Clinical and pathological staging of the cancer at the nanoscale

Clinical staging model at the nanoscale (CSMN) has been performed on adenocarcinoma of the colon from five patients ranging in age from 57 to 76 years based on determining their malignant size, estimating their doubling time through imaging techniques, and thus by measuring the average of the tumor nanoparticle doubling time their histologic grade has been identified at the nanoscale. Another two pathologic staging models at the nanoscale PSM [H-3] N and PSM [C-14] N for evaluating the histologic grade have been performed on those tumors based on the in vitro measuring of cell proliferating of tumor slices by either of the [H-3] tritiated and [C-14] thymidine incorporation hypothesizing in PSM [H-3] N that the malignant fraction of the detected tumor is the unlabeled fraction of the tumor by the [H-3] tritiated thymidine, while positing in PSM [C-14] N that the percentage increase of the tumor nanoparticle doubling time than that of the normal tissue at the Natural Background Radiation is equivalent to the percentage deficit of [C-14] incorporation in tumor cells. The consistency of results of the three staging models has been analyzed using ANOVA. Identical histologic grades have been identified by the three staging models for tumors of early stages (p < 0.0001). While for those of advanced disease, evaluation of the histologic grade was identical by CSMN and PSM [H-3] N only (p < 0.0001), whereas was invalid by PSM [C-14] N.


Introduction
Staging of cancer is the main objective of cancer screening, and considered the most important predictor of survival, where cancer treatment is primarily determined by staging which can be changed according to progression of the disease. There are two types for cancer staging, clinical and pathologic, where both are considered a supplement for each other (Lucas 2006), each of them describes the anatomic extent of the cancer at the time of diagnosis before the application of definitive treatment to develop classification into stages, which serves for treatment guidance and for comparing with the end results of the applied treatment (Wilson and Jungner 1968). Clinical stage is based on all of the available information obtained before a surgery to remove the tumor, while pathologic stage adds additional information gained by examination of the tumor microscopically after surgery expressing the stage before therapy only (Lucas 2006). Usually, cancer staging by either type expresses the extent that cancer has spread, and is usually described by numbers I to IV with IV having more progression. Such classification, which is well known by the TNM system, involves the tumor size (T) and the regional lymph node involvement (N) and/or distant metastasis (M), is based on the premise that cancers of the same histology and anatomic sites share similar patterns of growth and metastasis (AJCC 1998). Thereby, staging by those numbers which reflect the histologic grade is considered very wide and unspecified to describe the extent and aggressiveness of the disease in patients, allowing to either of over or lower estimation to the administered dose that contributes to risks of tumor regrowth and metastasis (Moawad 2011). E. Moawad has introduced a clinical staging by imaging techniques that allow accurate cancer staging that helps to administer the appropriate low-waste dose and modify it by monitoring an earlier response to therapy which contributes besides developing dose-delivery skills to the success of all types of cancer treatments (Moawad 2010(Moawad , 2011. In the same time, it was possible to correlate the in vitro data with patient response to therapy and the incorporation of [ 3 H] tritiated thymidine and the [ 14 C] thymidine by slices of their tumors (Baserga and Lisco 1963;Wimber and Quastler 1963). No responses to therapy were found in those patients whose tumors when incubated in vitro with thymidine showed poor nucleoside incorporation. In contrast, patients receiving benefit from cancer therapy were those whose tumors when incubated in vitro with thymidine showed good nucleoside incorporation (Wolberg and Brown 1962). Such great variability reflects their variability in growth rate propensity for metastasis, or in other words, in their stages and consequently their corresponding grades. Thus, pathological staging has been assessed on the basis of measurements of the incorporation of [ 3 H] tritiated thymidine and the [ 14 C] thymidine in vitro in the tumor slices. Current approach aims to present clinical and pathological staging models of the cancer at the nanoscale to obtain more accurate assessment for the main factors of the prognostic determinants in the classification for cancer staging.
