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) |
