1. Stoichiometric Tumor Model: Phosphorus Flow By: Bo Deng, Vladimir Ufimtsev and Melissa Wilson Funded By NSF/REU Grant to University of Nebraska-Lincoln

2. Stoichiometry- Mass Balance: The concept that matter is conserved. Whatever is put into a system either remains in the system or is excreted from it. On each side of the equation there are: 2-Oxygens 4-Hydrogens The quantitative relationship between elements in a system.

3. PHOSPHORUS!! Metabolic Pathways ATP – Adenosine Tri-Phosphate DNA/RNA Replication http://www.blc.arizona.edu/Molecular_Graphics/DNA_Structure/DNA_Tutorial.HTML#Components

4. http://www.accessexcellence.org/AB/GG/dna_replicating.html

5. Measuring Phosphorus Phosphorus makes up: 1% of Healthy Cells 2% of Tumor Cells Using a healthy person of average mass,70kg, excluding bone mass, 8.9kg, with no tumor, her mass becomes: 61.1 kg of Healthy Cells* (1 kg of Phos/100 kg of Healthy Cells) =.611 kg of Phos* (1000 g/kg) = 611 g of Phos Kuang et al. 2004, Williams 2002

6. Holling’s uptaking/capturing functional form (1959) P P P P P P P Total area =, Area of 1 P = Machine will tap at the board at a rate of: k taps per unit of time. P PP P P How many units of prey (discs) will the machine tap, in a given search time; ? Number of discs = P (remains constant)

7. P P P P P P P Total area = Area of 1 P = P PP P P How many units of prey (discs) will the machine capture, in a given time; ? The total time spent searching becomes: Handling time for each disc =

9. Total number of P captured by Y many machines or cells in a unit time is Also known as the Monod-Jacob form (1961) or the Michaelis-Menten form (1913)

10. http://www4.tpgi.com.au/users/amcgann/body/circulatory.html

11. Quantities H = Amount of Healthy cells that compose the body (without the organ). O = Amount of Healthy cells that compose the organ. P = Amount of Phosphorus in the blood stream. IMPORTANT: The amounts of all quantities in the system are specified by the amount of Phosphorus that each quantity possesses.

12. Quantities H = Amount of Healthy cells that compose the body (without the organ). O = Amount of Healthy cells that compose the organ. P = Amount of Phosphorus in the blood stream. IMPORTANT: The amounts of all quantities in the system are specified by the amount of Phosphorus that each quantity possesses.

13. http://www.robertsreview.com/cancer_pictures.html http://www.maths.dundee.ac.uk/~sanderso/tumour.htm Liver Cancer Angiogenesis Organ and Tumor

14. Quantities H = Amount of Healthy Cells that compose the body (without the organ) O = Amount of Healthy Cells that compose the organ T = Amount of Cancerous Cell that compose the tumor V = Amount of cells that compose the vessels in the tumor P = Amount of Phosphorus in the blood stream

16. The term for Tumor growth: The term is used to explain the distribution of Phosphorus throughout the circulatory system.

17. Immune Response Effector Cells NK Cells (Natural Killers) Attack like T-Cells

18. Natural Killer Cells http://www.cancerfoundation.com/NKcells.htmlhttp://www.cancerfoundation.com/NKcells.html, 2004 Natural Killer Cell (NK Cell) cell destroying a targeted tumor cell. Tumor cell NK Cell

20. Antigenicity

25. Days until tumor detected

26. Tumor Dynamics without Therapy

27. Chemotherapy and Tumor Death