Mutation Research 770 (2014) 120–127

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Optimal standard regimen and predicting response to docetaxel therapy Emad Y. Moawad ∗,1 Department of Engineering, Ain Shams University, Cairo, Egypt

a r t i c l e

i n f o

Article history: Received 16 May 2014 Received in revised form 2 August 2014 Accepted 20 August 2014 Available online 27 August 2014 Keywords: In vivo Antimicrotubule agent Cell-cycle specific drugs Docetaxel Emad formula Mitotic index

a b s t r a c t The purpose of this research is optimizing and predicting the potent activity of docetaxel through an efficient regimen to settle down a new protocol for the treatment of cancer. Effectiveness of docetaxel was examined in vivo in several mouse models engrafted either subcutaneously or intravenously with several types of cell lines. The effects of 147–5040 mg/L of docetaxel in treatments of different regimens in those xenograft growths were monitored and quantified to identify energy of those doses as described before in earlier studies. Mock processes were performed on untreated groups of mice for controls. Docetaxel had significant influence on all sizes of treated tumors compared to the control animals. The longer the induced tumor doubling time intraday to more than half the time period from the start of therapy to the time of delivery of the dose, the higher the energy of docetaxel doses and hence the effectiveness of the treatment and vice versa. The energy yield by drug doses in optimal standard regimens was perfectly power correlated (r = 1) with the drug dose. An efficient dose-energy model with a perfect fit (R2 = 1) estimating the energy yield by docetaxel doses in optimal standard regimens has been established to administer the personalized dose. Administration of docetaxel doses should be patient-specific and sufficient for the suggested regimen. Time periods from the start of therapy to the time of dose delivery of the efficient regimen are shorter than twice the tumor doubling time intraday on time of dose delivery. Patients with tumors of lower mitotic index may particularly benefit more from optimal standard regimens, whereas metronomic regimens would be more efficient in patients with tumors of higher mitotic index that need lower doses of docetaxel. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Microtubules are part of a structural network (the cytoskeleton) within the cell’s cytoplasm play a huge role in movement within a cell [1]. They are essential in a number of cellular processes and play a crucial role in multiple steps of mitosis including the formation of mitotic spindles [2]. They form the spindle fibers that manipulate and separate chromosomes during mitosis [3]. Docetaxel (as generic or under the trade name Taxotere) is an antimicrotubule agent belongs to a class of chemotherapy drugs called cell-cycle specific affect cells only when they are dividing [4]. Docetaxel is a clinically well-established anti-mitotic chemotherapy medication (that is, it interferes with cell division) [5]. Docetaxel binds to microtubules reversibly with high affinity and has a maximum

∗ Correspondence to: 217 Alhegaz Street, Alnozha, 11351 Cairo, Egypt. Tel.: +20 1223370090; fax: +20 226225933. E-mail address: [email protected] 1 A member of the Korean Society of Nuclear Medicine. http://dx.doi.org/10.1016/j.mrfmmm.2014.08.006 0027-5107/© 2014 Elsevier B.V. All rights reserved.

stoichiometry of 1 mole docetaxel per mole tubulin in microtubules [6]. This binding stabilizes microtubules and prevents depolymerisation from calcium ions, decreased temperature and dilution, preferentially at the plus end of the microtubule [6]. The main mode of therapeutic action of docetaxel is the suppression of microtubule dynamic assembly and disassembly, rather than microtubule bundling leading to apoptosis, or the blocking of bcl-2 which also encourages apoptosis [4,6]. As microtubules do not disassemble in the presence of docetaxel, they accumulate inside the cell and cause initiation of apoptosis [6]. Furthermore, it has also been found that docetaxel leads to the phosphorylation of oncoprotein bcl-2, which is apoptosis-blocking in its oncoprotein form [4]. Both in vitro and in vivo analysis show the anti-neoplastic activity of docetaxel to be effective against a wide range of known cancer cells, cooperate with other anti-neoplastic agents activity, and have greater cytotoxicity than paclitaxel, possibly due to its more rapid intracellular uptake [4]. Many studies have been shown that docetaxel has been found to accumulate to higher concentration in ovarian adenocarcinoma cells than kidney carcinoma cells, which may contribute to the more effective treatment of ovarian cancer

E.Y. Moawad / Mutation Research 770 (2014) 120–127

by docetaxel [4,6]. But effectiveness of docetaxel treatment was related to the mitotic index of the treated tumors as all cell cycle specific drugs so that in some cases docetaxel treatment had not shown a significant effect on the tumor stage. However the effectiveness of docetaxel versus paclitaxel and other taxanes is still controversial. Several more recent articles have found “no evidence those regimens containing docetaxel yield greater benefits than those including paclitaxel [7]. Additionally, the optimal scheduling of docetaxel and other taxanes remains unconfirmed. Recently, Moawad developed a model of clinical based staging of the cancer at the cellular level in which the effect on the cancer stage due to therapy can be estimated and consequently effectiveness of the treatment can be determined [8–13]. Further exploration into the mechanism(s) of action is required for optimizing docetaxel administration through an efficient regimen for this anticancer molecule whose full therapeutic potential is yet to be realized. Current approach investigates several regimens of docetaxel treatments applied on models of murine tumors xenografts of different types and cell lines. Assessment of the efficient regimen for optimizing cell-cycle specific therapy would be based on achieving an accumulated doubling time-energy conversion [8–24] in the tumor cells by the regimen doses. 2. Materials and methods 2.1. Monitoring the mechanical behavior of the tumor response to therapy Comparing the mechanical behavior of tumor response of the treated groups to that of the control groups is assessed by determining the growth/or shrinkage constants of those tumors of different volumes along the corresponding periods [25,26]. The growth/or shrinkage constant of the tumor at a certain time expresses the rate of the difference between Mitosis and Apoptosis with respect to the total number of the tumor cells (M–A) that characterize the tumor response at that time [8–19]. If rate of mitosis is greater than that of apoptosis, tumor grows by growth constant of ln 2/tD , where tD is the tumor doubling time and vice versa if rate of mitosis is less than that of apoptosis, tumor shrinks by shrinkage constant of ln 2/t1/2 , where t1/2 is the tumor half-life time [8–19,25,26], i.e. (M − A) =

