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Probabilidad de Control del Tumor (TCP)

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>Model

ID:(740, 0)

Probabilidad de Control del Tumor (TCP)

Storyboard

Variables

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

$N^n$

N^n

Exponential $N^n$

$n$

Number

$N$

Número de celulas cancerigenas

$N$

Número total de pasos

$TCP$

TCP

Probabilidad de Control Tumoral TCP

$SF_n$

SF_n

Probabilidad de Sobrevivencia de Celulas

Calculations

Equation

Number

First, select the equation:

, then, select the variable:

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable

Given

Calculate

Target :

Equation

To be used

Equations

$TCP=P(0)$

TCP=P(0)

$P_k(\lambda)=\displaystyle\frac{\lambda^k e^{-\lambda}}{k!}$

P_k(lambda)=(lambda^k e^-lambda)/k!

$P(N)=e^{-N/N_0}$

P(N)=e^(-N/N_0)

$ TCP(D) =e^{- N SF_n }$

TCP_D =exp(- N * SF_n )

$TCP=\prod_{i=1}^MP(D_i)^{v_i}$

TCP=prod_i=1^MP(D_i)^v_i

$N^n\sim\displaystyle\frac{N!}{(N-n)!}$

N^n\sim\displaystyle\frac{N!}{(N-n)!}

Examples

Probabilidad de Control del Cancer

TCP=P(0)

Application of the Sterling Approach

Therefore expressions such as N!/(Nn)! for N large (N\gg 1) and n small (N\gg n) can be approximated with

equation=8966

with what you get with N\gg n

\displaystyle\frac{N!}{(N-n)!}\sim\displaystyle\frac{\sqrt{2\pi N}}{\sqrt{2\pi (N-n)}}\displaystyle\frac{N^N}{(N-n)^{N-n}}\displaystyle\frac{e^{N-n}}{e^N}\sim N^n

that is

equation

Probabilidad con el Modelo de Poisson

P_k(\lambda)=\displaystyle\frac{\lambda^k e^{-\lambda}}{k!}

Probabilidad de Control Tumoral con Modelo de Poisson

P(N)=e^{-N/N_0}

Probabilidad de Control Tumoral con Modelo L-Q

TCP(D)=e^{-SF}

Probabilidad de Control Tumoral real

TCP=\prod_{i=1}^MP(D_i)^{v_i}

>Model

ID:(740, 0)