Experimental metastasis: a novel application of the variance-to-mean power function.

An empiric power function relationship between a population's mean density (m) and its corresponding variance (v), written v = a.mb (a, b, constants), may be applied to the analysis of experimentally induced pulmonary metastases within syngeneic (C57BL/6 X C3H)F1 mice. The mean and variance of the numbers of resultant B16 F1 and B16 F10 melanoma metastases strongly correlated with the power function (r2 greater than 0.8). The exponent b was 1.4 +/- 0.1 and 1.6 +/- 0.2 for the F1 and F10 melanomas, respectively, indicating a clustering of metastases within certain mice. This clustering of metastases within more highly affected animals may reflect a diffusion-limited aggregation of tumor cells within the circulation and the resultant greater ability of these aggregates to form metastases.

Pitfalls and practice of Luria-Delbrück fluctuation analysis: a review.

Luria-Delbrück fluctuation analysis provides a method to estimate mutation rates in cell populations. Originally designed for bacterial populations, the method now is widely applied in somatic cell genetics and in cancer biology. However, there are fundamental genetic differences between bacteria and somatic cells, and this together with the inherent mathematical complexity of fluctuation analysis can lead to many pitfalls in its application. In addition there is considerable statistical error associated with the method. The use, misuse, and limitations of fluctuation analysis are reviewed here with the hope that such problems may be avoided.

Metastatic potential and spontaneous mutation rates: studies with two murine cell lines and their recently induced metastatic variants.

To investigate the hypothesis that increased malignant potential correlates with increased genetic instability, we measured spontaneous mutation rates for the production of ouabain-resistant mutants in two benign (nonmetastatic) murine cell lines and their recently induced metastatic variants. Metastatic variants of the NIH 3T3 and CBA SP-1 cells were induced by transfection with the h-ras oncogene. Metastatic variants were also induced from the CBA SP-1 cell line by treatment with either 2'-deoxy-5-azacytidine or hydroxyurea. Mutation rates for the parent NIH 3T3 cells and their metastatic variants were less than 3 X 10(-8) variants per cell per generation, with no significant differences between them. Rates for the CBA SP-1 line and its variants ranged from 9 X 10(-9) to 8 X 10(-8) variants per cell generation, again without statistically significant differences. We conclude that in the cell lines studied the rate of spontaneous mutation for ouabain resistance was unrelated to the acquisition of the metastatic phenotype. This conclusion was based on the view that the generation of ouabain-resistant mutants is a reflection of the overall stability of the genome. Since the spontaneous mutation rate for ouabain resistance was unchanged in cells that had recently acquired the ability to metastasize, other genetic or epigenetic events were probably responsible for progression to the malignant (metastatic) phenotype.

Rate of generation of major karyotypic abnormalities in relationship to the metastatic potential of B16 murine melanoma.

To test the hypothesis that genetic instability correlates with malignant potential, we compared the rate of generation of marker chromosomal abnormalities in clones of B16 F1 and B16 F10 murine melanoma. These rates were estimated through an adaptation of fluctuation analysis of Luria and Delbruck (S. E. Luria and M. Delbruck, Genetics, 28: 491-511, 1943). The highly metastatic F10 line showed the same degree of marker chromosomal instability as the poorly metastatic F1 line (0.01 variants/cell/generation). When subclones of a karyotypically unstable F10 clone were compared with those of a more stable F10 clone, both groups caused the same number of pulmonary metastases, thus demonstrating a further lack of correlation of malignant potential with the level of genomic instability. Since measurements based on marker chromosomes may not truly reflect all of the changes detectable by G-banding, we also analyzed the G-banded karyotypes of the cell lines and their clones (chromatid or chromosomal breaks were not considered in this study). The F10 clones possessed an additional copy of chromosome 1 and also a significantly higher prevalence of the translocation t(9,12) when compared with the F1 clones. Rather than general rates of major karyotypic change determining tumor progression, we suggest the importance of other genetic or epigenetic mechanisms, particularly subtle nonrandom genetic or molecular changes, as the determining factors for malignant potential.