ln 2 −1 S in case of tumor growth, tD (1)

and ln 2 −1 S in case of tumor shrinkage (A − M) = t1/2

where tD and t1/2 in seconds, Eq. (1) The clinical staging model presented by Moawad showed that the tumor histologic grade (HG ) that expresses tumor response can be identified by using Emad formula [8–24] as follows: In case of tumor growth:



HG = ln ln

ln 2 tD

2

121

first from mitosis. The greater the shrinkage portion of the tumor, the more the efficiency of the treatment and hence replaced by a smaller virtual growing portion and vice versa. Thus, rate of the virtual growth would be inversely proportional to the rate of the tumor shrinkage as follows:

V

Initial

− VFinal

VInitial



= Shrinkage



VInitial VFinal − VInitial

 (3) Virtual growth

where V is the tumor volume. Accordingly from Eqs. (1) and (2), the alteration in the treated tumor HG to that of the control tumor induced by the drug dose would be equivalent to the energy yield by the drug dose according to the following model: EDose = [ln (ln (M − A)Treated )2 − ln (ln (M − A)Control )2 ] × C0 × h × 23234.59 MeV

(4)

3. Effectiveness of docetaxel treatment assay It should be noted that, clinical evidence indicates tumor growth is not constant over the life cycle of a tumor, but varies over time with increased doubling time and decreased growth. This model allows the tumor to approach, but not exceed, a maximum volume as it ages, consistent with the biological behavior of tumors in which tumor growth rate decreases as the metabolic demands of the enlarging tumor exceed the host’s capacities to provide nutrients. Thus, tumor tD intraday increases linearly with time for specific initial and final volumes according to the exponential growth model as follows: TumortD intraday =

ln 2 × t sec ln VFinal − ln VInitial

(5)

as the time period (t) from initiating therapy increases the tumor doubling time (tD ) intraday increases and hence the effectiveness of the treatment. Accordingly, the criterion of the efficient regimen of docetaxel treatment can be determined by comparing the tumor tD intraday to the time period from initiating therapy on time of dose delivery in the studied regimen. As described and conducted by several authors, Table 1 shows growth inhibition in tumors of different cell lines in murine experiments by docetaxel in different regimens [27–34]. 4. Results and analysis From data shown in Table 1 and Eqs. (1)–(5), tumor tD and energy yield by docetaxel doses were derived as follows: 4.1. For treatment 1 of metronomic regimen

× C0 × h × 23234.59 MeV

(2)

where C0 × h is number of the hypoxic cells in the tumor or number of the inoculated cells in the transplanted tumor in xenografted models. In case of tumor shrinkage: The chemotherapeutic drugs affect the tumor cells such that the more the drug dose the less of mitotic cells or the more of apoptotic cells. Since the portion of tumor cells underwent apoptosis due to anti-microtubule agents therapy had been prevented first from mitosis. Thus to apply Eq. (2) in the shrinking case, the apoptotic tumor portion of half-life time (t1/2 ) would be replaced by virtual growing portion of doubling time (tD ) which had been prevented

4.1.1. HeyA8 xenograft From Table 1 and Eq. (5), the average tumor size of control group grew from 100 mm3 (0.1 g) at the beginning of the treatment to 1200 mm3 in 24.5 days (3.5 weeks) with doubling time (tD ) of 6.834102168 days. While, the average tumor size of the treated group grew from 100 mm3 to 288 mm3 in 24.5 days with tD of 16.05432194 days. Metronomic regimen of 0.5 mg/kg docetaxel thrice a week for 3.5 weeks in human (70 kg, 2.5 L plasma) is equivalent to (0.5 × 3 × 3.5 × 70 mg/2.5 L) 147 ␮g/mL. Thus from Eqs. (1) and (4), the energy yield by 147 ␮g/mL of docetaxel (EDocetaxel(147 ␮g/mL) ) in tumor xenograft of transplanted 2.5 × 105 HeyA8 cells was equivalent to:

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Table 1 shows data presented in several studies of docetaxel anticancer effect on different types of tumor models of different cell lines. Treatment Number

Authors

Injected cell line

1

Kamat et al. (2007) [25]

(2.5 × 105 ) HeyA8 cells

147

2

Williams et al. (2000) [26]

(1 × 106 )MAT-LyLu (MLL) cells

392

3

Liu et al. (2008) [27]

(5 × 106 ) Hep-2 cells

420

4

Li et al. (2006) [28]

(1 × 106 ) PC-3 cells

420

5

Sanjeev Banerjee et al. (2007) [29]

(1 × 10 ) C4-2b cells

560

6

Williams et al. (2000) [26] Sweeney et al. (2005) [30] Ichite et al. (2009) [31] Kamat et al. (2007) [25] Kamat et al. (2007) [25] Kamat et al. (2007) [25] Yoo et al. (2005) [32]

