67:
simplified method that transforms the model equations into a linear equation evaluated at multiple time points and provides fewer parameters (i.e., slope and intercept). Although the slope and the intercept can be interpreted in terms of a combination of model parameters if a compartmental model configuration is assumed, the graphical methods are independent of any specific model configuration. In case of irreversible tracers, certain fraction of the radioactivity is trapped in the tissue or the binding site during the course of the experiment, whereas reversible tracers show uptake and loss from all compartments throughout the study. The theoretical foundation of graphical analysis for irreversible tracers (also called
1203:
897:
845:
481:
1198:{\displaystyle {{\int _{0}^{t}\mathrm {ROI} (\tau )\,d\tau } \over \mathrm {ROI} (t)}=(-\mathbf {U} _{n}^{T}\mathbf {K} ^{-1}\mathbf {Q} +V_{p}){{\int _{0}^{t}C_{p}(\tau )\,d\tau } \over \mathrm {ROI} (t)}+{{\mathbf {U} _{n}^{T}\mathbf {K} ^{-1}\mathbf {A} } \over {\mathbf {U} _{n}^{T}\mathbf {A} +V_{p}C_{p}}}}
66:
is used to fit the individual model parameters in the solution of a compartmental model of specific configuration to the measurements with a measured plasma time-activity curve that serves as an forcing (input) function, and the binding of the tracer can then be described. Graphical analysis is a
99:
The kinetics of radiolabeled compounds in a compartmental system can be described in terms of a set of first-order, constant-coefficient, ordinary differential equations. The time course of the activity in the multicompartmental system driven by a metabolite-corrected plasma input function
648:
1658:
311:
1475:
214:
1389:
1551:
1936:
1304:
2107:
2175:
840:{\displaystyle \int _{0}^{t}\mathrm {ROI} (\tau )\,d\tau =(-\mathbf {U} _{n}^{T}\mathbf {K} ^{-1}\mathbf {Q} +V_{p})\int _{0}^{t}C_{p}(\tau )\,d\tau +\mathbf {U} _{n}^{T}\mathbf {K} ^{-1}\mathbf {A} }
2528:
572:
1991:
1556:
1788:
2039:
518:
476:{\displaystyle \int _{0}^{t}A(\tau )\,d\tau =-\mathbf {U} _{n}^{T}\mathbf {K} ^{-1}\mathbf {Q} \int _{0}^{t}C_{p}(\tau )\,d\tau +\mathbf {U} _{n}^{T}\mathbf {K} ^{-1}\mathbf {A} }
2300:
2265:
889:
613:
2457:
2387:
1237:
303:
281:
239:
2202:
2407:
134:
2354:
2327:
2229:
1846:
1815:
1742:
1715:
1688:
640:
2588:
J. Logan; J.S. Fowler; N.D. Volkow; A.P. Wolf; S.L. Dewey; D.J. Schlyer; R.R. MacGregor; R. Hitzemann; B. Bendriem; S.J. Gatley; D.R. Christman (September 1990).
2688:
2642:
2594:
2590:"Graphical analysis of reversible radioligand binding from time-activity measurements applied to [N-C-methyl]-(-)-cocaine PET studies in human subjects"
259:
1394:
1306:, i.e., the steady-state condition. When this condition is satisfied, the intercept has reached its constant value so that after some time a plot of
142:
1309:
1480:
1851:
1242:
2044:
2112:
2761:
88:
29:
305:
is the vector of plasma-to-tissue transfer constants. Patlak and
Blasberg showed that the above equation can be written as:
2462:
523:
1653:{\displaystyle {{\mathbf {U} _{n}^{T}\mathbf {K} ^{-1}\mathbf {A} } \over {\mathbf {U} _{n}^{T}\mathbf {A} +V_{p}C_{p}}}}
2549:
1941:
2771:
1751:
1996:
2766:
2544:
59:
48:
2684:"Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. Generalizations"