Characterization of the frequency distribution for human hematogenous metastases: evidence for clustering and a power variance function.

When groups of mice are injected with cells from a metastasizing tumor, a minority of individuals within a given group tends to sustain disproportionately larger numbers of metastases relative to the remaining group members. This clustering of metastases obeys a power function relationship, sigma2 = amub, between the variance sigma2 and the mean number of lung metastases per animal mu (a and b constant). To see whether such clustering occurs with human lung, brain, and liver metastases, a meta-analysis of clinical and pathological series was performed. Thirty-three published series were identified that provided data regarding the numbers of organ metastases sustained by 5582 people. The data were grouped according to the primary tumor, site of metastasis and method of detection of metastases. Clustering of metastases within individuals of each subgroup (similar to the murine systems) was demonstrated by variance to mean ratios greater than 1, and by a strong correlation to the variance to mean power function (a approximately 0.49, b approximately 2.24, r2 = 96%, p < 10(-6)). The cause of this clustering remains unclear, but it may in part relate to heterogeneities in regional blood flow. As a consequence of this clustering, limited metastases would be expected to occur more frequently than predicted from random chance-providing for some optimism in the management of limited metastasis. As well, the frequency distribution for metastases revealed certain scaling symmetries, likely reflective of the underlying mechanisms of metastasis, that could be of interest to both clinicians and experimentalists working with metastasis.

Respiratory-induced prostate motion: quantification and characterization.

PURPOSE: The precise localization of the prostate is critical for dose-escalated conformal radiotherapy. This study identifies and characterizes a potential cause of inaccurate prostatic localization-respiratory-induced movement. METHODS AND MATERIALS: Prostate movement during respiration was measured fluoroscopically using implanted gold fiducial markers. Twenty sequential patients with CT(1)-T(3) N(0) M(0) prostate carcinoma were evaluated prone, immobilized in customized thermoplastic shells. A second 20 patients were evaluated both prone (with and without their thermoplastic shells) and supine (without their shells). RESULTS: When the patients were immobilized prone in thermoplastic shells, the prostate moved synchronously with respiration. In the study the prostate was displaced a mean distance of 3.3 +/- 1.8 (SD) mm (range, 1-10.2 mm), with 23% (9/40) of the displacements being 4 mm or greater. The respiratory-associated prostate movement decreased significantly when the thermoplastic shells were removed. CONCLUSION: Significant prostate movement can be induced by respiration when patients are immobilized in thermoplastic shells. This movement presumably is related to transmitted intraabdominal pressure within the confined space of the shells. Careful attention to the details of immobilization and to the possibility of respiratory-induced prostate movements is important when employing small field margins in prostatic radiotherapy.

Repeated tandem translocations in a clone and subclones of B16-F10 murine melanoma.

In one clone and three subclones isolated from the F10 line of the B16 mouse melanoma, a family of extraordinarily long marker chromosomes was found. Banding analyses showed that these long markers represented repeated tandem translocations. Most of these markers exhibited only two or three C-bands. Immunofluorescence staining using antikinetochore serum revealed that these markers had either two active kinetochores or one active and one inactive kinetochore. The original clone and one of the subclones were highly unstable with respect to the composition of the markers and to the ability for retaining the markers. The other two subclones were found to be relatively stable. Because all three subclones were derivatives of one clone, which was unstable, our data suggest that stable genomes can be generated from unstable progenitors.

Technical report. The application of probability-generating functions to linear-quadratic radiation survival curves.