Clinical staging model at the nanoscale (CSMN) E. Moawad has presented a clinical model for cancer grading in which the patient-specific histologic grade has been identified by evaluating the tumor energy (E Tumor ) based on measuring tumor doubling time (t D ) which expresses the rate of growth by imaging techniques (Moawad 2010(Moawad , 2011, and estimating the percentage of the hypoxic cells (H%) which expresses the tumor histologic classification, and inversely proportional to the total number of the malignant cells of the tumor whose value is ranging between 8 and 20 % (Moawad 2010(Moawad , 2011. Thus, the energy of the hypoxic cell (E Hypoxic.cell ) which expresses the histologic grade at the cellular level can be estimated from Emad formula after measuring the tumor t D as follows: Emad ¼ 23; 234:59MeV: Thus, provided that patient-specific histologic grade (E Tumor ) is the summation of energies of all the tumor hypoxic cells (ΣE Hypoxic.cell ) then: where M% is the percentage of the tumor malignant fraction, and C 0 is the total number of tumor cells (Moawad 2010(Moawad , 2011. Knowing that a tumor of 1 g converted into 10 9 ng contains 10 9 cells, it would be more convenient to express the tumor histologic grade by nanoscale as equivalent to the average growth energy of a tumor of 1 ng or one nanoparticle (E ng ) investigating whether we can directly control matter on the molecular scale. Hereby, in all sections of the current approach the tumor cell will be expressed by the tumor nanoparticle, i.e., E Cell 0E ng . Thus, from Eq. 3, it can be deduced that and consequently the average doubling time of the tumor nanoparticle would be equivalent to: Thus, from Emad formula the histologic grade of the tumor nanoparticle would be:  (Lieb and Lisco 1966), conversely the unlabeled tumor fraction (U%) has been hypothesized by this model as an indicator for the inhibition to cell-proliferating rate. As inhibition to cell-proliferating rate accompanied by cell cycle arrest distinguishes the malignant cells from the normal ones, then the unlabeled tumor fraction (U%) can be considered the malignant tumor fraction (M%) that previously presented as one of the factors of the clinical staging shown in Eq. 3, i.e., U%0M%. Thus, such inhibition to cell-proliferating rate can be monitored by the deficit of [ 3 H] tritiated thymidine incorporation in the tumor malignant cells, provided that energy of such deficit part (U%) of the thymidine dose is equivalent to the energy of the malignant fraction (M%) of that tumor and denoted by E Tumor which expresses the patient-specific histologic grade. Accordingly, by knowing the percentage of the unlabeled cells (U%) of the tumor then: on condition that U%<1. Consequently, the patient-specific histologic grade at the nanoscale would be: Pathological staging model by [ 14 C] thymidine at the nanoscale It is well known that in all cancer stages from early to advanced disease, cancer cells are known to have alterations in multiple cellular signaling pathways drives normal cell to carcinoma (Wu et al. 2009). One of the most important signals is the continuous deficit in cell proliferation rate accompanied by a progressive cell cycle arrest along those stages (Reiskin and Mendelsohn 1964). Significant efforts have been made to understand the kinetic analysis of cell proliferation that drives cancer development and progression (Allard et al. 2004).
There is as yet little to distinguish the cancerous cell from a variety of normal cells which have also been analyzed (Reiskin and Mendelsohn 1964) as basis of such efforts. Since labeling of cells by [ 14 C] thymidine is commonly used as well in vitro in measuring cell proliferation rate, where the incorporation of the [ 14 C] thymidine into the dividing cells and the level of this incorporation is proportional to the amount of cell proliferation (Reszka et al. 2001 Since the identified histologic grade (E ng ) by those models shown in Eqs. 6, 8, and 10 should be identical, and as factors concerned in those models should confirm basis of the main factors assessment of the prognostic determinants in the classification for cancer staging by the TNM system. The objective of the current approach is to investigate the consistency of the results of those models to provide a clear-cut criterion for accepting or rejecting the hypotheses of those models.

Methods and materials
As conducted and described by Larry M. Lieb and Hermann Lisco (1966), adenocarcinomas of the colon from five patients ranging in age from 57 to 76 years were obtained immediately following tumor resection in the operating room. The in vitro uptake of [ 3 H] tritiated thymidine by those tumors cells was studied. The tumors were incubated for 1 h at 37.5±0.5°C in a beaker containing 100 ml of Ringer's solution and 100 μCi of [ 3 H] tritiated thymidine (Schwarz Laboratories, Inc., Mt. Vernon, New York) with a specific activity of 3.0 Ci/mmole . The tumor doubling time (t D ) has been estimated, total numbers of tumor cells (C o ), and the percentages of labeled cells in each tumor were measured for all five tumors. At the same time as conducted and described by Reszka et al. (Reszka et al. 2001), the corresponding in vitro uptake of [ 14 C] thymidine by those tumors cells was studied after incubation of 72 h, where the amount of [ 14 C] thymidine (NEN, Boston, MA) for measuring cell proliferation rate for each sample was proportional to its number of cells. The amount of [ 14 C] thymidine that used for measuring the largest tumor (25,838 cells) was 0.5 μCi, while the amounts used for other tumors has been proportionally decreased by ratio of their number of cells to that of the largest one. Data and results as shown by Larry M. Lieb and Hermann Lisco, and the amount of the used [ 14 C] thymidine for each tumor according to its C o with respect to that of the largest tumor along with its corresponding in vitro uptake carried out by current approach are tabulated in Table 1 to cover all data required for determining factors of the prognostic determinants of the presented pathological and clinical staging models; PSM [ 3 H] N, clinical staging model at the nanoscale (CSMN), and PSM [ 14 C] N.

