BME 150 Challenge Based LearningGroup 26

Amanda HongRonald Luu

Roland ModerTony Nguyen

Calvin Song

64-year-old male. Coming into the Emergency Department with chief complaint of abdominal swelling.

Patient X seems to have a yellow pigment which he says is abnormal.

Upon physical examination, patient has an enlarged liver.

Past medical history indicates patient has compensated cirrhosis.

Ultrasound and CT scans◦ Indicate a single large tumor mass that has not

metastasized

◦ Diameter >5 cm

L. Criotti et al.: Peri-intraproceduralimaging: US, CT, and MRI

Liver cancer or hepatocellular carcinoma◦ Is an increasingly common tumor

◦ With a poor prognosis

◦ Limited systemic treatment options

◦ Approximately 80% of patients die within a year of diagnosis

◦ In men, it is the fifth most common cancer worldwide and the third leading cause of cancer-related death

Describes the severity of the cancer – size, metastasis, etc.

Tells physicians survival rates and cancer treatment

Many staging systems for hepatocellular carninoma including:◦ Cancer of the Liver Italian Program Score

◦ Chinese University Prognostic Index

◦ Barcelona Liver Clinic

Useful because it integrates liver function and tumor features into classification.

O'Neil, B. H. et al. Oncologist 2007;12:1425-1432

Model the drug transport from the microsphere into the tumor mass.

Decide whether TACE is an appropriate treatment over traditional chemotherapy.

Treat patient X successfully and thoroughly.

Catheter through the leg up to the hepatic artery◦ Hepatic artery chosen since ~90% of blood supplied

to liver is from hepatic artery during cancer.

◦ During procedure, use imaging device to locate specific arteries that lead to the tumor.

1. How are conventional chemotherapy and TACE drug delivery similar/different?

2. How do the two methods deliver drugs similarly/differently (in terms of drug concentration/delivery rate/time), how does this affect their models?

3. How do the drugs travel through the occluded blood vessel to the tumor cell?

4. At what rate does the microsphere elute the drug?

Conventional chemotherapy TACE

Difference

Chemotherapeutic agents end up in the

rest of the body.

Systemic side effects

Liver failure can be developed with

advanced cirrhosis patients.

Embolization blocks all the

small blood vessels.

No blood flow can take

chemotherapeutic agents to other

part of the body.

Increased concentration of

chemotherapy.

Cutting off blood flow leads to

tumor cell apoptosis

Future attempts at intra-arterial

infusions are impossible.

Similarity

Takes advantage of the fact that liver cancer is very vascularized and the blood

supply exclusively from the hepatic artery.

Drugs are delivered by inserting catheter into hepatic artery which supplies the

liver tumor.

The type and frequency of complications are simular.

Conventional Chemotherapy TACE

Higher Dosage Necessary % of drug that reaches the tumor

Immediate delivery, some gets processed by liver, the rest is toxic throughout the body

Slow paced elution of drugs over a long period of time

Modeled with mass convective surface boundary that will decrease exponentially over time

Modeled with constant elution rate, decreasing concentration over time

Occluded blood vessel: a blood vessel that is closed or stopped due to an obstruction

Assume that the blood after the microsphere is not moving.

Model can be simplified, drug travels through blood follows diffusion principles.

Tumor Mass

5 cm

1D or 2D?

Analytical or Numerical?

Simplifications◦ No mass generation/consumption

◦ Storage is not equal to 0

Boundary Condition possibilities◦ Convective?

◦ Constant surface concentration?

◦ Constant mass flux?

1) 1D, not 2D2) Transient, not steady state

◦ model drug release over long period of time◦ consider initial release of drug from microsphere as fast

and, over a long duration of time, a slow release of drug

3) Not semi-infinite◦ drug needs reach a certain depth of the tumor cell

cannot neglect the distance that the drug travels through the tumor cell compared to the entire length of the tumor cell

4) Numerical, not analytical finite difference,5) No consumption of drug within tumor cell Eg = 06) Constant mass flux (j‖) 7) The microsphere approaches tumor cell as close as

possible such that the drugs are release directly into tumor cell and does not pass through the blood (fluid)

Therefore, no diffusion occurs through the layer of blood in the vessel, but directly to the tumor cell from the microsphere.

This is the best case scenario for maximum drug diffusion.

1-D transient Finite difference model with constant mass flux as a boundary condition

Surface node:C0

p+1 = (1-2Fom)C0p+2*Fo((∆x/D)j‖+C1

p)

Internal nodes:Ci

p+1 = (1-2Fom)Cip+Fo(Ci-1

p+Ci+1p)

Where Fom is Fourier’s number for mass transfer

and it is defined as Fom = (D*∆t)/((∆ x)^2)

How to create a simple model that can be remodeled easily.◦ Use Excel – label all constants and variables, link

values to the equations

To qualitatively show the effectiveness of TACE.◦ Find [Dox] where cell death occurs

How is Dox transport across membranes affect rate of diffusion?◦ Success of clinical trials show that it doesn’t greatly

affect the rate of diffusion => model without internal membranes

Value Description

0 cm Minimum depth

0.1 cm Depth interval

0 g/cm3 Uniform initial concentration

1.50E-06 cm2/s Mass diffusivity

0 hours Initial Time Point

0.92592593 hours Time interval

6.32E-07 g/cm2 s Constant mass flux

1.83E-01 cm2 Area of hepatic artery

0.5 Mass Fourier number

1.16E-07 g/s Drug elution rate

5.80E+02 g/mol Molecular Mass of Doxorubicin

2.25E-05 g/cm3 Cell Death Concentration

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 24 48 72 96 120 144

Co

nce

ntr

atio

n (

g/c

m^3

)

Time (Hours)

1D Transient Finite Difference Constant Mass Flux Model

0.000

0.200

0.500

0.900

1.400

2.000

178

Depth (cm)

0.00E+00

2.25E-05

4.50E-05

6.75E-05

9.00E-05

1.13E-04

1.35E-04

1.58E-04

1.80E-04

96 120 144 169

Co

nce

ntr

atio

n (

g/c

m^3

)

Time (Hours)

1D Transient Finite Difference Constant Mass Flux Model (From 4.4 to 5 cm)

4.4

4.5

4.6

4.7

4.8

4.9

5

Cell DeathConcentration

Depth (cm)

Our model with no limitations or consumption predicts:

Cell at center of tumor will die in 6.40 days.

Compare this to conventional chemotherapy with necrosis in less than 50% of patients.

In scenarios close to ideal, TACE works extremely well.

Microspheres absorbed into tumor tissue increases drug delivery.

TACE is a good option for patient X◦ Localized, Semi-Specific (Doxorubicin is more

prone to affect proliferating cells)◦ Small concentrations of Dox in blood stream will

quickly be nullified by the liver => no systemic damage

◦ Dual action – drug elution and blocking transmission of nutrients to the tumor

Chance of great success with minimal risk.Patients have longer lifespan after diagnosed, when treated with TACE instead of standard Chemotherapy and less severe side affects

Different possible models: ◦ Drugs flow into interstitial space (2D and infinite sink

as side boundary conditions) then to cancerous cell and normal cell.

◦ Constant convective flow of mass (probably lower concentration) with diffussion directly to the center(nucleus) of the cancer cell.

Permeability of the drug into the tumor mass. If that would slow or speed up the mass transport model.

Consumption term, how drug is used as it travels through the tumor.

Also we would model the conventional chemotherapy for comparison.

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