PURPOSE: To illustrate how probability-generating functions (PGFs) can be employed to derive a simple probabilistic model for clonogenic survival after exposure to ionizing irradiation. METHODS: Both repairable and irreparable radiation damage to DNA were assumed to occur by independent (Poisson) processes, at intensities proportional to the irradiation dose. Also, repairable damage was assumed to be either repaired or further (lethally) injured according to a third (Bernoulli) process, with the probability of lethal conversion being directly proportional to dose. Using the algebra of PGFs, these three processes were combined to yield a composite PGF that described the distribution of lethal DNA lesions in irradiated cells. RESULTS: The composite PGF characterized a Poisson distribution with mean, chiD+betaD2, where D was dose and alpha and beta were radiobiological constants. This distribution yielded the conventional linear-quadratic survival equation. To test the composite model, the derived distribution was used to predict the frequencies of multiple chromosomal aberrations in irradiated human lymphocytes. The predictions agreed well with observation. This probabilistic model was consistent with single-hit mechanisms, but it was not consistent with binary misrepair mechanisms. CONCLUSIONS: A stochastic model for radiation survival has been constructed from elementary PGFs that exactly yields the linear-quadratic relationship. This approach can be used to investigate other simple probabilistic survival models.

A closed-form description of tumour control with fractionated radiotherapy and repopulation.

PURPOSE: To derive a closed form expression of tumour control probability (TCP) following the geometric stochastic approach of Tucker and Taylor. METHODS: A model was constructed based upon a Galton-Watson branching process with cell killing represented by a Bernoulli random variable, and repopulation represented by a Yule Fury process. A closed-form expression of the probability-generating function was derived, which yielded an explicit expression for the mean number of surviving clonogens and the TCP. RESULTS: The mean number of surviving cells, after i clonogens have been treated with n fractions of irradiation, was [equation: see text], where s is the surviving fraction, lambda is the rate of cell division, and delta t is the interfraction time interval. The tumour control probability was [equation: see text]. CONCLUSIONS: Tucker and Taylor provided improvements upon the conventional Poisson model for TCP, mainly through numerical simulation. Here a model based upon their geometric stochastic approach has been derived in closed form. The resultant equations provide a simpler alternative to numerical simulation allowing the effects of fractionated radiotherapy on a replicating population of tumour cells to be more easily predicted.

The role of multiple somatic point mutations in metastatic progression.

To test the hypothesis that the ability to metastasize is determined by multiple point mutations during the expansion of a neoplastic clone, a mathematical model for sequential mutations was derived. Development of the metastatic phenotype was attributed to the mutation of a specific group of genes. The average tumor size was estimated for when a cell should manifest a set number of these mutated genes. In a tumor of 10(9) cells subject to 10(-6) mutations/gene per generation, only one of these genes, on average, should have mutated. To explain the multiplicity of changes associated with the metastatic phenotype, genetic variation at rates greater than 10(-3) variations/gene per generation seems necessary. Possible mechanisms for this variation involve gene amplification, chromosomal aneuploidy, and altered gene regulation rather than point mutation.

The use of information theory to analyze genomic changes in neoplasia.

How the cell maintains and uses its heritable information may be a critical factor in neoplasia. For example, neoplastic development is thought to depend upon the interplay between random genomic instability and nonrandom selective forces. Information theory provides a means to analyze these processes. One may quantitate not only the amount and lability of information contained within a segment of genetic code, but also the genotypic heterogeneity and the degree of selection affecting a population of cells. In addition, it is theoretically possible to monitor genetic information as it is processed by cells during replication, transcription, and translation. These parameters could permit a detailed analysis of the evolutionary changes hypothesized to underlie neoplastic development.

Suicide and cancer: a gender-comparative study.

