Deterministic Parsing model of CBE factor for Intra-cellular 10B Distribution in Boron

Neutron Capture Therapy

Shintaro ISHIYAMA a※ and Yoshio IMAHORIb

※a　 Quantum Beam Science Center, Japan Atomic Energy Agency, 　　　 Tokai-mura, Naka-gun Ibaragi 319-1195 Japan b Cancer Intelligent Care System Ltd, Ariake 3-5-7 Kouto-Ku, 　　　 Tokyo Japan

1

No. TissueNB-max

(μg/g)CBE factor

11） Tumor 72 3.8

22) Normal skin tissue 28.8 2.5

33) Normal brain tissue 20 1.34

44) Normal oral mucosal tissue 21.5 4.87

55) Normal liver tissue 24 4.25

66) Normal lung tissue 24 2.3

77) Normal heart tissue 24 1.35

1 ） Fukuda et al,. 1994, 2 ） Kiger et al., 2008, 3 ） Suzuki et al., 2000,4-7 ） Morris et al., 1997 with BPA experiments of mice

Physical Dose Rate of BNCT D= （ 6.78×N×RN+6.93×NB×CBE ） ×Φ×10-14+γ　 N ： Nitrogen density, RN:14N(n,p)14C, NB: Boron density, CBE ： 10B(n,α)7Li BPA : Boronophenylalanine

CBE=Compound Biological Effectiveness

B

OH

OH

18F

CO2HH2N

2

No relation was found between NB-max and CBE factor !

3

1 2 3 4 5 600

20

40

60

80

CBE factor

NB

-max

　(μ

g/g) Tumor

Liver

SkinLung

Heart

Brain

Oral

Normal tissues

10BPA

B

OH

OH

18F

CO2HH2N

?

4

Ⅰ. How to express the CBE factor model for tissues/tumor ?

Presentation

Ⅱ. How to define CBE factor for Human Brain Tumor by CBE

factor model ?

BB

Atomic distance :2r

r0 r≦ r0>r

BNCT

Atomic distance :2r

B Br0

α range: r0 (8 ～ 9μm ）

What is CBE in BNCT ?

nnn nn nnn nn

γ ray

Single hit events

Duplicative volume : Vd 5

CBE factorγ ray

1 CBE

Cell

(Beam oriented) (Boron distribution oriented)

10B(n,α)7Li

Selective concentration in nucleus is

dominant

CBE 　∝　 F ・ Vdnol

F: Proximityof boron atoms

How can be defined the CBE factor model with Vd ?

Vdnol=Vd/V0

V0=4/3πr03

BB

BB

BB B

B

BBB r0

Vd

6

r

V0

Volume of spherical cap

(1) Duplicative volume model

1

r0

Vdn

ol

(2) Space filling modelCell 2r0

2r1

2r2

N0

N1(>N0)

N2(>N1)

Boron

00

How can be expressed Vdnol ?

n: Dimension number(=1,2,3)Nth: Eigen-value of N 7

Volume of spherical cap

How can be expressed for CBE factor ?From model (1) From model (2)

Deterministic Parsing model of CBE factor

Where constants: CBE0, F and n(=1,2,3)Eigen-value: Nth, Saturation density: Nmax

where

8

0 ＜ Nth/Nmax ＜1

How to obtain CBE0, F, n and Nth ? Data set (Nimax, CBEi)

i=1,2,3 ・・・ nInitial data

(CBE0, F, n(=1,2,3)0)

Eigen-value: Nith

Data set:(Nith/Nimax, CBEi)

(CBE0, F ）i

Least square method

YES NO

Determination (CBE0, F, n, Nthi)

Correlation (CBE, Nmax/Nth ）

r>0.999?

n=1,2,3

(CBE0, F ） i 　

+Δ

Iteration

9

Simulation results of the CBE factors obtained for normal and tumor tissues

by deterministic parsing model

Results of simulation

Where constants: CBE0, F and n(=1,2,3)Eigen-value of N: Nth

Maximum uptake of Boron: Nmax

10

No relation was found between NB-max and CBE factor !

11

1 2 3 4 5 600

20

40

60

80

CBE factor

NB

-max

　(μ

g/g) Tumor

Liver

SkinLung

Heart

Brain

Oral

Normal tissues

10BPA

B

OH

OH

18F

CO2HH2N

?

1

Deterministic Parsing Model for the CBE factor with Nth/Nmax

12

0.10.010

1

2

3

4

5

6

Nth/Nmax （＝FD)

CB

E　

fact

or

10BPA

Tumor

Oral mucosal

Liver

Skin

Lung

Heart

Brain

CBE0 = 0.5 F = 8 n = 3

CBE factor model

CBE 1-N∝ th/Nmax

No.

TissueNmax

(μg/g)Nth

(μg/g)

CBE factor

CBE(Calc.)

