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

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


  • 57 Views
  • Uploaded on

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

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

PowerPoint Slideshow about ' The growth of tumor masses G. Dattoli ENEA FRASCATI' - shay-kim


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 masses g dattoli enea frascati

The growth of tumor massesG. DattoliENEA FRASCATI

The point of view of a laser physicist

(a theoritician)


Power laws
Power laws

Math. Formulation

  • Self- Symilarity (Invariance under

  • Scale trasformation, Kallan-Szymanzik)



Bode law
Bode-law

  • Distance of planets from the sun

  • n=n-th planet



Biology echology the new fronteer
Biology& EchologyThe New fronteer

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


Echology damouth law
Echology: Damouth-law



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


3/4 ???


Kleiber and dynamics
Kleiber and dynamics…

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



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


Logistic function gompertz
Logistic-function,Gompertz….

  • The solutions of the Eq.

  • Is a logistic type



Growth of tumor masses
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 and energetic
Prostate and breast cancer andenergetic

  • age 40 years


Tumor cell evolution
Tumor cell evolution

Evolution of the tumor cell number vs time, final mass

671 g, different evolution times


Tumor and host organ
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
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



Tumor and methastases
Tumor and methastases spreading

  • Statistical model, Poissonian distribution

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


Evolution of methastasis
Evolution of methastasis spreading

  • 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 spreading 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)


Angiogenesis
Angiogenesis spreading


Conclusions
Conclusions spreading

  • 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


Conclusions1
…Conclusions spreading

  • E=6 eV typical value of biochemical reactions




spreading


ad