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(#(# Ifa1/8dilutionofthestocksolutionismadefollowedbya1/6dilutionwhatisthefinaldilution.  0  Thefinaldilutionis:p(#(# 0   (#(# 0  1/8x1/6=1/48H(#(# 0   (#(# 0  Thistypeofdilutionistrickierandnotusedveryfrequentlyintheclinicallab. p(#(#  Doublingdilutionsareverypopular.Thisisaseriesofdilutions.Eachsuccessivetubewill H theamountoftheoriginalconcentratedsolution.Ifthisisdone6timesthisiswhatyouwould 4 endupwith:   0  1stdilution=1/2(#(# 0  2nddilution=1/2x1/2=1/4(#(# 0  3rddilution=1/4x1/2=1/8 (#(# 0  4thdilution=1/8x1/2=1/16l!(#(# 0  5thdilution=1/16x1/21/32X" (#(# 0  6thdilution=1/32x1/2=1/64D#!(#(# 0   (#(# 0  Thisresultsinaseriesofdilutions,eachadoublingdilutionofthepreviousone.%l #(#(#  h-(, .A .HH .  Tocalculateadilutionfactor: H 0  Thedilutionfactor(DF)isthefinalvolume/aliquotvolume. (#(# 0   (#(# 0  EXAMPLE:Whatisthedilutionfactorifyouadd0.1_mL_Ԁaliquotofaspecimento9.9  _mL_Ԁofdiluent?(#(# 0   (#(#  "(#33""$3"  0  $3 2#  1  .3  0` (#(#  Thefinalvolumeisequaltothealiquotvolumeplusthediluentvolume:$3 ݌ t` (#` (# Ќ     ` 0.1_mL_Ԁ+9.9_mL_Ԁ=10_mL_  ` "$3"  0  $3|2#  2  .3  0` (#(#  Thedilutionfactorisequaltothefinalvolumedividedbythealiquotvolume:$3|݌ L ` (#` (# Ќ     ` 10_mL_/0.1_mL_Ԁ=1:100dilution  8  0   (#(#  Problem: Whatisthedilutionfactorwhen0.2_mL_Ԁisaddedto3.8_mL_Ԁdiluent? X    Setuptheproblem:dilutionfactor=finalvolume/aliquotvolume 4  0   ` 0.2+3.8=4.0totalvolume (#(# 0   ` 4.0/0.2=1:20dilutionfactor(#(# Rememberthatserialdilutionsarealwaysmadebytakingasetquantityoftheinitialdilutionand  addingitsuccessivelytotubeswiththesamevolume.Soeachsuccessivedilutionwouldbe t multipliedbythedilutionfactor. ` Sointheaboveproblemallsuccessivetubeswouldhave3.8_mLs_Ԁofdiluent.Youwouldthen 8 transfer0.2oftheinitialdilutedsampleintothenexttube,mixtransfer0.2,mixandsoon.If l$ youhad4tubeswhatwouldbethefinaldilutionoftube4? X *+_,ddd Xdd Xdd X(#(#,dd ,dd ,dd ,dd ,dd +  00 Tube =3 L  ?1?=_@@  1_ dZ0L"  ?1 ?  @2@d_2_ dZ0L"  @2 @  @3@d_3_ dZ0L"  @3 @  @4@d_4_ <20L "  @4 @ <aliquot ?5 ! ?0.2?? @ 0.2 h^2"" ?0.2 ? ?0.2?h0.2 h^2#" ?0.2 ? ?0.2?h0.2 h^2$" ?0.2 ? ?0.2?h0.2 C92%" ?0.2 ? VCdiluent ?5 L& ffffff@3.8ffffff@? @ 3.8 h^2L'" ffffff@3.8 ffffff@ ffffff@3.8ffffff@h3.8 h^2L(" ffffff@3.8 ffffff@ ffffff@3.8ffffff@h @ 3.8 h^2L)" ffffff@3.8 ffffff@ ffffff@3.8ffffff@h__3.8 C97L*" ffffff@3.8 V ffffff@ CMath  !