(1×106 ) MAT-LyLu (MLL) cells (1 × 106 ) MDA-MB-231 cells (1 × 106 ) A549 cells

649.6

(1 × 106 ) SKOV3ip1 cells (1 × 106 ) HeyA8 MDR cells (2.5 × 105 ) HeyA8 cells (15 × 106 ) of HNSCC line; HN30

840

13

Yoo et al. (2005) [32]

(15 × 106 ) of HNSCC lines; HN30

5040

14

Yoo et al. (2005) [32]

(15 × 106 ) of HNSCC line; and HN12

5040

7 8 9 10 11 12

  

EDocetaxel (147 ␮g/mL) = ln ln

 

− ln ln

Docetaxel dose (␮g/mL)

6

840

840 840 2100

ln 2 6.834102168 × 24 × 60 × 60

2 

2

× 2.5 × 105

× 23234.59 = 7.04777881 × 108 MeV

Control tumor volume (cm3 )

Treated tumor volume (cm3 )

0.5 mg/kg thrice weekly for 3.5 weeks Two doses of 7 mg/kg on days 4 and 11 Two doses of 7.5 mg/kg/week

From 0.1 to 1.2 in 3.5 weeks

From 0.1 to 0.288 in 3.5 weeks

From 0.5 to 4.8 in 10 days

From 0.5 to 4.4 in 10 days

From 0.15 to 0.45 in 14 days

From 0.57 to 1.93 in 11 days From 0.1 to 0.99 in 31.5 days (4.5 weeks)

Shrunk from 0.15 to 0.09 in 6 days and then grew from 0.09 to 0.17 in 8 days From .54 to 1.28 in 11 days From 0.1 to 0.371 in 31.5 days (4.5 weeks)

From 0.5 to 4.8 in 10 days From 0.06 to 0.24 in 14 days From 0.05 to 0.26 in 14 days From 0.1 to 0.75 in 3.5 weeks From 0.1 to 2.2 in 3.5 weeks From 0.1 to 1.2 in 3.5 weeks From 0.4 to 1.7 in 35 days

From 0.5 to 1.63 in 10 days From 0.232 to 0.42 in 17 days From 0.05 to 0.09 in 14 days From 0.1 to 0.201 in 3.5 weeks From 0.1 to 2.0 in 3.5 weeks From 0.1 to 0.42 in 3.5 weeks From 0.4 to 0.192 in 35 days

From 0.4 to 1.7 in 35 days

From 0.4 to 0.02 in 85 days

From 0.25 to 2.5 in 35 days

From 0.25 to 0.05 in 40 days

Three doses of 5 mg/kg on 6 days 5 mg/kg body weight given i.v. every 3rd day (total of four doses) 11.6 mg/kg on days 4 and 11 5 mg/kg/week for 6 weeks 10 mg/kg on days 14, 18 and 22 15 mg/kg/2 weeks for 4 weeks 15 mg/kg/2 weeks for 4 weeks 15 mg/kg/2 weeks for 4 weeks 7.5 mg/kg per injection twice a week for 6 weeks 15 mg/kg per injection twice a week for 6 weeks 15 mg/kg per injection twice a week for 6 weeks

840

ln 2 16.05432194 × 24 × 60 × 60

Regimen

to:

  

EDocetaxel (392 ␮g/mL) = ln ln

 

ln 2 3.19 × 24 × 60 × 60

ln 2 − ln ln 2.06 × 24 × 60 × 60

2 

2

× 1 × 106 × 23234.59

= 1.41615948 × 108 MeV From Eq. (5), the tumor tD intraday of the treated tumor at the delivery of the second dose after 2 days from initiating therapy was equivalent to (ln 2/(ln 0.288 − ln 0.1) × 2) 1.31055689 days > 1 day (longer than half the interval (2 days) between doses).

4.2. For treatment 2 of standard regimen 4.2.1. MAT-LyLu (MLL) xenograft From Table 1 and Eq. (5), the average tumor size of control group grew from 50 mm3 at the beginning of the treatment to 480 mm3 in 10 days with doubling time (tD ) of 3.06463211 days. While, the average tumor size of the treated group grew from 50 mm3 to 440 mm3 in 10 days with tD of 3.18724742 days. On day 4 and day 11, two doses of docetaxel of 7 mg/kg were delivered. Those doses in human (70 kg, 2.5 L plasma) are equivalent to (7 × 2 × 70 mg/2.5 L) 392 ␮g/mL. Thus from Eqs. (1) and (4), the energy yield by 392 ␮g/mL of docetaxel (EDocetaxel (392 ␮g/mL) ) in tumor xenograft of transplanted 1 × 106 MLL cells was equivalent

From Eq. (5), the tD intraday of the treated tumor at the delivery of the second dose on day 11 was equivalent to ((ln2/ln4.4 − ln0.5) × (11 − 4)) · 2.231073191 days < 3.5 days (shorter than half the interval (7 days) between doses which were on day 4 and day 11). Similarly, energy yield by other docetaxel doses along with the induced tumor tD intraday in the treated tumor on time of second dose delivery in the presented xerographs in treatments 2–11 were derived as shown in Table 2. 4.3. For treatment 12 of standard regimen 4.3.1. HN30 xenograft From Table 1 and Eq. (5), the average tumor size of control group grew from 400 mm3 at the beginning of the treatment to 1700 mm3 in 35 days with doubling time (tD ) of 16.76676552 days. While, the average tumor size of the treated group by 7.5 mg/kg per injection twice a week shrunk from 400 mm3 to 192 mm3 in 35 days. From Eq. (3), the volume of the virtual growing portion of the tumor that prevented from mitosis first before shrinking was

