A Quantitative Look at Problems in Cancer Chemotherapy

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A Quantitative Look at Problems in Cancer
Chemotherapy

• David Isaacson
• RPI

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Main Problem

• Can we improve the treatment of cancer by using
  mathematical models?

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Problem

• How to use existing Drugs?

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BREAST CANCER Adjuvant Therapy Combination
Regimens AC Doxorubicin 60 mg/m2 IV on day
1 Cyclophosphamide 600 mg/m2 IV on day 1 Repeat
cycle every 21 days for a total of 4 cycles
(21). AC?T Doxorubicin 60 mg/m2 IV on day
1 Cyclophosphamide 600 mg/m2 IV on day 1 Repeat
cycle every 21 days for a total of 4 cycles,
followed by Paclitaxel 175 mg/m2 IV Repeat cycle
every 21 days for a total of 4 cycles (22).
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CAF Cyclophosphamide 600 mg/m2 IV on day
1 Doxorubicin 60 mg/m2 IV on day
1 5-Fluorouracil 600 mg/m2 IV on day 1 Repeat
cycle every 21 days for a total of 6 cycles
(23). or Cyclophosphamide 100 mg/m2 PO on days
114 Doxorubicin 30 mg/m2 IV on days 1 and
8 5-Fluorouracil 500 mg/m2 IV on days 1 and
8 Repeat cycle every 28 days for a total of 6
cycles (24). CMF (Bonadonna regimen) Cyclophospham
ide 100 mg/m2/day PO on days 114 Methotrexate
40 mg/m2 IV on days 1 and 8 5-Fluorouracil 600
mg/m2 IV on days 1 and 8 Repeat cycle every 28
days for a total of 6 cycles (25). Physicians
Cancer Chemotherapy Drug Manual 396
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CMF (IV regimen) Cyclophosphamide 600 mg/m2 IV
on day 1 Methotrexate 40 mg/m2 IV on day
1 5-Fluorouracil 600 mg/m2 IV on day 1 Repeat
cycle every 21 days for a total of 6 cycles
(26). Doxorubicin CMF Doxorubicin 75 mg/m2 IV
on day 1 Repeat cycle every 21 days for a total
of 4 cycles. then Cyclophosphamide 600 mg/m2 IV
on day 1 Methotrexate 40 mg/m2 IV on day
1 5-Fluorouracil 600 mg/m2 IV on day 1 Repeat
cycle every 21 days for a total of 8 cycles
(27). FEC 5-Fluorouracil 500 mg/m2 IV on day
1 Epirubicin 100 mg/m2 IV on day
1 Cyclophosphamide 500 mg/m2 IV on day 1 Repeat
cycle every 21 days for a total of 6 cycles
(28). CMFP Cyclophosphamide 100 mg/m2 PO on days
114 Methotrexate 40 mg/m2 IV on days 1 and
8 5-Fluorouracil 600 mg/m2 IV on days 1 and
8 Prednisone 20 mg PO qid on days 17 Repeat
cycle every 28 days (29).
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Tamoxifen Tamoxifen 20 mg PO daily for 5 years
in patients with ER tumors or ER status
unknown Repeat daily for 5 years (30).
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Metastatic Disease Combination Regimens AC Doxorub
icin 60 mg/m2 IV on day 1 Cyclophosphamide 600
mg/m2 IV on day 1 Repeat cycle every 21 days
(21). AT Doxorubicin 50 mg/m2 IV on day
1 Paclitaxel 150 mg/m2 IV over 24 hours on day
1 Repeat cycle every 21 days (31). CAF Cyclophosph
amide 600 mg/m2 IV on day 1 Doxorubicin 60
mg/m2 IV on day 1 5-Fluorouracil 600 mg/m2 IV on
day 1 Repeat cycle every 21 days
(23). CEF Cyclophosphamide 75 mg/m2/day PO on
days 114 Epirubicin 60 mg/m2 IV on days 1 and
8 5-Fluorouracil 500 mg/m2 IV on days 1 and
8 Repeat cycle every 28 days (32).
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CMF (Bonadonna regimen) Cyclophosphamide 100
mg/m2/day PO on days 114 Methotrexate 40 mg/m2
IV on days 1 and 8 5-Fluorouracil 500 mg/m2 IV
on days 1 and 8 Repeat cycle every 28 days
(25). CMFIV Bolus Cyclophosphamide 600 mg/m2 IV
on day 1 Methotrexate 40 mg/m2 IV on day
1 5-Fluorouracil 600 mg/m2 IV on day 1 Repeat
cycle every 21 days (26). Physicians Cancer
Chemotherapy Drug Manual 398 Capecitabine
Docetaxel (XT) Capecitabine 1,250 mg/m2 PO bid
on days 114 Docetaxel 75 mg/m2 IV on day
1 Repeat cycle every 21 days (33). Docetaxel
Doxorubicin Docetaxel 75 mg/m2 IV on day
1 Doxorubicin 50 mg/m2 IV on day 1 Repeat cycle
every 21 days (34). FEC-100 5-Fluorouracil 500
mg/m2 IV on day 1 Epirubicin 100 mg/m2 IV on day
1 Cyclophosphamide 500 mg/m2 IV on day 1 Repeat
cycle every 21 days (35).
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Paclitaxel Vinorelbine Paclitaxel 135 mg/m2 IV
over 3 hours on day 1, starting 1 hour after
vinorelbine Vinorelbine 30 mg/m2 IV over 20
minutes on days 1 and 8 Repeat cycle every 28
days (36). Vinorelbine Doxorubicin Vinorelbine
25 mg/m2 IV on days 1 and 8 Doxorubicin 50 mg/m2
IV on day 1 Repeat cycle every 21 days
(37). Trastuzumab-Paclitaxel Trastuzumab 4 mg/kg
IV loading dose, then 2 mg/kg weekly Paclitaxel
175 mg/m2 IV over 3 hours every 21 days Repeat
cycle every 21 days (38) or Trastuzumab 4 mg/kg
IV loading dose, then 2 mg/kg weekly Paclitaxel
80 mg/m2 weekly Repeat cycle every 4 weeks (39).
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Mitomycin Vinblastine Mitomycin 20 mg/m2 IV on
day 1 Vinblastine 1.42 mg/m2 IV continuous
infusion on days 15 Repeat cycle every 6-8 weeks
(40). Single-Agent Regimens Tamoxifen Tamoxifen
20 mg PO daily (41) Toremifene citrate Toremifene
60 mg PO daily (42) Exemestane Exemestane 25 mg
PO daily (43) Anastrozole Anastrozole 1 mg PO
daily (44) Letrozole Letrozole 2.5 mg PO daily
(45) Fulvestrant Fulvestrant 250 mg IM on day
1 Repeat injection every month (46). Megestrol Meg
estrol 40 mg PO qid (47)
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Trastuzumab Trastuzumab 4 mg/kg IV loading dose,
then 2 mg/kg IV weekly Repeat cycle weekly for a
total of 10 weeks. In the absence of disease
progression, continue weekly maintenance dose of
2 mg/kg (48). Capecitabine Capecitabine 1,250
mg/m2 PO bid for 2 weeks followed by 1 week rest
period Repeat cycle every 21 days (49). May
decrease dose to 1,000 mg/m2 PO bid on days 114
to reduce the risk of toxicity without
compromising antitumor activity. Docetaxel Docetax
el 100 mg/m2 IV on day 1 Repeat cycle every 21
days (50). Physicians Cancer Chemotherapy Drug
Manual 400 or Docetaxel 3540 mg/m2 IV weekly
for 6 weeks Repeat cycle every 8 weeks (51).
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Paclitaxel Paclitaxel 175 mg/m2 IV over 3 hours
on day 1 Repeat cycle every 21 days
(52). or Paclitaxel 80100 mg/m2 IV weekly for 3
weeks Repeat cycle every 4 weeks
(53). Vinorelbine Vinorelbine 30 mg/m2 IV on day
1 Repeat cycle every 7 days (54). Doxorubicin Doxo
rubicin 20 mg/m2 IV weekly Repeat cycle weekly
(55). Gemcitabine Gemcitabine 725 mg/m2 IV
weekly for 3 weeks Repeat cycle every 28 days
(56). Liposomal Doxorubicin Liposomal
Doxorubicin 4560 mg/m2 IV on day 1 Repeat cycle
every 2128 days (57).
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Which combinations, order, schedule, and doses
should one use for each patient? 1.Which
Drugs?2.What dose?3.What order?3.What
frequency of dose?4.How many doses?
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Problem