+ @@   '!," '1/20x1/20 '!-" '1/400x1/20 '!." '1/8000x1/20 !/" dilution  "L0  @ 1:20 '"L1" ' @ 1:400 '"L2" '1:8000 '"L3" '1:160,000""L4"  "1/20x1/20x1/20x1/20=1:160,000 %@"6 _   `     h      p _ .x+@ Inthecoldagglutinintiteravolumeofindicator,redbloodcells,wasaddedtoeachtube.The H dilutionfactorthiscausesmustbecalculatedsothatthefinaldilutioncanbedetermined.The 4 chartbelowhastheoriginaldilutionlistedonthesecondrow.Thedilutionfactorthisresultsin   iscalculatedandthisisthenmultipliedtimeseachoftheoriginaldilutionstocalculatethefinal   dilution.REMEMBER:Inaserialdilutiontowhichsomeotherreagentsareaddeditis  CRITICALtoremoveanaliquotfromthelasttubesothatALLvolumesarethesameandthe  dilutionfactorstaysunchanged.  *7_8dddd dd dd dd dd +_,(#(#,dd ,dd ,dd ,dd ,dd +   ` ` Tube =3     ?1?=@@  1 dZ0  "  ?1 ?  @2@d2 dZ0  "  @2 @  @3@d3 dZ0  "  @3 @  @4@d_4 <20  "  @4 @ <Dilution   D   @ 1:20 ' D " ' @ 1:400 ' D " '1:8000 ' D " '1:160,000  D " _RBCs_ ?5    ?0.2??0.2 h^2  " ?0.2 ? ?0.2?h0.2 h^2  " ?0.2 ? ?0.2?h0.2 h^2  " ?0.2 ? ?0.2?h0.2 C92  " ?0.2 ? VCVolumeLeft ?5 D  ffffff@3.8ffffff@? @ 3.8 h^2D " ffffff@3.8 ffffff@ ffffff@3.8ffffff@h3.8 h^2D " ffffff@3.8 ffffff@ ffffff@3.8ffffff@h @ 3.8 h^2D " ffffff@3.8 ffffff@ ffffff@3.8ffffff@h__3.8 C97D " ffffff@3.8 V ffffff@ CDilutionfactor     4.0/0.2=20 2b  " 2 Ab,!  "b A Ab,!  "b A -#!  !"b -Math  D" 20x20 'D#" '20x400 'D$" '20x8000 'D%" '20x160,000 D&" Final@   ' 1:400 ' (" '1:8000 ' )" '1:160,000 ' *" '1:320,000" +"  "Whenperformingserialdilutionsintheclinicallaboratoryonemustknowthedilutionofeach - tubesoachartisalwayscreatedtoindicatethedilutionofeachtube.Ifyouknowthedilution . factoryoumultiplyeachsuccessivetubebyitandcaneasilydeterminetheconcentrationofeach / tube. |0 _TITERS_Ԁarereportedoutasthereciprocalofthelasttubegivingapositivereaction.Soiftube2 T2 wastheendpoint,1:400thetiterisreportedoutas400/1=400 @3  L6   ProblemSet H Foreachofthefollowingcalculatethedilutionofeachtube.Youmustshowyourwork.   ! ! "(#33""$3"  $312#  1  .3  0    Youadd1.5_mLs_Ԁofdiluentto5tubes.Youadd0.5_mLs_Ԁofserumtotubeone.You  transfer0.5_mLs_Ԁsequentiallytoeachofthenext5tubes.