The growth of tumor masses g dattoli enea frascati
1 / 31

The growth of tumor masses G. Dattoli ENEA FRASCATI - PowerPoint PPT Presentation

  • Uploaded on
  • Presentation posted in: General

The growth of tumor masses G. Dattoli ENEA FRASCATI. The point of view of a laser physicist (a theoritician). Power laws. Math. Formulation Self- Symilarity (Invariance under Scale trasformation, Kallan-Szymanzik). TAYLOR-”Law”. Bode-law. Distance of planets from the sun

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Presentation

The growth of tumor masses G. Dattoli ENEA FRASCATI

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

The growth of tumor massesG. DattoliENEA FRASCATI

The point of view of a laser physicist

(a theoritician)

Power laws

Math. Formulation

  • Self- Symilarity (Invariance under

  • Scale trasformation, Kallan-Szymanzik)



  • Distance of planets from the sun

  • n=n-th planet


Biology& EchologyThe New fronteer

  • Volterra-Lotka, Malthus, Gompertz, Damouth, Kleiber…

Echology: Damouth-law

Biology & Ecology: the Paradise of the scaling law

  • Kleiber:mass- metabolyc rate

Kleiber-Law 18-orders of magnitude!!!!!

…3/4 ???

Kleiber and dynamics…

  • Rate eq. (West, Brown, Enquist (1997))

Eq. Di evoluzione

Living body EvolutionVon-Bartalanffy- Quantitative laws in metabolism and growth-Quarterly review on Biology 32, 217-231 (1957).


  • The solutions of the Eq.

  • Is a logistic type

Analisi dei dati West & Brown)

Growth of tumor masses

Prostate cancer

Mass (grams) of the human prostate cancer vs. time (days) using

the WBE equation and the parameters

Prostate and breast cancer andenergetic

  • age 40 years

Tumor cell evolution

Evolution of the tumor cell number vs time, final mass

671 g, different evolution times

Tumor and host organ

  • Human prostate cancer mass in grams (continuous line) and cancer metabolic rate in (continuous line), vs time in days (the dash curve refers to the average human metabolic rate). The cancer power density has been calculated assuming that the tumour has a spherical shape with a density comparable to that of the water.

Required Power

  • For a practically vanishing initial tumour mass and at small times we can evaluate the power associated to the tumour evolution, during its early stages is given by

  • while the energy used to generate the corresponding tumour mass is

Carrying Capacity and critical times for methastases spreading

Tumor and methastases

  • Statistical model, Poissonian distribution

  • Il parametro is, along with the growth time, a measure of the tumour aggressivity

Evolution of methastasis

  • Probability vs. time (days) that s-malignant cells leaves the primary tumour

  • s=10 cells (solid line), s=50 cells (dash line), s=130 cells (dot line)

  • for M=671 g and

Probability of spreading

  • Probability of colony formation vs. time (days) for a tumour with days and 1 colony (solid line), 10 colonies (dot line), 50 colonies (dash line), number of cells normalized to the saturation number (dash-dot), the parallel line corresponds to the clinical level (cells)



  • Biol. Evolution relies on complex mechanisms

  • Simple mathematical models are welcome

  • The same applies to tumor mass evolution

  • Concepts like carrying capacity e methastases spreading could be understoo in enegetic terms

  • The Kleiber “law” should be considered as the manifestation of a more general LAW

  • The dependence on the temperature should be included


  • E=6 eV typical value of biochemical reactions

Frattali e legge di Kleiber

….Fractal dimensions

  • Login