Results and analysis
The released energy of 100 μCi of [ 3 H] tritiated thymidine (halflife time012.32 years, decay energy00.01859 MeV (Barbalace 1995a)) during the incubation of 1 h is equivalent to:   5 tumors are shown in table 2, where the consistency of the results of the three staging models has been analyzed using ANOVA ( Table 2). The relation of the derived values of H% from CSMN which represents the histologic classification and the measured values of E ng from PSM [ 3 H] N, which represents the histologic grade at the cellular level or at the nanoscale, shows perfect direct correlation (r00.9999) between them for all studied tumors as shown in Fig. 1. Thereby, H% can be estimated by the following equation model: (R 2 00.9998).
While  evaluating the tumors of advanced disease (higher percentage of hypoxic cells) is less than that of the earlier stages as illustrated in the last two cases shown in Fig. 6 which is consistent with its validity condition (D%<1 or t D.ng <2 t D.NBR ). Thereby, it can be easily concluded that the fraction of the deficit part of [ 14 C] thymidine incorporation (D%) in tumor compared to the control tissue at the NBR expresses the factor of the cell proliferation rate in cancer staging and grading. The identical evaluation of the histologic grades for the first three detected tumors of relatively earlier stages by the PSM [ 3 H] N, CSMN, and PSM [ 14 C] N (p<0.0001) boost the confidence to accept the hypotheses of those models and to comply with the basis of the main factors assessment of the prognostic determinants in the classification for cancer staging by the TNM system.

Discussion
Although, variations in tumor response to cancer therapies have been observed frequently by clinicians in patients of tumors have been identified by same stage and degree, so that those tumors appeared identical by all gross and histological parameters according to the TNM system. In some, the tumors may respond effectively, whereas in the others the tumors are unaffected by the drug and rapidly disseminate and kill them (Wolberg and Brown 1962). Such variations have led latter to believe that dosimetry never inherits identical results! (Matthay KK 2001). Recently, E. Moawad has attributed such random variations to the wide and insufficient staging by the TNM system that leads to dose assessment using standard models and consequently to a wide range of doses, responsible for tumor regrowth and second cancer risks (Moawad 2010(Moawad , 2011. And emphasized that tumor growth rate is a major factor should be considered in cancer staging to target a patient-specific histologic grade and consequently a patient-specific appropriate dose (Moawad 2010(Moawad , 2011. Thus, patient-specific histologic grade is the main objective of the advanced cancer staging and considered the most important predictor of survival, where cancer treatment is primarily determined according to it. As cancer staging by either of the clinical or pathological type should conform to each other to strengthen the confidence to both types, then basis for staging by either type should be assessed on identifying the factors of the prognostic determinants for the histologic classification and the anatomic extent of the cancer that lead to identical histologic grade identified by either type for the same tumor. According to the TNM system, the factors of the staging that should be considered focus on tumor location, size, rate of growth, histologic classification, and the anatomic extent which the disease has spread (AJCC 1998). Those different factors measured by both types of staging should be linked together such that from clinical measurements, the pathologic ones can be predicted and vice versa. The goal of this study is to present models of clinical and pathological staging of the cancer at the nanoscale parallel and comply with what is applied and achieved in the staging by the TNM system. Recently, rate of cell proliferation has been expressed using Emad formula by cell growth energy (CGE) which is the amount of energy of all cellular kinetics including all the aberrant genetic variations that drive normal cell to cancer (Moawad 2010(Moawad , 2011. Thus, the progress through measuring cellular kinetics allowed the improvement of the factors of the clinical model CSMN as (E Hypoxic.cell , t Dng , and E ng ) to distinguish the normal tissue from the cancerous one which must be given prime consideration in evaluating and comparing different therapeutic regimens. For the pathological models PSM [ 3 H] N and PSM [ 14 C] N, [ 3 H] tritiated thymidine and [ 14 C] thymidine are commonly used in vitro in cell proliferation assays, where both are incorporated into dividing cells and the level of this incorporation, measured using a liquid scintillation counter, is proportional to the amount of cell proliferation (Reszka et al. 2001). It was possible to correlate the in vitro data with patient response to therapy and the incorporation of [ 14 C] thymidine and [ 3 H] tritiated thymidine by slices of their tumors. No responses to therapy were found in those patients whose tumors when incubated in vitro with either of them showed poor nucleoside incorporation. In contrast, patients receiving