851:
489:
2302:
is the ligand-binding dissociation constant. For a one-tissue compartment model with transfer constants
2410:
2270:
2232:
2238:
857:
581:
2416:
76:
2359:
2559:
1818:
1745:
25:
286:
264:
222:
575:
84:
2180:
2707:
2661:
2613:
2554:
2392:
103:
33:
1817:(dissociation constant) to analyze enzyme or receptor system, the slope represents the total
1211:
2697:
2651:
2603:
63:
41:
37:
2332:
2305:
2207:
1824:
1793:
1720:
1693:
1666:
618:
615:, is a combination of radioactivities from all compartments plus a plasma volume fraction (
2638:"Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data"
44:
244:
2755:
1470:{\displaystyle {{\int _{0}^{t}\mathrm {ROI} (\tau )d\tau } \over \mathrm {ROI} (t)}}
2539:
72:
68:
40:
of tracers involving reversible uptake. It is mainly used for the evaluation of
47:
data after the injection of a labeled ligand that binds reversibly to specific
209:{\displaystyle {\frac {d\mathbf {A} }{dt}}=\mathbf {KA} +\mathbf {Q} C_{p}(t)}
2608:
2589:
1384:{\displaystyle {{\int _{0}^{t}C_{p}(\tau )d\tau } \over \mathrm {ROI} (t)}}
2711:
2702:
2683:
2665:
2617:
1546:{\displaystyle (-\mathbf {U} _{n}^{T}\mathbf {K} ^{-1}\mathbf {Q} +V_{p})}
241:
is a column vector of activity concentration for each compartment at time
2656:
2637:
1931:{\displaystyle {\frac {K_{1}}{k_{2}}}(1+{\frac {k_{3}}{k_{4}}})+V_{p}}
52:
1663:
For a catenary two-tissue compartment model with transfer constants
1299:{\displaystyle \mathbf {A} =-\mathbf {K} ^{-1}\mathbf {Q} C_{p}(t)}
283:
is the matrix of the transfer constants between compartments, and
2102:{\displaystyle {\frac {k_{3}}{k_{4}}}={\frac {B_{\max }}{K_{d}}}}
80:
2636:
C.S. Patlak; R.G. Blasberg; J.D. Fenstermacher (March 1983).
2744:(2nd ed.). The University of Michigan Press, Ann Arbor.
2170:{\displaystyle K_{d}=k_{\mathrm {off} }/k_{\mathrm {on} }}
91:
extended the method to tracers with reversible kinetics.
2523:{\displaystyle {\frac {-1}{k_{2}(1+V_{p}/\lambda )}}}
2465:
2419:
2395:
2362:
2335:
2308:
2273:
2241:
2210:
2183:
2115:
2047:
1999:
1944:
1854:
1827:
1796:
1754:
1723:
1696:
1669:
1559:
1483:
1397:
1312:
1245:
1214:
900:
860:
651:
621:
584:
567:{\displaystyle A(t)=\mathbf {U} _{n}^{T}\mathbf {A} }
526:
492:
314:
289:
267:
247:
225:
145:
106:
2522:
2451:
2401:
2381:
2348:
2321:
2294:
2259:
2223:
2196:
2169:
2101:
2033:
1985:
1930:
1840:
1809:
1782:
1736:
1709:
1682:
1652:
1545:
1469:
1383:
1298:
1231:
1197:
883:
839:
634:
607:
566:
512:
475:
297:
275:
253:
233:
208:
128:
2189:
2082:
1986:{\displaystyle k_{3}=B_{\max }k_{\mathrm {on} }}
1963:
1760:
2742:Compartmental Analysis in Biology and Medicine
2204:is the concentration of ligand binding sites,
2689:Journal of Cerebral Blood Flow and Metabolism
2643:Journal of Cerebral Blood Flow and Metabolism
2595:Journal of Cerebral Blood Flow and Metabolism
891:, one obtains the following linear equation:
8:
2677:
2675:
2631:
2629:
2627:
2267:is the ligand-binding association constant,
2583:
2581:
2579:
2577:
2575:
1717:(reverse transport from tissue to plasma),
1690:(forward transport from plasma to tissue),
2727:Compartmental Models and Their Application
1783:{\displaystyle B_{\max }k_{\mathrm {on} }}
2701:
2682:C.S. Patlak; R.G. Blasberg (April 1985).