• How to design new drugs?

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Extremely Simple ExamplesTo illustrate
mathematical modeling of Cell Growth and
Treatment
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Possible Solution

• Use quantitative modeling experiment to
  rationally design treatment regimens with
  existing drugs.
• Develop methods of patient monitoring to measure
  important quantities during treatment.
• Test with Clinical trials.
• Make and test quantitative models of signal
  transduction and cell cycle control networks .

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How do cells grow?DefineN(t) of cells at
time t (hours).TDoubling time
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How do we treat cancer?
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Why not just give a large dose or many rapid
doses in succession until cancer is wiped out?
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Limited by destruction of normal proliferating
cells!ExBlood cells (Pluripotent stem cells)
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How to take this into account ?Simple Model
follows
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What do we need to measure?

• N(0) Number of cancer cells initially
• r Proliferation rate of cancer cells
• f Fraction of cancer cells killed/dose
• Nb(0) Number of normal proliferating cells
  (blood)
• rb Proliferation rate of blood cells
• fb Fraction of blood cells killed/dose

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For cure SIMPLE model says

• Choose drug so that

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How do we decide the order of the drugs?Need
more accurate model with cell cycle and
resistance and ???.
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Show New Models- if time permits for N(t,c) or
more accuratelyN(t,x,g,p)
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Final ProblemCan mathematical modeling improve
the treatment of cancer?
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Thank you!

• Especially
• I.R.