Predicting the course of Gompertzian growth

Norton, Larry; Simon, Richard; Brereton, Harmar D.; Bogdén, Arthur E.

doi:10.1038/264542a0

Cited by 287 publications

(184 citation statements)

References 6 publications

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“…Mice with tumor sizes of 100 mm 3 are generally used to investigate drug effects. This is because solid tumors typically display Gompertzian kinetics (35), and they are typically found to be in a log phase of growth when at a size of 100 mm 3 , where the new tumor vessels are robustly developing and no necrosis in the interior of the tumor has appeared yet (36). The tumors in free Dox-, free HFn-, or PBS-treated groups grew rapidly, and the average volume of tumors reached >1,000 mm 3 on day 18 after tumor implantation (Fig.…”

Section: Resultsmentioning

confidence: 99%

H-ferritin–nanocaged doxorubicin nanoparticles specifically target and kill tumors with a single-dose injection

Liang

Fan

Zhou

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

412

438

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An ideal nanocarrier for efficient drug delivery must be able to target specific cells and carry high doses of therapeutic drugs and should also exhibit optimized physicochemical properties and biocompatibility. However, it is a tremendous challenge to engineer all of the above characteristics into a single carrier particle. Here, we show that natural H-ferritin (HFn) nanocages can carry high doses of doxorubicin (Dox) for tumor-specific targeting and killing without any targeting ligand functionalization or property modulation. Doxloaded HFn (HFn-Dox) specifically bound and subsequently internalized into tumor cells via interaction with overexpressed transferrin receptor 1 and released Dox in the lysosomes. In vivo in the mouse, HFn-Dox exhibited more than 10-fold higher intratumoral drug concentration than free Dox and significantly inhibited tumor growth after a single-dose injection. Importantly, HFn-Dox displayed an excellent safety profile that significantly reduced healthy organ drug exposure and improved the maximum tolerated dose by fourfold compared with free Dox. Moreover, because the HFn nanocarrier has well-defined morphology and does not need any ligand modification or property modulation it can be easily produced with high purity and yield, which are requirements for drugs used in clinical trials. Thus, these unique properties make the HFn nanocage an ideal vehicle for efficient anticancer drug delivery.

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Section: Resultsmentioning

confidence: 99%

H-ferritin–nanocaged doxorubicin nanoparticles specifically target and kill tumors with a single-dose injection

Liang

Fan

Zhou

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

412

438

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“…However, exponential growth is unlikely to be sustained in larger lesions, which may be limited by lack of adequate vasculature (23). Gompertzian dynamics, which feature an initial exponential growth phase followed by saturation, may be a more appropriate model for such systems (24). Stem cells from the bulge region of hair follicles may be responsible for repair of more macroscopic epidermal wounds (25), which could result in dynamics different from those described in the present model, which assumes that stem-like cells of the interfollicular epidermis are responsible for skin maintenance (26,27).…”

Section: Discussionmentioning

confidence: 99%

Preneoplastic lesion growth driven by the death of adjacent normal stem cells

Chao

Eck

Brash

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

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Clonal expansion of premalignant lesions is an important step in the progression to cancer. This process is commonly considered to be a consequence of sustaining a proliferative mutation. Here, we investigate whether the growth trajectory of clones can be better described by a model in which clone growth does not depend on a proliferative advantage. We developed a simple computer model of clonal expansion in an epithelium in which mutant clones can only colonize space left unoccupied by the death of adjacent normal stem cells. In this model, competition for space occurs along the frontier between mutant and normal territories, and both the shapes and the growth rates of lesions are governed by the differences between mutant and normal cells' replication or apoptosis rates. The behavior of this model of clonal expansion along a mutant clone's frontier, when apoptosis of both normal and mutant cells is included, matches the growth of UVB-induced p53-mutant clones in mouse dorsal epidermis better than a standard exponential growth model that does not include tissue architecture. The model predicts precancer cell mutation and death rates that agree with biological observations. These results support the hypothesis that clonal expansion of premalignant lesions can be driven by agents, such as ionizing or nonionizing radiation, that cause cell killing but do not directly stimulate cell replication.clonal expansion ͉ computer simulation ͉ skin cancer ͉ TP53 ͉ UVB

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“…The Gompertz model was first employed in the paper of Laird (1964) to model real tumor growth. Ever since, Gompertz's empirical equation remains the most popular one in describing cancer cell population growth in a wide spectrum of bio-medical situations due to its good fit to data and simplicity (Norton (1976)). Many efforts were documented in the literature aimed at understanding the mechanisms that may support Gompertz's elegant model equation (Frenzen and Murray (1986), Gyllenberg and Webb (1989), Marusic and Vuk-Pavlovic (1993), Marusic et al (1994), Kozusko and Bajzer (2003), Thalhauser et al (2009)).…”

Section: Introductionmentioning

confidence: 99%

Quiescence as an explanation of Gompertzian tumor growth revisited

Alzahrani¹,

Asiri²,

El-Dessoky³

et al. 2014

Mathematical Biosciences

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Abstract. Gompertz's empirical equation remains the most popular one in describing cancer cell population growth in a wide spectrum of biomedical situations due to its good fit to data and simplicity. Many efforts were documented in the literature aimed at understanding the mechanisms that may support Gompertz's elegant model equation. One of the most convincing efforts was carried out by Gyllenberg and Webb. They divide the cancer cell population into the proliferative cells and the quiescent cells. In their two dimensional model, the dead cells are assumed to be removed from the tumor instantly. In this paper, we modify their model by keeping track of the dead cells remaining in the tumor. We perform mathematical and computational studies on this three dimensional model and compare the model dynamics to that of the model of Gyllenberg and Webb. Our mathematical findings suggest that if an avascular tumor grows according to our three-compartment model, then as the death rate of quiescent cells decreases to zero, the percentage of proliferative cells also approaches to zero. Moreover, a slow dying quiescent population will increase the size of the tumor. On the other hand, while the tumor size does not depend on the dead cell removal rate, its early and intermediate growth stages are very sensitive to it.

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Predicting the course of Gompertzian growth

Cited by 287 publications

References 6 publications

H-ferritin–nanocaged doxorubicin nanoparticles specifically target and kill tumors with a single-dose injection

H-ferritin–nanocaged doxorubicin nanoparticles specifically target and kill tumors with a single-dose injection

Preneoplastic lesion growth driven by the death of adjacent normal stem cells

Quiescence as an explanation of Gompertzian tumor growth revisited

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