E.Y. Moawad / Mutation Research 770 (2014) 120–127

123

Table 2 shows the energy yield by docetaxel doses in different regimens applied on different types of tumor models. Treatment Number

Xenograft model

Control tumor doubling time in days

Treated tumor doubling time in days

Doubling time in the treated tumor on time of dose delivery after starting growth in days

Half the interval from the beginning of growth until the next dose delivery in days

Docetaxel dose ␮g/mL

Energy yield by Docetaxel dose in MeV

1 2 3 4 5 6 7 8 9 10 11 12 13 14

HeyA8 cells MLL cells Hep-2 cells PC-3 cells C4-2b cells MLL cells MDA-MB-231 cells A549 cells SKOV3ip1 cells HeyA8 MDR cells HeyA8 cells HNSCC line; HN30 HNSCC line; HN30 HNSCC line; HN12

6.834102168 3.06463211 8.83301655 6.251537938 9.52401534 3.064632105 7 5.88603388 8.42824977 5.493973693 6.834102168 16.76676552 16.76676552 10.53604985

16.05432194 3.18724742 9.472633871 8.821018346 16.6575174 5.87220054 19.8956135 16.5094942 24.5 5.66876622 11.83352313 22.6222159 55.8213612 33.75614154

1.31055689 2.231073191 1.184079234 1.603821517 1.057620152 4.110540378 8.192311441 4.716998343 14 3.239294983 3.38100661 2.26222159 2.298526638 2.953662385

1 3.5 0.5 1.5 1 3.5 3.5 2 7 7 7 1.75 1.75 1.75

147 392 420 420 560 649.6 840 840 840 840 840 2100 5040 5040

7.04777881 × 108 1.41615948 × 108 1.16467863 × 109 1.16467863 × 109 1.82115572 × 109 2.29354712 × 109 3.41958514 × 109 3.41958514 × 109 3.41958514 × 109 1.08187618 × 108 4.57932236 × 108 1.420130246 × 1010 5.5352137 × 1010 5.5352137 × 1010

(400 − 192/400 = 400/VF − 400) · 1168.96 mm3 in 35 days with tD of 22.6222159 days according to Eq. (5). A treatment of 7.5 mg/kg per injection twice a week for 5 weeks (35 days) in human (70 kg, 2.5 L plasma) is equivalent to (7.5 × 2 × 5 × 70 mg/2.5 L) 2100 ␮g/mL. Thus from Eqs. (1) and (4), (EDocetaxel (2100 ␮g/mL) ) yield in tumor xenograft of transplanted 15 × 106 HN30 cells was equivalent to:

  

EDocetaxel (2100 ␮g/mL) = ln ln

 

ln 2 22.6222159 × 24 × 60 × 60

ln 2 − ln ln 16.76676552 × 24 × 60 × 60

2 

2

× 15 × 106

× 23234.59 = 1.420130246 × 1010 MeV From Eq. (5), the tD intraday of the treated tumor at the delivery of the second dose after 3.5 days from treatment initiation was equivalent to (ln2/(ln1.16896 − ln0.4) × 3.5) · 2.26221874 days > 1.75 days (longer than half the interval (twice a week = 3.5 days) between doses). Similarly, energy yield by other docetaxel doses along with the induced tD intraday in the treated tumor on time of second dose delivery in the presented xerographs in treatments 13 and 14 were derived as shown in Table 2. From Table 2, it has been noticed that the longer the induced tumor doubling time intraday to more than half the time period from the start of therapy to the time of delivery of the dose, the higher the energy of docetaxel doses and hence the effectiveness of the treatment and vice versa. Energy yield in all the presented treatments of standard regimens except treatments (2, 10 and 11) was perfectly power correlated (r = 1) with drug dose as shown in Table 2 and Fig. 1. The following efficient power dose-energy model with a perfect fit (R2 = 1) shown in Fig. 2 and expressed in Eq. (6) estimating the energy yield by docetaxel dose in treatment of an optimal standard regimen. EDocetaxel

Dose

= 97716.267161 × (D)1.553889389 MeV

(6)

where D is the Docetaxel dose in ␮g/mL, EDocetaxel Dose is the corresponding energy yield of that dose in MeV. All the treated tumors by optimal standard regimens of correlated responses were characterized by tD intraday longer than half the time period from the start of therapy to time of dose delivery. Also, the energy yield by 147 ␮g/mL docetaxel in the metronomic