2655:
2607:
2506:
2500:
2481:
2466:
2464:
2442:
2437:
2432:
2425:
2420:
2418:
2394:
2373:
2361:
2340:
2334:
2313:
2307:
2279:
2278:
2272:
2247:
2246:
2240:
2215:
2209:
2188:
2182:
2157:
2156:
2147:
2134:
2133:
2120:
2114:
2091:
2081:
2075:
2064:
2054:
2048:
2046:
2018:
2017:
2004:
1998:
1973:
1972:
1962:
1949:
1943:
1922:
1904:
1894:
1888:
1871:
1861:
1855:
1853:
1832:
1826:
1801:
1795:
1770:
1769:
1759:
1753:
1728:
1722:
1701:
1695:
1674:
1668:
1641:
1631:
1619:
1613:
1608:
1603:
1601:
1595:
1586:
1581:
1574:
1569:
1564:
1562:
1560:
1558:
1534:
1522:
1513:
1508:
1501:
1496:
1491:
1482:
1444:
1416:
1410:
1405:
1400:
1398:
1396:
1358:
1335:
1325:
1320:
1315:
1313:
1311:
1281:
1272:
1263:
1258:
1246:
1244:
1213:
1186:
1176:
1164:
1158:
1153:
1148:
1146:
1140:
1131:
1126:
1119:
1114:
1109:
1107:
1105:
1079:
1070:
1055:
1045:
1040:
1035:
1033:
1024:
1012:
1003:
998:
991:
986:
981:
948:
939:
919:
913:
908:
903:
901:
899:
861:
859:
832:
823:
818:
811:
806:
801:
790:
775:
765:
760:
747:
735:
726:
721:
714:
709:
704:
687:
667:
661:
656:
650:
626:
620:
585:
583:
559:
553:
548:
543:
525:
504:
499:
494:
491:
468:
459:
454:
447:
442:
437:
426:
411:
401:
396:
387:
378:
373:
366:
361:
356:
342:
324:
319:
313:
290:
288:
268:
266:
246:
226:
224:
191:
182:
171:
152:
146:
144:
111:
105:
83:. Based on the original work of Patlak,
2034:{\displaystyle k_{4}=k_{\mathrm {off} }}
1239:, Patlak and his colleagues showed that
2571:
2235:for the ligand-binding site complex,
7:
513:{\displaystyle \mathbf {U} _{n}^{T}}
1477:becomes a straight line with slope
2295:{\displaystyle k_{\mathrm {off} }}
2286:
2283:
2280:
2251:
2248:
2161:
2158:
2141:
2138:
2135:
2025:
2022:
2019:
1977:
1974:
1774:
1771:
1451:
1448:
1445:
1423:
1420:
1417:
1365:
1362:
1359:
1086:
1083:
1080:
955:
952:
949:
926:
923:
920:
868:
865:
862:
674:
671:
668:
592:
589:
586:
520:represents a row vector of 1s and
14:
2260:{\displaystyle k_{\mathrm {on} }}
884:{\displaystyle \mathrm {ROI} (t)}
608:{\displaystyle \mathrm {ROI} (t)}
1620:
1604:
1596:
1582:
1565:
1523:
1509:
1492:
1273:
1259:
1247:
1165:
1149:
1141:
1127:
1110:
1013:
999:
982:
833:
819:
802:
736:
722:
705:
560:
544:
495:
469:
455:
438:
388:
374:
357:
291:
269:
227:
183:
175:
172:
153:
28:analysis technique based on the
2452:{\displaystyle {K_{1}}/{k_{2}}}
2514:
2487:
2382:{\displaystyle \lambda +V_{p}}
1912:
1879:
1540:
1484:
1461:
1455:
1433:
1427:
1375:
1369:
1347:
1341:
1293:
1287:
1096:
1090:
1067:
1061:
1030:
974:
965:
959:
936:
930:
878:
872:
787:
781:
753:
697:
684:
678:
602:
596:
536:
530:
423:
417:
339:
333:
203:
197:
123:
117:
89:Brookhaven National Laboratory
1:
574:. The total activity in the
2550:Positron emission tomography
298:{\displaystyle \mathbf {Q} }
276:{\displaystyle \mathbf {K} }
234:{\displaystyle \mathbf {A} }
2729:. Academic Press, New York.
