Table 8 Expected survival time (SD) for two resections (days). Expected survival time after two resections: Assume tumor initial size is v0. After random time T1, the tumor reaches size vc1, then resection with c1%; then after another random time T2, the tumor reaches size vc2, the second resection with c2%; then the patient survives with some period of time T3. To demonstration, taking v0 = 1 mL, c1% = 80%, c2% = 50%, and correlation coefficients ρ12, ρ13, ρ23 among T1, T2 and T3. For example, the total survival time will be 492 days if the first resection with 80% is performed when the tumor reaches 50 mL and the second resection with 50% is performed when the tumor reaches 90 mL.

From: Stochastic growth pattern of untreated human glioblastomas predicts the survival time for patients

\({\boldsymbol{(}}{{\boldsymbol{\rho }}}_{{\bf{12}}}{\boldsymbol{,}}{{\boldsymbol{\rho }}}_{{\bf{13}}}{\boldsymbol{,}}{{\boldsymbol{\rho }}}_{{\bf{23}}}{\boldsymbol{)}}\)

\(2\)

5

10

20

40

50

\((0,0,0)\)

15

271(34)

278(34)

290(33)

312(32)

358(32)

381(32)

\((0.5,0,0.5)\)

15 

271(41)

278(40)

290(39)

312(38)

358(37)

381(38)

\((0.8,0,0.8)\)

 15

271(44)

278(44)

290(43)

312(41)

358(40)

381(40)

\((0,0,0)\)

20

279(34)

286(33)

297(33)

320(32)

365(32)

388(32)

\((0.5,0,0.5)\)

 20

279(41)

286(40)

297(39)

320(38)

365(37)

388(38)

\((0.8,0,0.8)\)

20 

279(43)

286(43)

297(42)

320(40)

365(39)

388(39)

\((0,0,0)\)

40

309(33)

315(32)

327(32)

349(31)

395(31)

418(31)

\((0.5,0,0.5)\)

 40

309(38)

315(38)

327(37)

349(36)

395(35)

418(35)

\((0.8,0,0.8)\)

 40

309(41)

315(41)

327(40)

349(39)

395(38)

418(38)

\((0,0,0)\)

50

323(33)

330(32)

342(32)

364(31)

410(31)

433(31)

\((0.5,0,0.5)\)

 50

323(39)

330(38)

342(38)

364(37)

410(36)

433(36)

\((0.8,0,0.8)\)

 50

323(42)

330(42)

342(41)

364(40)

410(39)

433(39)

\((0,0,0)\)

70

353(34)

360(34)

371(33)

394(32)

439(32)

462(32)

\((0.5,0,0.5)\)

 70

353(42)

360(42)

371(41)

394(40)

439(39)

462(39)

\((0.8,0,0.8)\)

 70

353(46)

360(46)

371(45)

394(44)

439(43)

462(43)

\((0,0,0)\)

80

368(36)

375(35)

386(35)

409(34)

454(33)

477(34)

\((0.5,0,0.5)\)

 80

368(45)

375(45)

386(44)

409(43)

454(42)

477(42)

\((0.8,0,0.8)\)

 80

368(50)

375(49)

386(49)

409(47)

454(46)

477(47)

\((0,0,0)\)

90

383(38)

389(38)

401(37)

424(37)

469(36)

492(36)

\((0.5,0,0.5)\)

 90

383(49)

389(49)

401(48)

424(47)

469(46)

492(46)

\((0.8,0,0.8)\)

 90

383(55)

389(54)

401(53)

424(52)

469(51)

492(51)