BACKGROUND: Persons with cancer commit suicide more frequently than those without, and males generally commit suicide more frequently than females. A population-based analysis of cancer patients was carried out here, comparing suicide risk between the genders, to elucidate the features specific to each gender. PATIENTS AND METHODS: A total of 1.3 million cancer cases from the Surveillance, Epidemiology, and End Results program were analyzed. Cox proportional hazards models were fitted to personal, tumor-related, and social variates. RESULTS: A total of 265 female and 1307 male suicides were enumerated, reflecting 0.04% and 0.19% from each gender, and providing an overall hazard ratio for male suicide of 6.2 [95% confidence interval (CI) 5.4-7.1]. Females with colorectal (P = 0.01) and cervical (P < 0.0001) cancers showed decreased suicide rates. Males with head and neck cancers (P < 0.0001) and myeloma (P = 0.02) had increased rates, whereas rates were decreased in males with lung cancer (P = 0.01), liver (P = 0.01), brain tumors (P = 0.04), and leukemia (P = 0.007). The hazard ratio associated for male suicide with distant metastasis was 2.84 (95% CI 2.49-3.24); for married status, 0.46 (95% CI 0.39-0.54); and for African-American ancestry, 0.24 (95% CI 0.17-0.34)-comparable ratios were seen here for female suicides. In head and neck cancers, with both genders analyzed together, the suicide hazard was increased if surgery was contraindicated (3.0, 95% CI 1.3-6.8), but not if refused. CONCLUSIONS: The high-risk patient was male, with head and neck cancer or myeloma, advanced disease, little social or cultural support, and limited treatment options. Oncologists and allied health professionals should be aware of the potential for suicide in cancer patients and their associated risk factors.

The size distribution of human hematogenous metastases.

The development of primary cancers and their subsequent metastases occur through a complex sequence of discrete steps. A hypothesis is proposed here whereby the time available for the growth of metastases is normally distributed, presumably as a consequence of the summation of multiple independently distributed time intervals from each of the steps and of the Central Limit Theorem. For exponentially growing metastases, the corresponding size distribution would be lognormal; Gompertzian growth would imply a modified (Gompertz-normal) distribution, where larger metastases would occur less frequently as a consequence of a decreased growth rate. These two size distributions were evaluated against 18 human autopsy cases where precise size measurements had been collected from over 3900 macroscopic hematogenous organ metastases. The lognormal distribution provided an approximate agreement. Its main deficiency was a tendency to over-represent metastases greater than 10 mm diameter. The Gompertz-normal distribution provided more stringent agreement, correcting for this over-representation. These observations supported the hypothesis of normally distributed growth times, and qualified the utility of the lognormal and Gompertz-normal distributions for the size distribution of metastases.

Fractal heterogeneity of peripheral blood flow: implications for hematogenous metastases.

BACKGROUND AND OBJECTIVES: To determine how inhomogeneities in blood perfusion might affect the number of metastases that develop within an individual with cancer. METHODS: Experiments with lung metastases in mice, involving 320 treatment groups and 3165 mice, were reviewed. Inhomogeneities in the distribution of metastases amongst identically treated mice were analyzed by calculating the relative dispersion and clumping index. RESULTS: The relative dispersion exhibited fractal self-similarity on change of scale, and paralleled the effects observed with pulmonary blood flow. Clustering of metastases was also apparent: a minority of mice developed relatively large numbers of metastases; a majority of mice developed few metastases. CONCLUSIONS: Clustering of lung metastases occurred within groups of identically treated mice, and could be attributed to inhomogeneous blood perfusion. Consequently, the number of metastases in any individual was highly variable and correlated only partly with malignant potential. Inhomogeneities in blood flow favored the development of relatively few metastases, such that solitary or nil metastasis should occur more frequently than expected from chance alone.

A stochastic model for the self-similar heterogeneity of regional organ blood flow.

The theory of exponential dispersion models was applied to construct a stochastic model for heterogeneities in regional organ blood flow as inferred from the deposition of labeled microspheres. The requirements that the dispersion model be additive (or reproductive), scale invariant, and represent a compound Poisson distribution, implied that the relative dispersion (RD = standard deviation/mean) of blood flow should exhibit self-similar scaling in macroscopic tissue samples of masses m and m(ref) such that RD(m) = RD(m(ref)). (m/m(ref))(1-D), where D was a constant. Under these circumstances this empirical relationship was a consequence of a compound Poisson-gamma distribution that represented macroscopic blood flow. The model also predicted that blood flow, at the microcirculatory level, should also be heterogeneous but obey a gamma distribution-a prediction supported by observation.