2788:
1748:parameter proportional to
2197:{\displaystyle B_{\max }}
69:Patlak graphical analysis
2402:{\displaystyle \lambda }
129:{\displaystyle C_{p}(t)}
87:and her colleagues from
22:Logan graphical analysis
2545:Multi-compartment model
2459:) and the intercept is
1232:{\displaystyle t>t'}
2609:10.1038/jcbfm.1990.127
2524:
2453:
2403:
2383:
2350:
2323:
2296:
2261:
2225:
2198:
2171:
2103:
2035:
1987:
1932:
1842:
1811:
1784:
1738:
1711:
1684:
1654:
1547:
1471:
1385:
1300:
1233:
1199:
885:
841:
636:
609:
568:
514:
477:
299:
277:
255:
235:
210:
130:
79:and his colleagues at
60:compartmental analysis
2762:Mathematical modeling
2740:J.A. Jacquez (1985).
2703:10.1038/jcbfm.1985.87
2525:
2454:
2411:partition coefficient
2404:
2384:
2351:
2349:{\displaystyle k_{2}}
2324:
2322:{\displaystyle K_{1}}
2297:
2262:
2233:dissociation constant
2226:
2224:{\displaystyle K_{d}}
2199:
2172:
2104:
2036:
1988:
1933:
1843:
1841:{\displaystyle V_{d}}
1812:
1810:{\displaystyle k_{4}}
1785:
1739:
1737:{\displaystyle k_{3}}
1712:
1710:{\displaystyle k_{2}}
1685:
1683:{\displaystyle K_{1}}
1655:
1548:
1472:
1386:
1301:
1234:
1200:
886:
842:
637:
635:{\displaystyle V_{p}}
610:
569:
515:
478:
300:
278:
256:
236:
211:
136:can be described by:
131:
2657:10.1038/jcbfm.1983.1
2463:
2417:
2393:
2360:
2333:
2306:
2271:
2239:
2208:
2181:
2113:
2045:
1997:
1942:
1852:
1825:
1794:
1752:
1721:
1694:
1667:
1557:
1481:
1395:
1310:
1243:
1212:
898:
858:
649:
619:
582:
524:
490:
312:
287:
265:
245:
223:
143:
104:
2725:K. Godfrey (1983).
2560:Distribution volume
2231:is the equilibrium
1819:distribution volume
1618:
1579:
1506:
1415:
1330:
1163:
1124:
1050:
996:
918:
816:
770:
719:
666:
558:
509:
452:
406:
371:
329:
2520:
2449:
2399:
2379:
2346:
2319:
2292:
2257:
2221:
2194:
2167:
2099:
2031:
1983:
1928:
1848:) and is given by
1838:
1807:
1780:
1734:
1707:
1680:
1650:
1602:
1563:
1543:
1490:
1467:
1401:
1381:
1316:
1296:
1229:
1195:
1147:
1108:
1036:
980:
904:
881:
837:
800:
756:
703:
652:
632:
605:
576:region of interest
564:
542:
510:
493:
473:
436:
392:
355:
315:
295:
273:
251:
231:
206:
126:
2555:Binding potential
2518:
2097:
2070:
1910:
1877:
1648:
1465:
1379:
1193:
1100:
969:
254:{\displaystyle t}
166:
34:linear regression
2779:
2772:Plots (graphics)
2746:
2745:
2737:
2731:
2730:
2722:
2716:
2715:
2705:
2679:
2670:
2669:
2659:
2633:
2622:
2621:
2611:
2585:
2529:
2527:
2526:
2521:
2519:
2517:
2510:
2505:
2504:
2486:
2485:
2475:
2467:
2458:
2456:
2455:
2450:
2448:
2447:
2446:
2436:
2431:
2430:
2429:
2408:
2406:
2405:
2400:
2388:
2386:
2385:
2380:
2378:
2377:
2355:
2353:
2352:
2347:
2345:
2344:
2328:
2326:
2325:
2320:
2318:
2317:
2301:
2299:
2298:
2293:
2291:
2290:
2289:
2266:
2264:
2263:
2258:
2256:
2255:
2254:
2230:
2228:
2227:
2222:
2220:
2219:
2203:
2201:
2200:
2195:
2193:
2192:
2176:
2174:
2173:
2168:
2166:
2165:
2164:
2151:
2146:
2145:
2144:
2125:
2124:
2108:
2106:
2105:
2100:
2098:
2096:
2095:
2086:
2085:
2076:
2071:
2069:
2068:
2059:
2058:
2049:
2040:
2038:
2037:
2032:
2030:
2029:
2028:
2009:
2008:
1992:
1990:
1989:
1984:
1982:
1981:
1980:
1967:
1966:
1954:
1953:
1937:
1935:
1934:
1929:
1927:
1926:
1911:
1909:
1908:
1899:
1898:
1889:
1878:
1876:
1875:
1866:
1865:
1856:
1847:
1845:
1844:
1839:
1837:
1836:
1816:
1814:
1813:
1808:
1806:
1805:
1789:
1787:
1786:
1781:
1779:
1778:
1777:
1764:
1763:
1743:
1741:
1740:
1735:
1733:
1732:
1716:
1714:
1713:
1708:
1706:
1705:
1689:
1687:
1686:
1681:
1679:
1678:
1659:
1657:
1656:
1651:
1649:
1647:
1646:
1645:
1636:
1635:
1623:
1617:
1612:
1607:
1600:
1599:
1594:
1593:
1585:
1578:
1573:
1568:
1561:
1552:
1550:
1549:
1544:
1539:
1538:
1526:
1521:
1520:
1512:
1505:
1500:
1495:
1476:
1474:
1473:
1468:
1466:
1464:
1454:
1442:
1426:
1414:
1409:
1399:
1390:
1388:
1387:
1382:
1380:
1378:
1368:
1356:
1340:
1339:
1329:
1324:
1314:
1305:
1303:
1302:
1297:
1286:
1285:
1276:
1271:
1270:
1262:
1250:
1238:
1236:
1235:
1230:
1228:
1204:
1202:
1201:
1196:
1194:
1192:
1191:
1190:
1181:
1180:
1168:
1162:
1157:
1152:
1145:
1144:
1139:
1138:
1130:
1123:
1118:
1113:
1106:
1101:
1099:
1089:
1077:
1060:
1059:
1049:
1044:
1034:
1029:
1028:
1016:
1011:
1010:
1002:
995:
990:
985:
970:
968:
958:
946:
929:
917:
912:
902:
890:
888:
887:
882:
871:
846:
844:
843:
838:
836:
831:
830:
822:
815:
810:
805:
780:
779:
769:
764:
752:
751:
739:
734:
733:
725:
718:
713:
708:
677:
665:
660:
641:
639:
638:
633:
631:
630:
614:
612:
611:
606:
595:
573:
571:
570:
565:
563:
557:
552:
547:
519:
517:
516:
511:
508:
503:
498:
482:
480:
479:
474:
472:
467:
466:
458:
451:
446:
441:
416:
415:
405:
400:
391:
386:
385:
377:
370:
365:
360:
328:
323:
304:
302:
301:
296:
294:
282:
280:
279:
274:
272:
260:
258:
257:
252:
240:
238:
237:
232:
230:
215:
213:
212:
207:
196:
195:
186:
178:
167:
165:
157:
156:
147:
135:
133:
132:
127:
116:
115:
64:iterative method
58:In conventional
42:nuclear medicine
38:pharmacokinetics
32:model that uses
2787:
2786:
2782:
2781:
2780:
2778:
2777:
2776:
2752:
2751:
2750:
2749:
2739:
2738:
2734:
2724:
2723:
2719:
2681:
2680:
2673:
2635:
2634:
2625:
2587:
2586:
2573:
2568:
2536:
2496:
2477:
2476:
2468:
2461:
2460:
2438:
2421:
2415:
2414:
2391:
2390:
2369:
2358:
2357:
2356:, the slope is
2336:
2331:
2330:
2309:
2304:
2303:
2274:
2269:
2268:
2242:
2237:
2236:
2211:
2206:
2205:
2184:
2179:
2178:
2152:
2129:
2116:
2111:
2110:
2087:
2077:
2060:
2050:
2043:
2042:
2013:
2000:
1995:
1994:
1968:
1958:
1945:
1940:
1939:
1918:
1900:
1890:
1867:
1857:
1850:
1849:
1828:
1823:
1822:
1797:
1792:
1791:
1765:
1755:
1750:
1749:
1724:
1719:
1718:
1697:
1692:
1691:
1670:
1665:
1664:
1637:
1627:
1580:
1555:
1554:
1530:
1507:
1479:
1478:
1443:
1393:
1392:
1357:
1331:
1308:
1307:
1277:
1257:
1241:
1240:
1221:
1210:
1209:
1182:
1172:
1125:
1078:
1051:
1020:
997:
947:
896:
895:
856:
855:
817:
771:
743:
720:
647:
646:
622:
617:
616:
580:
579:
522:
521:
488:
487:
453:
407:
372:
310:
309:
285:
284:
263:
262:
243:
242:
221:
220:
187:
158:
148:
141:
140:
107:
102:
101:
97:
77:Clifford Patlak
12:
11:
5:
2785:
2783:
2775:
2774:
2769:
2767:Systems theory
2764:
2754:
2753:
2748:
2747:
2732:
2717:
2696:(4): 584–590.