regimen of treatment (1) was higher than that estimated by the dose-energy model (Eq. (6)) for the equivalent dose in optimal standard regimen. The tD intraday of the treated tumor by the metronomic regimen in treatment (1) was also longer than half the time period from the start of therapy to time of dose delivery as in the optimal standard regimens. Such consistency clarifies that no complete tD interval had passed without dose delivery in the efficient regimens of docetaxel treatments. While in the other non-optimal regimens of treatments 2, 10 and 11 of uncorrelated responses, energy yield by the docetaxel dose was lower than that estimated by dose-energy model (Eq. (6)) for the equivalent dose in optimal standard regimen. The tD intraday of the treated tumor by the non-optimal regimen of treatments of uncorrelated responses was shorter than half the time period from the start of therapy to time of dose delivery. This clarifies that non-optimal regimens of the treatments of lower efficiency had included complete tD interval(s) without dose delivery. Table 3 shows that the metronomic regimen of treatment 1 was the most efficient regimen and classifies the applied standard regimens of treatments 2–14 whether optimal or non-optimal according to fitting paired data (docetaxel dose, energy yield) to curve of dose-energy model (perfect fit means R2 = 1) and the efficiency with respect to energy yield by docetaxel dose. 4.4. Predicting tumor response to optimal standard regimen (dosing and scheduling) It is possible to predict the therapeutic response to optimal standard regimen (dosing and scheduling) of docetaxel treatment prior therapy to avoid treatment failure and non-optimal treatments. Prediction of the therapeutic response requires to identify the histologic grade (HG ) of the patient prior therapy (control tumor) (Eq. (2)) and the estimated energy yield by the administered dose in optimal standard regimen by doseenergy model (Eq. (6)). Predicting tumor response by the end of the suggested regimen enables to check the sufficiency of the administered dose for the suggested regimen. The administered dose is sufficient for the suggested regimen whenever the time periods from start of therapy to time of doses delivery would be shorter than twice the doubling time intraday and vice versa. With respect to the insufficient administered dose for a suggested regimen, it is recommended to minimize the duration of the regimen until satisfying such condition. Thus, scheduling of the optimal regimens of docetaxel must take into account that no complete doubling time interval would pass

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E.Y. Moawad / Mutation Research 770 (2014) 120–127

Energy in MeV vs. Docetaxel doses in mg/L

Energy in MeV

60000000000 50000000000 40000000000 30000000000 20000000000 10000000000 0 1000

0

2000

3000

4000

5000

6000

Docetaxel doses in mg/L Fig. 1. shows the scatter plot of docetaxel doses in ␮g/mL administered in different regimens and energy yield by those doses in MeV.

Energy yield by docetaxel doses in optimal standard regimens

Energy in MeV

60000000000 50000000000 40000000000 30000000000

Energy in MeV

20000000000 10000000000

5040

4500

4000

3500

3000

2500

2100

1800

1400

1000

840

650

560

420

0

0

Docetaxel doses in mg/L Fig. 2. shows energy yield by docetaxel doses in treatments of optimal standard regimens.

Table 3 shows a classification to regimens of different docetaxel treatments applied on different types of tumor xenografts according to fitting paired data (docetaxel dose, energy yield) to dose-energy model (Eq. (6), Fig. 2), and the efficiency with respect to energy yield by docetaxel dose. Treatment Number

Xenograft model

Docetaxel dose (␮g/mL)

1

HeyA8 cells

147

2

MLL cells

392

3 4

Hep-2 cells PC-3 cells

420 420

5

C4-2b cells

560

6 7 8 9 10 11 12

MLL cells MDA-MB-231 cells A549 cells SKOV3ip1 cells HeyA8 MDR cells HeyA8 cells HNSCC line; HN30

649.6 840 840 840 840 840 2100

13

HNSCC line; HN30

5040

14

HNSCC line; HN12

5040

Regimen

Fitting to curve of dose-energy model

Efficiency with respect to energy yield by docetaxel dose

Type of the regimen

0.5 mg/kg thrice weekly for 3.5 weeks Two doses of 7 mg/kg on days 4 and 11 Two doses of 7.5 mg/kg/week Three doses of 5 mg/kg on 6 days 5 mg/kg body weight given i.v. every 3rd day (total of four doses) 11.6 mg/kg on days 4 and 11 5 mg/kg/week for 6 weeks 10 mg/kg on days 14, 18 and 22 15 mg/kg/2 weeks for 4 weeks 15 mg/kg/2 weeks for 4 weeks 15 mg/kg/2 weeks for 4 weeks 7.5 mg/kg per injection twice a week for 6 weeks 15 mg/kg per injection twice a week for 6 weeks 15 mg/kg per injection twice a week for 6 weeks

Unfit above

Most efficient

Metronomic

Unfit below

Low efficiency

Non-optimal standard

Perfect fit (R2 = 1) Perfect fit (R2 = 1)

High efficiency High efficiency

Optimal standard Optimal standard

Perfect fit (R2 = 1)

High efficiency

Optimal standard

Perfect fit (R2 = 1) Perfect fit (R2 = 1) Perfect fit (R2 = 1) Perfect fit (R2 = 1) Unfit below Unfit below Perfect fit (R2 = 1)

High efficiency High efficiency High efficiency High efficiency Low efficiency Low efficiency High efficiency

Optimal standard Optimal standard Optimal standard Optimal standard Non-optimal standard Non-optimal standard Optimal standard

Perfect fit (R2 = 1)

High efficiency

Optimal standard

Perfect fit (R2 = 1)

High efficiency

Optimal standard

E.Y. Moawad / Mutation Research 770 (2014) 120–127

without dose delivery. For a delivery of couple of doses only, the second dose delivery should be in the second half of the interval of the predicted doubling time. While for a delivery of more than two doses, the administered dose should be distributed equally on Maximum Tolerated Doses (MTDs) on long time periods between doses or on relatively lower doses on shorter time periods in the same duration of the suggested regimen. The following are predictions of therapeutic responses to optimal standard regimens suggested for three of the presented treatments as if those treatments had not been performed yet. (1) In treatment 2, the tumor of the control group of MLL xenograft model has a doubling time (tD ) of 3.06463211 days (p < 0.001) as determined clinically or pathologically [10–13]. Administered dose of docetaxel is 14 mg/kg equivalent to 392 ␮g/mL in human as shown before. From Eq. (6), the energy yield by 392 ␮g/mL docetaxel in an optimal standard regimen is 1.04627674 × 109 MeV. Accordingly from Eq. (4), the difference in tumor energy induced in the treated group of MLL tumor model of injected 1 × 106 MLL cells by 392 ␮g/mL docetaxel in an optimal standard regimen would be:

 

ln ln

ln 2 tD.Treated × 24 × 60 × 60



− ln ln

2

ln 2 3.06463211 × 24 × 60 × 60

2 

125

on time of second dose delivery less than that necessary for the optimal regimen as shown before. (2) In treatment 9, the tumor of the control group of SKOV3ip1 xenograft model has a doubling time (tD ) of 8.42824977 days (p < 0.001) as determined clinically or pathologically [10–13]. The administered dose within 3.5 weeks (24.5 days) is 30 mg/kg of docetaxel (2 doses of 15 mg/kg every two weeks) in human (70 kg, 2.5 L plasma) is equivalent to (30 × 70 mg/2.5 L) 840 ␮g/mL. From Eq. (6), the energy yield by 840 ␮g/mL docetaxel in an optimal standard regimen is 3.41958514 × 109 MeV. Accordingly from Eq. (4), difference in tumor energy induced in treated group of SKOV3ip1 tumor model of injected 1 × 106 SKOV3ip1 cells by 840 ␮g/mL docetaxel in optimal standard regimen would be:

 

ln ln

ln 2 tD.Treated × 24 × 60 × 60



− ln ln

2

ln 2 8.42824977 × 24 × 60 × 60

2 

× 1 × 106 cells

× 23234.59 = 3.41958514 × 109 MeV Thus, the predicted tumor tD of the treated group of SKOV3ip1 tumor model prior therapy (tD.Predicted ) would be:



× 1 × 106 cells tD.Predicted =

× 23234.59 = 1.04627674 × 109 MeV

ln 2 × e

3.41958514×109



+ln ln

ln 2

2

8.42824977×24×60×60 e 23234.59×15×106 24 × 60 × 60

= 24.29710878 days Thus, the predicted tumor tD of the treated group of MLL tumor model prior therapy (tD.Predicted ) would be:



tD.Predicted =

ln 2 × e

e

1.04627674×109 23234.59×106



ln 2 +ln ln 3.06463211×24×60×60

2

24 × 60 × 60

= 4.10664296 days As the maximum tolerated dose (MTD) of docetaxel is 15 mg/kg [25]. Thus the administered dose (14 mg/kg) is suggested as a single dose or two doses of 7 mg/kg each. Thus according to the standard of the optimal regimens, the two administered doses should be delivered at the start of therapy and within the second half of the predicted tumor tD interval after 2–4 days from starting therapy. Accordingly, the time period between the 2 doses in the suggested regimen would be 3 days to deliver doses on day 4 and on day 7 from starting therapy instead of day 4 and day 11 as actually performed in treatment 2. The actual response to treatment 2 was monitored up till 3 days after second dose delivery (day 14). Thus to compare with the actual response to treatment 2, predicting the response to the suggested regimen should cover a similar duration from initiating therapy up till 3 days after second dose delivery (day 10). The response to the suggested regimen is expected to grow with tD.Predicted of 4.1 days from volume of 50 mm3 at initiating therapy on day 4 to 137.7 mm3 on day 10 after the second dose delivery by 3 days. Thus, the predicted tumor tD intraday on time of second dose delivery is equal to ((ln2/ln137.7 − ln50) × (7 − 4)) · 2.053 days which is longer than half the time period from the start of therapy to time of dose delivery (3 days). This clarifies that the administered dose is sufficient for the suggested regimen to satisfy the necessary condition for the optimal regimen. This also explains why the actual response of MLL tumor model was non-correlated with dose-energy model (Eq. (6)). The same administered dose was insufficient for the actually applied regimen in treatment 2. Doses were delivered within a greater interval by 233.3% (on day 4 and day 11 instead of day 4 and day 7) that induced tumor tD intraday

which is 99.2% identical to the actual induced tumor tD due to therapy in treatment 9 as shown in Table 2. As the MTD of docetaxel is 15 mg/kg [27]. Thus the administered dose (30 mg/kg) is suggested on two doses of 15 mg/kg each. Thus according to the standard of the optimal regimens, the two administered doses should be delivered at the start of therapy and within the second half of the predicted tumor tD interval after 12–24 days from starting therapy. Accordingly, the time period between the 2 doses of the suggested regimen is 14 days to compare with the actual response to treatment 9 along the same duration of 3.5 weeks from initiating therapy. Tumor response to the suggested regimen is expected to grow with tD.Predicted of 24.3 days from volume of 100 mm3 at initiating therapy to 201.55 mm3 in 3.5 weeks. Thus, the predicted tumor tD intraday on time of second dose delivery is (ln 2/(ln 201.55 − ln 100) × 14) 13.85 days which is too longer than half the time period from the start of therapy to time of dose delivery (7 days) clarifying that the administered dose is sufficient for the suggested regimen to satisfy the necessary condition for the optimal regimen. (3) In treatment 12, the tumor of the control group of HN30 xenograft model had a doubling time (tD ) of 16.76676552 days (p < 0.001) as determined clinically or pathologically [10–13]. The administered dose is 75 mg/kg of docetaxel in human equivalent to 2100 ␮g/mL as shown before. From Eq. (6), the energy yield by 2100 ␮g/mL docetaxel in an optimal standard regimen is 1.420130246 × 1010 MeV. Accordingly from Eq. (4), difference in tumor energy induced in treated group of HN30 tumor model of injected 15 × 106 HN30 cells by 2100 ␮g/mL docetaxel in optimal standard regimen would be:

 

ln ln

ln 2 tD.Treated × 24 × 60 × 60



− ln ln

2

ln 2 16.76676552 × 24 × 60 × 60

2 

× 23234.59 = 1.420130246 × 1010 MeV

× 15 × 106 cells

126

E.Y. Moawad / Mutation Research 770 (2014) 120–127

Thus, the predicted tumor tD of the treated group of HN30 tumor model prior therapy (tD.Predicted ) would be:



tD.Predicted =

ln 2 × e

1.420130246×1010



+ln ln

ln 2

2

16.76676552×24×60×60 e 23234.59×15×106 24 × 60 × 60

= 22.62221589 days which is 100% identical to the virtual tumor growth tD due to therapy in treatment 12 as shown in Table 2. As the MTD of docetaxel is 15 mg/kg [27]. Thus the administered dose (75 mg/kg) may be suggested to be delivered in a regimen of a minimum of 5 doses of 15 mg/kg each. To compare with the actual response to treatment 12 in the same duration of 35 days, time period between the MTDs would be 7 days. Alternatively, the administered dose (75 mg/kg) is suggested to be distributed on lower doses of 7.5 mg/kg each every 3.5 days similar to the actually performed regimen in treatment 12. Tumor response to the suggested regimen is expected to grow with tD.Predicted of 22.62 days from volume of 400 mm3 at initiating therapy to 1168.96 mm3 in 35 days that replaces the induced tumor shrinkage from 400 mm3 to 192 mm3 in 35 days according to Eq. (3). Thus, the predicted tumor tD intraday at any time during therapy is (ln2/(ln1.16896 − ln0.4) × t) 0.6463482 t longer than half the time period (t) from starting therapy to time of dose delivery, clarifying that the administered dose is sufficient for the suggested regimen to satisfy the necessary condition for the optimal regimen. This also clarifies why the actual responses of SKOV3ip1 and HN30 tumor models were perfectly correlated with dose-energy model to provide a clear-cut criterion for the efficient regimens of docetaxel and strengthen the confidence in predictability of the response to the optimal standard regimens clinically. 5. Discussion Docetaxel has been in use for over a decade without demonstrating a predictable response in the treatment of cancer. Although several administered schedules were investigated, the relative therapeutic advantage of high versus low doses has not been identified yet. Thus, optimal dosing and scheduling are still the most important issues regarding the use of docetaxel. The purpose of this study is optimizing and predicting the potent activity of docetaxel through an efficient regimen to develop future strategies for optimizing the proper ranges of docetaxel doses. This study used in vivo tumor models in athymic mice which are commonly used to study tumorigenesis and assay efficacy of novel chemotherapeutics [35]. A clinical methodology for staging tumors was conducted to determine the energy yield by docetaxel doses as described in earlier studies [15–19]. From Table 2, the energy yield by equivalent doses in treatments conducted by different research institutes (3 and 4), (7, 8 and 9) and (13 and 14) was 100% identical to boost the confidence in the current approach. Those matching responses provides also a clear-cut criterion for accepting the hypotheses of the equivalence between the effect on the tumor HG induced by docetaxel doses and the energy yield by those doses as described before in earlier studies [15–19]. The perfect power correlation (r = 1) between docetaxel dose and its corresponding energy yield in all the presented treatments-except treatments (1, 2, 10 and 11) – as shown in Fig. 1 and Table 2 strengthens the confidence in EDocetaxel Dose whether identified from the presented in vivo studies or estimated from the derived dose-energy model shown in Eq. (6). The efficient power model of current approach with perfect fit (R2 = 1) enables to find out dose equivalency between docetaxel doses and different drugs used for therapeutic interventions to differentiate between using docetaxel as a monotherapy or in combination with other anticancer drugs targeting efficient treatments

more than the conventional therapies. Predicting the effectiveness of chemotherapeutics regimen is based on the aphid accumulative effect of its successive doses on the patient’s HG [15–19]. Docetaxel as a cell-cycle specific drug affected the growth of a variety of tumor types but with great variation. Several regimens of docetaxel treatment were applied on those murine models in which the lower dose (147 ␮g/mL) in metronomic regimen of treatment 1 was more effective than the higher one (840 ␮g/mL) in standard regimen of treatment 11 in the same tumor model ((2.5 × 105 ) HeyA8 cells) as shown in Table 2. Furthermore, Table 3 demonstrated also that significant growth inhibition by efficient regimen was induced in the treatment of metronomic regimen (Treatment 1) and in the treatments of standard regimens of correlated responses (Treatments from 3 to 9 and 12 to 14). This variation in docetaxel impact has revealed the importance of scheduling the treatment regimen for optimizing docetaxel therapy. Efficient (metronomic and optimal standard) regimens of those therapies were of time periods from the start of therapy to time of dose delivery less than twice the tumor doubling time intraday on time of dose delivery. Docetaxel in optimal standard regimens had an accumulated and predictable impact on tumor cells as shown for predicting the responses to treatments 9 and 12 prior therapy in section of results and analysis. On the contrary, a complete doubling time interval(s) without dose delivery had been included in the non-optimal regimens of other treatments (2, 10 and 11) of uncorrelated responses. The actual response to treatment 2 of non-optimal regimen was too poor than the predicted response to same dose in the suggested optimal regimen as shown in section of results and analysis. Accordingly, docetaxel in non-optimal regimens had not showed an accumulated or predictable impact. In the non-optimal regimens, the effect of first dose had been vanished before delivery of the second dose. The portion of tumor cells that had been triggered to apoptosis by the first dose was substituted through mitosis before delivery of the second dose. This was because of the long periods between the successive doses of the non-optimal standard regimens which were longer than twice the tumor doubling time intraday. Accordingly, the longer the induced tumor doubling time intraday to more than half the time period from the start of therapy to the time of delivery of the dose, the higher the energy of docetaxel doses and hence the effectiveness of the treatment and vice versa. Such condition was fulfilled in all the efficient regimens (metronomic and optimal standard) in Table 3 (treatments 1, 3–9 and 12–14) in which an accumulated effect on the tumor HG had been induced by all the delivered doses. As soon as a portion of tumor cells enters the G2 -phase, docetaxel dose bind to and inhibit the microtubule structures within the cell preventing cells from mitosis and replication inducing aphid apoptosis. Thus, docetaxel therapy in standard regimens would be more effective in killing cells that are slowly dividing. These findings suggest that patients with tumors of advanced stages of low mitotic index may particularly benefit more from standard docetaxel regimens than those with tumors of early stages of higher mitotic index. On the contrary, metronomic docetaxel regimens are more efficient for patients with tumors of early stages of higher mitotic index due to their lower HG that need lower doses of docetaxel. Accordingly, scheduling of docetaxel treatments should be based on the time at which the given drug is likely to be effective, and the rate at which cells divide. This underscores the importance of individual patient treatment planning in which patient should be protected against treatment failure or non-optimal treatments. Patient’s tumor response by the end of the suggested standard regimen should be predicted prior therapy to check the sufficiency of the administered dose for the suggested regimen. The administered dose would be sufficient for the suggested regimen whenever the time periods from start of therapy to time of doses delivery would be shorter than twice the doubling time intraday. This was previously confirmed in predicting the

