications in (R/H)p, (Xc/H)p and θp observed in cancer patients, explaining in part why (Xc/H)p < (Xc/H)r for all (R/H)p value observed in the majority of patients with Ts/Tns. This finding may suggest that losses of the body energy reserves of the patient with Ts/Tns (related to (Xc/H)p) are faster than the body heat loss (related to (R/H)p). This corroborates that θp < θr, as in [15, 43], and the body metabolism and body composition alterations of these cancer patients, as in [34, 60, 61]. It is important to note that heat loss is noticeable as Rp increases.
The finding (R/H)p > (R/H)r observed in some patients with Ts/Tns may be explained because body heat loss and water and ions body imbalances in cancer patient are noticeable compared to those in apparently healthy subjects. In turn, these alterations may be related to the biophysical-chemical-bioelectrical-energetic changes in the cell membrane, as discussed above.
Despite the increase of (R/H)p in these cancer patients, θp decreases slightly with respect to θr, for each gender and age group. This may suggest that these patients still have sufficient energy reserves to compensate the possible heat loss. If these losses prevail, θp would decrease and therefore a low quality of life and short survival of the patient with Ts/Tns, in agreement with . This statement would be noticeable when Xcp also decreases, in accordance with .
In general, |Z| and θ fix the position of any bioelectrical state in the plane R-Xc (R/H-Xc/H). The Cuban experience suggests that the simultaneous analysis of these two bioelectrical parameters is a necessary but not sufficient condition to absolutely differentiate one cancer patient from another or patients with any pathology from a population of apparently healthy subjects [30, 62]. This statement may be argued because cancer patients and apparently healthy individuals are inside 50 and 75% tolerance ellipses. Some of these patients evolve unfavorably during and after the application of chemotherapy. Nevertheless, other cancer patients out 95% tolerance ellipse (3.5 < θp ≤ 5) evolve favorably after this therapy . Additionally, similar results are observed in lung cancer adult patients treated with surgery, radiotherapy, chemotherapy and/or immunotherapy (unpublished data). On the other hand, patients with acquired immune deficiency syndrome are also inside 50, 75 and 90% tolerance ellipses. In addition, there are no significant differences in body bioelectric parameters and body composition of these patients compared with those of an apparently healthy individual population .
The above-mentioned is why dpr is proposed in this study. dpr does not contradict |Z| or θ, but they complement each other. It should be expected that there is a minimum value of dpr, from which a sick subject can be differentiated from an apparently healthy subject, although the patient is in any position inside the ellipse 95% tolerance ellipse. Other distance criteria for dpr may be used, such as Mahalanobis distance  or a Hausdorff distance . For instance, Hausdorff distance may be suggested to calculate this minimum distance. A longitudinal study is required to know this minimum value of dpr.
From bivariate statistics, it is well known that tolerance ellipses can be applied if R and Xc (R/H and Xc/H) are strongly correlated (r ≥ 0.8) [23, 31]. The values of r show in Table 1 are less than 0.8 (correlation strength between moderate and fair). Rigorously speaking, the tolerance region should not be an ellipse but a rectangle in this R-Xc (R/H-Xc/H) plot, in agreement with . This and the low correlations of r* (fair-poor) among Rp, Xcp and θp ((R/H)p, (Xc/H)p and θp) are why the rectangular tolerance region is used in this study. Rectangular tolerance region has been used in other studies [65,66,67]. In some studies, elliptical and rectangular tolerance regions are simultaneously analyzed [68, 69]. Additionally, the representation of multiple rectangles in the same XY plane is possible taking into account the work published by Wald .
As ellipse tolerance and rectangular tolerance regions (95%) are the same and the rectangle and the ellipse are both centered at the same point, an ellipse can be inscribed in a rectangle . In this case, it is easy to demonstrate that the ratio of the area of the rectangle/area of the ellipse is 1.27 and the difference between their respective areas is 0.21L1L2. As a result, both areas are approximately equal. L1 (L1 = 2a1) and L2 (L2 = 2a2) are the length and width of the rectangle, respectively. The variable a1 is the length of the semi-major axis of the ellipse whereas a2 is the length of the semi-minor axis. L1 = 2a1 and L2 = 2a2 guarantee the biggest area of an ellipse within a rectangle.
Unlike the studies reported in this area of knowledge, the body bioelectric state of each cancer patient is individually represented in this study. This will permit an individualized integral diagnosis and the proposal of a personalized therapy for each of them. In addition, the analysis on animals or humans is suggested individually in a previous study . Therefore, each cancer patient is represented in the Xc/H versus R/H plot, according to its age and gender.
Our results suggest performing a longitudinal study that permits to know how bioelectrical and physiological parameters of these patients with Ts/Tns change over time and what relationships can be established between them. This longitudinal study will allow to establish prognostic indicators of the possible evolution of a cancer patient under the application of a therapeutic scheme.