2671:
2623:
2602:(5): 740–747.
2570:
2569:
2567:
2564:
2563:
2562:
2557:
2552:
2547:
2542:
2535:
2532:
2516:
2513:
2509:
2503:
2499:
2495:
2492:
2489:
2484:
2480:
2474:
2471:
2445:
2441:
2435:
2428:
2424:
2398:
2376:
2372:
2368:
2365:
2343:
2339:
2316:
2312:
2288:
2285:
2282:
2277:
2253:
2250:
2245:
2218:
2214:
2191:
2187:
2163:
2160:
2155:
2150:
2143:
2140:
2137:
2132:
2128:
2123:
2119:
2094:
2090:
2084:
2080:
2074:
2067:
2063:
2057:
2053:
2027:
2024:
2021:
2016:
2012:
2007:
2003:
1979:
1976:
1971:
1965:
1961:
1957:
1952:
1948:
1925:
1921:
1917:
1914:
1907:
1903:
1897:
1893:
1887:
1884:
1881:
1874:
1870:
1864:
1860:
1835:
1831:
1804:
1800:
1776:
1773:
1768:
1762:
1758:
1731:
1727:
1704:
1700:
1677:
1673:
1644:
1640:
1634:
1630:
1626:
1622:
1616:
1611:
1606:
1598:
1592:
1589:
1584:
1577:
1572:
1567:
1553:and intercept
1542:
1537:
1533:
1529:
1525:
1519:
1516:
1511:
1504:
1499:
1494:
1489:
1486:
1463:
1460:
1457:
1453:
1450:
1447:
1441:
1438:
1435:
1432:
1429:
1425:
1422:
1419:
1413:
1408:
1404:
1377:
1374:
1371:
1367:
1364:
1361:
1355:
1352:
1349:
1346:
1343:
1338:
1334:
1328:
1323:
1319:
1295:
1292:
1289:
1284:
1280:
1275:
1269:
1266:
1261:
1256:
1253:
1249:
1227:
1224:
1220:
1217:
1206:
1205:
1189:
1185:
1179:
1175:
1171:
1167:
1161:
1156:
1151:
1143:
1137:
1134:
1129:
1122:
1117:
1112:
1104:
1098:
1095:
1092:
1088:
1085:
1082:
1076:
1073:
1069:
1066:
1063:
1058:
1054:
1048:
1043:
1039:
1032:
1027:
1023:
1019:
1015:
1009:
1006:
1001:
994:
989:
984:
979:
976:
973:
967:
964:
961:
957:
954:
951:
945:
942:
938:
935:
932:
928:
925:
922:
916:
911:
907:
880:
877:
874:
870:
867:
864:
854:both sides by
848:
847:
835:
829:
826:
821:
814:
809:
804:
799:
796:
793:
789:
786:
783:
778:
774:
768:
763:
759:
755:
750:
746:
742:
738:
732:
729:
724:
717:
712:
707:
702:
699:
696:
693:
690:
686:
683:
680:
676:
673:
670:
664:
659:
655:
629:
625:
604:
601:
598:
594:
591:
588:
562:
556:
551:
546:
541:
538:
535:
532:
529:
507:
502:
497:
484:
483:
471:
465:
462:
457:
450:
445:
440:
435:
432:
429:
425:
422:
419:
414:
410:
404:
399:
395:
390:
384:
381:
376:
369:
364:
359:
354:
351:
348:
345:
341:
338:
335:
332:
327:
322:
318:
293:
271:
250:
229:
217:
216:
205:
202:
199:
194:
190:
185:
181:
177:
174:
170:
164:
161:
155:
151:
125:
122:
119:
114:
110:
96:
93:
75:) was laid by
13:
10:
9:
6:
4:
3:
2:
2784:
2773:
2770:
2768:
2765:
2763:
2760:
2759:
2757:
2743:
2736:
2733:
2728:
2721:
2718:
2713:
2709:
2704:
2699:
2695:
2691:
2690:
2685:
2678:
2676:
2672:
2667:
2663:
2658:
2653:
2649:
2645:
2644:
2639:
2632:
2630:
2628:
2624:
2619:
2615:
2610:
2605:
2601:
2597:
2596:
2591:
2584:
2582:
2580:
2578:
2576:
2572:
2565:
2561:
2558:
2556:
2553:
2551:
2548:
2546:
2543:
2541:
2538:
2537:
2533:
2531:
2511:
2507:
2501:
2497:
2493:
2490:
2482:
2478:
2472:
2469:
2443:
2439:
2433:
2426:
2422:
2412:
2396:
2374:
2370:
2366:
2363:
2341:
2337:
2314:
2310:
2275:
2243:
2234:
2216:
2212:
2185:
2153:
2148:
2130:
2126:
2121:
2117:
2092:
2088:
2078:
2072:
2065:
2061:
2055:
2051:
2014:
2010:
2005:
2001:
1969:
1959:
1955:
1950:
1946:
1923:
1919:
1915:
1905:
1901:
1895:
1891:
1885:
1882:
1872:
1868:
1862:
1858:
1833:
1829:
1820:
1802:
1798:
1766:
1756:
1747:
1729:
1725:
1702:
1698:
1675:
1671:
1661:
1642:
1638:
1632:
1628:
1624:
1614:
1609:
1590:
1587:
1575:
1570:
1535:
1531:
1527:
1517:
1514:
1502:
1497:
1487:
1458:
1439:
1436:
1430:
1411:
1406:
1402:
1372:
1353:
1350:
1344:
1336:
1332:
1326:
1321:
1317:
1290:
1282:
1278:
1267:
1264:
1254:
1251:
1225:
1222:
1218:
1215:
1187:
1183:
1177:
1173:
1169:
1159:
1154:
1135:
1132:
1120:
1115:
1102:
1093:
1074:
1071:
1064:
1056:
1052:
1046:
1041:
1037:
1025:
1021:
1017:
1007:
1004:
992:
987:
977:
971:
962:
943:
940:
933:
914:
909:
905:
894:
893:
892:
875:
853:
827:
824:
812:
807:
797:
794:
791:
784:
776:
772:
766:
761:
757:
748:
744:
740:
730:
727:
715:
710:
700:
694:
691:
688:
681:
662:
657:
653:
645:
644:
643:
627:
623:
599:
577:
554:
549:
539:
533:
527:
505:
500:
463:
460:
448:
443:
433:
430:
427:
420:
412:
408:
402:
397:
393:
382:
379:
367:
362:
352:
349:
346:
343:
336:
330:
325:
320:
316:
308:
307:
306:
248:
200:
192:
188:
179:
168:
162:
159:
149:
139:
138:
137:
120:
112:
108:
94:
92:
90:
86:
82:
78:
74:
70:
65:
61:
56:
54:
50:
46:
43:
39:
35:
31:
27:
23:
19:
2741:
2735:
2726:
2720:
2693:
2687:
2647:
2641:
2599:
2593:
1662:
1207:
849:
642:) and thus:
485:
218:
98:
57:
21:
17:
15:
2540:Patlak plot
2177:, in which
95:Description
73:Patlak plot
36:to analyze
30:compartment
2756:Categories
2650:(1): 1–7.
2566:References
85:Jean Logan
18:Logan plot
2512:λ
2470:−
2397:λ
2364:λ
1588:−
1515:−
1488:−
1440:τ
1431:τ
1403:∫
1354:τ
1345:τ
1318:∫
1265:−
1255:−
1133:−
1075:τ
1065:τ
1038:∫
1005:−
978:−
944:τ
934:τ
906:∫
825:−
795:τ
785:τ
758:∫
728:−
701:−
692:τ
682:τ
654:∫
461:−
431:τ
421:τ
394:∫
380:−
353:−
347:τ
337:τ
317:∫
26:graphical
2534:See also
2389:, where
1938:, where
1226:′
852:dividing
49:receptor
2712:4055928
2666:6822610
2618:2384545
2409:is the
1790:), and
1746:binding
1391:versus
45:imaging
24:) is a
2710:
2664:
2616:
2109:, and
486:where
219:where
53:enzyme
62:, an
2708:PMID
2662:PMID
2614:PMID
2329:and
1219:>
1208:For
20:(or
2698:doi
2652:doi
2604:doi
2190:max
2083:max
1964:max
1761:max
850:By
81:NIH
71:or
51:or
2758::
2706:.