A perspective on tumour progression.

During their natural history, tumours may acquire new phenotypic traits. This process, tumour progression, becomes clinically important when tumours acquire the ability to invade and metastasize or when they develop drug resistance. An acquired genetic instability modulated by selection likely contributes to this progression. More than one genetic mechanism is probably involved, a small number of point mutations being complemented by karyotypic events, gene amplification and altered gene expression. More complicated traits, such as the ability to invade and metastasize, may be acquired through the inappropriate and disorganized reexpression of genetic programs suppressed during embryologic development.

Clustering of murine lung metastases reflects fractal nonuniformity in regional lung blood flow.

In the experimental metastasis assay certain animals, from groups of similarly treated animals, develop more lung metastases than expected from random chance alone. This clustering of metastases is characterized by a power function relationship, sigma(2) = amu(b), between the variance, sigma(2), and mean, mu, of the numbers of lung metastases per animal (a and b are constants). To determine whether this clustering could be an artifact of experimental metastasis, whether it could be influenced by different experimental conditions, and to attempt to clarify its cause, 22 published data sets from experimental metastasis utilizing 2,145 mice, as well as 8 data sets from spontaneous metastasis utilizing 1,020 mice were analyzed. In these experiments cell cloning, cell-cell fusion, treatment with a protein kinase C inhibitor, treatment with cell adhesion compounds, and transfection with either the ras oncogene, the sialidase gene, or the urokinase sense and antisense genes were used to influence metastasis. They employed 14 different cell lines and 6 different strains of inbred mice. Clustering of metastasis was evident in animals from the spontaneous metastasis assays as well as from the experimental metastasis assays. It was apparent whether mice were injected with tumor cells derived from clones or from cell lines. Clustering was demonstrated within each data set, regardless of the experimental conditions employed. A single variance to mean power function (with a = 2.2 and b = 1.51) characterized the clustering in the 30 data sets. The regional distribution of blood flow through lungs and other organs is nonuniform, exhibiting a fractal symmetry on change of scale. This symmetry implies that the variance of a region's blood flow is related to its mean by the same power function as was observed with metastasis. Indeed, measurements of blood flow from isolated canine lungs yield b = 1.56, similar to the corresponding figure from murine lung metastasis. These findings lend support to the hypothesis that the observed clustering of metastases is a consequence of fractal variations in lung blood flow.

The recovery of organelle transport and microtubule integrity in myelinated axons that are frozen and thawed.

Myelinated axons of Xenopus laevis were rapidly frozen in liquid nitrogen and thawed in a potassium glutamate based medium. Organelles within isolated, thawed axons were visualized by light microscopy. After thawing, organelles were stationary for about 5 min. Following this quiescent period, organelles exhibited a low frequency oscillation in the longitudinal direction of the axon; some of the organelles then began to move in either the anterograde or retrograde directions. Electron microscopic examination of axonal cross sections showed that few microtubules were present immediately after thawing, but the numbers of microtubules recovered to approximately normal levels with a time course resembling that of the recovery of organelle transport. The effects of colchicine and taxol on the recovery of organelle transport and the microtubule content of axons was consistent with the hypothesis that the recovery in microtubule numbers was related to the recovery of organelle transport. Vanadate ions inhibited the recovery of organelle transport at concentrations known to inhibit dynein ATPase.

Incarceration of gastric fundus in a paraesophageal hernia after gastroplasty.

A tension hydropneumothorax developed suddenly in a 33-year-old woman, 5 days after gastroplasty. The cause was not immediately apparent. Radiologic investigation demonstrated incarceration of the fundus of the stomach together with the stapled pouch in a paraesophageal hernia. Abdominal exploration revealed a blow-out in the wall of the incarcerated fundus. After appropriate repair and management, the patient's course was uncomplicated. This case highlights the need for repairing paraesophageal hernias as soon as they are discovered, particularly during operations that require mobilization of the esophagus and cardia, as in gastroplasty.