Nth/Nmax

1 Tumor 72 8.71 3.8 3.81 0.121

2 Normal skin tissue 28.8 7.20 2.5 2.50 0.25

3 Normal brain tissue 20 9.30 1.34 1.35 0.465

4Normal oral mucosal tissue 21.5 1.27 4.87 4.87 0.059

5 Normal liver tissue 24 2.21 4.25 4.25 0.092

6 Normal lung tissue 24 6.67 2.3 2.31 0.278

7 Normal heart tissue 24 11.14 1.35 1.35 0.464

High degree of precision for the CBE factor estimation was achieved!

※

13

(Calc.)

What is the distribution factor DF in CBE factor model ?

14

DF=Nth/NmaxCell model

BPA

DF

1

Cell nucleus

Endoplasm

Nmax

1-DF

What is the CBE0 ?

BB

BB

B B

BB

B

BB

B

B

B

B B

B

B

B

B

B

B

B

B B

B B

B

B

B

B B

B

BB

B

B

B

B

B

B

B

B

B

B B

B B

B

B

B

B B

BB

BB

B

B BB

B

B

BB

B

B

N = Nth N > NthN < Nth

r< r0 r=r0 r> r0

15

What is the Proximity of boron atoms F (=8)?

B

B

B

B

BB

BB

B

B

B B

BB

B

Mode 2(F=2)

Mode 4(F=4)

Mode 6 (F=6)

Mode 8 (F=8)

Octahedron

B

B

BB

B

B BB

B

Tetrahedron HexahedronDihedral

16

What is the Space filing factor n ?

r/r0

DF

(=N

th/N

max

)

n=3(Stereo)

n=2(Planar)

n=1(Liner)

0 0.5 1.00.01

0.1

1

BBB

B

BB B

BB

17

18

Classification of normal tissues/tumor

Oral

Liver

Skin

Lung

Tumor Brain

0 0.2 0.40

4

8

12

DF(=Nth/Nmax)

Nth(C

alc.

), μ

g/g

Normal tissue

Heart

Group I

Group II

Group IIIGroup IV

4 3 2 1CBE factor

BPA

How to define CBE factor for Human Brain Tumor by CBE factor model ?

19

DF=Nth/Nmax

Patients with GliomaAII(8)

AIII(11)GBM(13)

Total 33

Imahori, Ueda et al., J Nucl Med (1998)

1,8000

20

Definition of DF for the case of tumor and normal tissues

5

10

15

20

25

30

35

40

4,000 8,000 1,2000 1,60000

Tis

sue

10B

con

ten

t,N (

μg/

g)

Dose of BPA 　（ mg/kg ）　　

BloodBrainSpinal cord

Morris MG et al. (1997)

Nth

DF=1-0.17 (=0.83)

(0.8)

(0.93)Nmax

Normal tissueDF=1-Nth/Nmax

TumorDF=Nth/Nmax

50

21Imahori Y., et al., J Nucl Med (1998)

Gjedde-Patlak plotting model(1983)

Cp(t) Ce(t) Cn(t)

K1

k2

k3

Endoplasm Cell nucleusB in blood

GBM AIII AII ControlL

00.005

0.010.015

0.020.025

0.030.035

0.040.045

Series1 Series2 Series3K1　　

k3k2

Dynamic PET

Tumor Normal

K1<k2<k3K1>k2>k3

22

0.01 0.1 10

1

2

3

4

5

CBE factor model

Oral （ N）

Liver（ N ）Tumor

Skin （ N）

Lung（ N ） Brain （ N

）Heart （ N

）

Human brain tumorN:Normal tissue

DF(=Nth/Nmax)

CB

E f

acto

r

GBM(L) AIII(L)AII(L)Control　　

Grade

GBM

AIII

AIIImahori Y., et al., J Nucl Med (1998)

23

BNCT effectiveness

0GBMAII AIII

1

2

3

4

5

CB

E f

acto

r

GBM(DL) AIII(DL) AII(DL) Control 　　

Grade

Control

BNCT effectiveness on tumor grade

B in blood

?

24

CBE transition process on the grade of glioma

Damage on toughness of membrane in cell and nucleus

K1

k3k2

K1

k2

k3

K1

k2

k3

Normal AII AIII GBM

CB

E

Cp(t)

K1

k2

k3Endoplasm

Cell nucleus

K1 k2 k3

Positive object Negative

K1↑ orientedk3↓

BPA

G-P model

Imahori Y., et al., J Nucl Med (1998)

Conclusion

25

(1) The CBE factor is well expressed by the following equation,

DF=Nth/Nmax , Nth: Threshold of boron concentration Nmax: Boron concentration at saturation point Constant: CBE0, F, n(2) Calculated CBE factor indicates the BNCT effectiveness on the grade of brain tumor CBE0=0.5, F=8,n=3 for BPA

26

Thanks you all for attentive listening

BNCT for health and happiness of all patients in the world