E.Y. Moawad / Mutation Research 770 (2014) 120–127

therapeutic response to the suggested optimal standard regimens of treatments 9 and 12 in section of results and analysis. With respect to the insufficient administered dose for the suggested regimen, it is recommended to reduce the schedule duration as suggested for optimizing the non-optimal regimen of treatment 2 in section of results and analysis. In case of a delivery of couple of doses only, the second dose delivery should be in the second half of the interval of the predicted doubling time as suggested for optimizing the regimen of treatment 2 and reconciled with the schedule of the optimal regimen of treatment 9. While for a delivery of more than two doses, the administered dose is suggested to be distributed equally on MTDs on long time periods between doses or on relatively lower doses on shorter time periods in the same duration of the suggested regimen. This was also previously reconciled with the schedule of the optimal regimen of treatment 12. Checking sufficiency of the administered dose for the suggested standard regimen would ensure that no complete doubling time interval would pass without dose delivery preserving the tumor doubling time intraday during therapy longer than half the time from starting therapy satisfying the necessary condition for the efficient regimens of docetaxel therapy. 6. Conclusion Effectiveness of docetaxel treatment is related to the mitotic index of the treated tumors as all cell cycle specific drugs. Administration of docetaxel doses should be patient-specific and sufficient for the suggested standard regimen. Time periods from the start of therapy to the time of dose delivery of the efficient regimen are shorter than twice the tumor doubling time intraday on time of dose delivery. Such regimen would cover a greater portion of the tumor cells in the G2 -phase in every time of dose delivery and so committed to all the tumor cells to undergo apoptosis. Patients with tumors of lower mitotic index may particularly benefit more from optimal standard regimens, whereas metronomic regimens would be more efficient in patients with tumors of higher mitotic index that need lower doses of docetaxel. Conflict of interest statement The author declares that there is no conflict of interest concerning this paper. References [1] R.D. Vale, The molecular motor toolbox for intracellular transport, Cell 112 (4) (2003) 467–480, http://dx.doi.org/10.1016/S0092-8674(03)00111-9, PMID: 12600311. [2] C.E. Walczak, R. Heald, Mechanisms of mitotic spindle assembly and function, Int. Rev. Cytol. 265 (2008) 111–158. [3] J. Howard, A.A. Hyman, Microtubule polymerases and depolymerases, Curr. Opin. Cell Biol. 19 (1) (2007) 31–35, http://dx.doi.org/10.1016/j. ceb.12.009.2006. [4] K.A. Lyseng-Williamson, C. Fenton, Docetaxel: a review of its use in metastatic breast cancer, Drugs 65 (17) (2005) 2513–2531, PMID: 16296875. [5] A. Michael, K. Syrigos, H. Pandha, Prostate cancer chemotherapy in the era of targeted therapy, Prostate Cancer Prostatic Dis. 12 (1) (2009) 13–16, http://dx.doi.org/10.1038/pcan.2008.32, PMID: 18521103. [6] A.M. Yvon, P. Wadsworth, M.A. Jordan, Taxol suppresses dynamics of individual microtubules in living human tumor cells, Mol. Biol. Cell 10 (4) (1999) 947–959, PMID: 10198049. [7] P. Arroyo Araque, P.R. Ubago, D.B. Cancela, Controversies in the management of adjuvant breast cancer with taxanes: review of the current literature, Cancer Treat. Rev. 37 (2) (2011) 105–110, http://dx.doi.org/10. 1016/j.ctrv.2010.06.002, PMID: 20655664 (retrieved 21.06.11). [8] E. Moawad, Isolated system towards a successful radiotherapy treatment, Nucl. Med. Mol. Imaging 44 (2010) 123–136. [9] E.Y. Moawad, Radiotherapy and risks of tumor regrowth or inducing second cancer, Cancer Nanotechnol. 2 (2011) 81–93.

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