benefit from cancer therapy were those whose tumors when incubated in vitro with either of them showed good nucleoside incorporation (Wolberg and Brown 1962 (Moawad 2010(Moawad , 2011. (2) Consequently, percentage of the hypoxic cell (H%) which represents the histologic classification should be considered in cancer staging. The consistent results of the perfect correlation between H% and their corresponding averages of energy of the tumor nanoparticle (E ng ) revealed that accurate histologic diagnosis is essential element in the specific evaluation of the tumor to confirm the basis of the main factors assessment of the prognostic determinants in the classification for cancer staging by the TNM system. In addition, the significant effect of H% on identifying the specific histologic grade is consistent with what has been noted by others that the extent of labeling of tumor cells by [ 3 H] tritiated thymidine in an in vitro system is dependent upon the oxygen concentration, the type and number of cells composing the tissue, and any fissuring or cracking of the tissue which might allow deeper penetration of the incubation fluid (Johnson and Bond 1961). Such note reveals the role of hypoxic cells in inhibition to cell labeling (i.e., to increase U% which expresses the increase of M% as well) by thymidine incorporation as it is believed that cell hypoxia contributes significantly to treatment failure because cells in the hypoxic zones resist traditional chemical disinfection. This happens for at least two reasons: First, most agents cannot penetrate beyond 50-100 μm from capillaries (Minchinton and Tannock 2006), therefore never reaching the cells in the hypoxic regions. Second, the lower nutrient and oxygen supply to cells in the hypoxic zones causes them to divide more slowly, i.e., longer cell t D than their well-oxygenated counterparts. Therefore and in agreement with Emad formula shown in Eq. 1, the hypoxic cells due to its higher CGE exhibit greater resistance to chemical treatments, radiation, and thus serve to inhibit thymidine incorporation that targets rapidly dividing cells or requires oxygen for efficacy (Gillies and Gatenby 2007;Sullivan and Graham 2007;Brown 1999;Castello and David 2006). (3) The malignant tumor fraction (M%) which is a dependent factor for cancer staging depends on the tumor t D and consequently the E Hypoxic.cell as shown in  H] N are more efficient in evaluating the tumors of advanced stages as those models consider the histologic classification as previously shown in Section 3 besides the cell proliferation rate. The main principal finding has emerged from this study was the wide variation shown in M% and the wide variation in the labeling index among the five cases so that Larry M. Lieb and Hermann Lisco noted that "Our data provide no explanation for such variations" (Lieb and Lisco 1966). The consistent results of the current approach provide such explanation: as t D varies among the five cases, their corresponding E Hypoxic.cell varies as well and consequently the unlabeled fraction of each fraction (U%0M%) as shown in Eq. 12. Results of the current approach are consistent with the results of models shown in the previous studies taking into consideration that the value of (M%) was 100 % in those prior studied cases as E Hypoxic.cell was greater than 5.2 Emad to satisfy the restriction of Eq. 12 (Moawad 2010(Moawad , 2011. The classification by the TNM system achieves reasonably precise description and recording of the anatomic extent of cancer, it allows patients of different histologic grades to be diagnosed by same stage, and consequently receive same treatment, and therefore, it is not surprising to find such random variations in responses of those patients to their unspecified treatment. Thus, the objective of those models which is the patient histologic grade is a combination of the stage groupings of the T, N, and M classifications in a specific-patient prognosis to provide a simple way by which this information can readily assist in choices of treatments and therapeutic decisions, and thus those models will erase the blame for non-matching results of the dosimetry.

Conclusion
CSMN, PSM [ 3 H] N, and PSM [ 14 C] N introduce innovative solutions to improve identification of effective diagnostic tool based on an individual's unique tumor well-tolerated with acceptably low rates of false positive and false negative results to establish an efficient cancer screening by a reasonable classification for staging of cancer. The anatomic extent to which the disease has spread is no longer alone the most important factor determining prognosis in the classification for cancer staging. The tumor doubling time and the histologic classification are the prognostic determinants to identify the specific tumor histologic grade at the nanoscale which is the most important variable that affects choices and allows physicians to develop customized treatment plans for patients. Models that consider each of cell proliferation rate and the histologic classification as CSMN and PSM [ 3 H] N are more efficient than the ones that consider the cell proliferation rate only as PSM [ 14 C] N in evaluating the histologic grade of tumors of advanced stages.