2692:.
2686:.
2674:^
2660:.
2646:.
2640:.
2626:^
2612:.
2600:10
2598:.
2592:.
2574:^
2530:.
2041:,
1993:,
1660:.
578:,
261:,
55:.
16:A
2714:.
2700::
2694:5
2668:.
2654::
2648:3
2620:.
2606::
2515:)
2508:/
2502:p
2498:V
2494:+
2491:1
2488:(
2483:2
2479:k
2473:1
2444:2
2440:k
2434:/
2427:1
2423:K
2413:(
2375:p
2371:V
2367:+
2342:2
2338:k
2315:1
2311:K
2287:f
2284:f
2281:o
2276:k
2252:n
2249:o
2244:k
2217:d
2213:K
2186:B
2162:n
2159:o
2154:k
2149:/
2142:f
2139:f
2136:o
2131:k
2127:=
2122:d
2118:K
2093:d
2089:K
2079:B
2073:=
2066:4
2062:k
2056:3
2052:k
2026:f
2023:f
2020:o
2015:k
2011:=
2006:4
2002:k
1978:n
1975:o
1970:k
1960:B
1956:=
1951:3
1947:k
1924:p
1920:V
1916:+
1913:)
1906:4
1902:k
1896:3
1892:k
1886:+
1883:1
1880:(
1873:2
1869:k
1863:1
1859:K
1834:d
1830:V
1821:(
1803:4
1799:k
1775:n
1772:o
1767:k
1757:B
1744:(
1730:3
1726:k
1703:2
1699:k
1676:1
1672:K
1643:p
1639:C
1633:p
1629:V
1625:+
1621:A
1615:T
1610:n
1605:U
1597:A
1591:1
1583:K
1576:T
1571:n
1566:U
1541:)
1536:p
1532:V
1528:+
1524:Q
1518:1
1510:K
1503:T
1498:n
1493:U
1485:(
1462:)
1459:t
1456:(
1452:I
1449:O
1446:R
1437:d
1434:)
1428:(
1424:I
1421:O
1418:R
1412:t
1407:0
1376:)
1373:t
1370:(
1366:I
1363:O
1360:R
1351:d
1348:)
1342:(
1337:p
1333:C
1327:t
1322:0
1294:)
1291:t
1288:(
1283:p
1279:C
1274:Q
1268:1
1260:K
1252:=
1248:A
1223:t
1216:t
1188:p
1184:C
1178:p
1174:V
1170:+
1166:A
1160:T
1155:n
1150:U
1142:A
1136:1
1128:K
1121:T
1116:n
1111:U
1103:+
1097:)
1094:t
1091:(
1087:I
1084:O
1081:R
1072:d
1068:)
1062:(
1057:p
1053:C
1047:t
1042:0
1031:)
1026:p
1022:V
1018:+
1014:Q
1008:1
1000:K
993:T
988:n
983:U
975:(
972:=
966:)
963:t
960:(
956:I
953:O
950:R
941:d
937:)
931:(
927:I
924:O
921:R
915:t
910:0
879:)
876:t
873:(
869:I
866:O
863:R
834:A
828:1
820:K
813:T
808:n
803:U
798:+
792:d
788:)
782:(
777:p
773:C
767:t
762:0
754:)
749:p
745:V
741:+
737:Q
731:1
723:K
716:T
711:n
706:U
698:(
695:=
689:d
685:)
679:(
675:I
672:O
669:R
663:t
658:0
628:p
624:V
603:)
600:t
597:(
593:I
590:O
587:R
561:A
555:T
550:n
545:U
540:=
537:)
534:t
531:(
528:A
506:T
501:n
496:U
470:A
464:1
456:K
449:T
444:n
439:U
434:+
428:d
424:)
418:(
413:p
409:C
403:t
398:0
389:Q
383:1
375:K
368:T
363:n
358:U
350:=
344:d
340:)
334:(
331:A
326:t
321:0
292:Q
270:K
249:t
228:A
204:)
201:t
198:(
193:p
189:C
184:Q
180:+
176:A
173:K
169:=
163:t
160:d
154:A
150:d
124:)
121:t
118:(
113:p
109:C
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