$31J1݌(#(# Ќ  */_0dddd dd dd dd dd 7_8(#(#,Fdd ,dd ,dd ,Fdd ,Fdd ,dd +   t t Tube =3    ?1?=@@  1 dZ0  "  ?1 ?  @2@d2 dZ0  "  @2 @  @3@d3 dZ0  "  @3 @  @4@d4 dZ0  "  @4 @  @5@d5 <20  "  @5 @ <Aliquot   X  ' X" ' ' X" ' ' X" ' ' X" ' # X" V#Diluent     ' " ' ' " ' ' " ' ' " ' # " V #Math  X   2bX " 2 Ab,!X "b A Ab,!X "b A Ab,!X "b A -#!X "b -Dilution      '  !" ' '  "" ' '  #" ' '  $" '"  %"  ""$3"  $3~:2#  2  .3  0    Youadd2_mLs_Ԁofdiluentto5tubes.One_mL_Ԁofserumisaddedtotubeone.You ' transfer1.0_mLs_Ԁsequentiallytoeachofthenext5tubes.$3~::݌((#(# Ќ  *1_2ddFdd Fdd dd Fdd FFdd Fdd /_0(#(#,Fdd ,dd ,dd ,Fdd ,Fdd ,dd +  |+| Tube =3 (,  ?1?=@@  1 dZ0(-"  ?1 ?  @2@d2 dZ0(."  @2 @  @3@d3 dZ0(/"  @3 @  @4@d4 dZ0(0"  @4 @  @5@d5 <20(1"  @5 @ <Aliquot  `2  '`3" ' '`4" ' '`5" ' '`6" ' #`7" V#Diluent  (8  '(9" ' '(:" ' '(;" ' '(<" ' #(=" V #Math  `>  2b`?" 2 Ab,!`@"b A Ab,!`A"b A Ab,!`B"b A -#!`C"b -Dilution  (D  '(E" ' '(F" ' '(G" ' '(H" '"(I"  ""$3"  $3C2#  3  .3  0    Youadd1.8_mLs_Ԁofdiluentto5tubes.Youadd0.2_mLs_Ԁofserumtotubeone.You  K transfer0.2_mLs_Ԁsequentiallytoeachofthenext4tubes.$3CD݌!L(#(# Ќ  *3_4ddFdd Fdd dd Fdd FFdd Fdd 1_2(#(#,Fdd ,dd ,dd ,Fdd ,Fdd ,dd +  # O#  Tube =3 0$ P  ?1?=@@  1 dZ00$ Q"  ?1 ?  @2@d2 dZ00$ R"  @2 @  @3@d3 dZ00$ S"  @3 @  @4@d4 dZ00$ T"  @4 @  @5@d5 <200$ U"  @5 @ <Aliquot  %h"V  '%h"W" ' '%h"X" ' '%h"Y" ' '%h"Z" ' #%h"[" V#Diluent  0'#\  '0'#]" ' '0'#^" ' '0'#_" ' '0'#`" ' #0'#a" V #Math  (h%b  2b(h%c" 2 Ab,!(h%d"b A Ab,!(h%e"b A Ab,!(h%f"b A -#!(h%g"b -Dilution  0*&h  '0*&i" ' '0*&j" ' '0*&k" ' '0*&l" '"0*&m"  "_ .+q "$3"  $3M2#  4  .3  0    Youadd1.9_mLs_Ԁofdiluentto5tubes.Youadd0.1_mLs_Ԁofserumtotubeone.You H transfer0.1_mLs_Ԁsequentiallytoeachofthenext5tubes.$3MM݌4(#(# Ќ  *5_6ddFdd Fdd dd Fdd FFdd Fdd 3_4(#(#,Fdd ,dd ,dd ,Fdd ,Fdd ,dd +   Tube =3 \  ?1?=@@  1 dZ0\"  ?1 ?  @2@d2 dZ0\"  @2 @  @3@d3 dZ0\"  @3 @  @4@d4 dZ0\ "  @4 @  @5@d5 <20\ "  @5 @ <Aliquot     ' " ' ' " ' '" ' '" ' #" V#Diluent  \   '\ " ' '\ " ' '\ " ' '\ " ' #\ " V #Math     2b " 2 Ab,! "b A Ab,! "b A Ab,! "b A -#! "b -Dilution  \    '\  " ' '\  " ' '\  " ' '\  !" '"\  ""  ""$3"  $3V2#  5  .3  0    Youadd0.5_mLs_Ԁofdiluentto5tubes.Youadd0.5_mLs_Ԁofserumtotubeone.You P $ transfer0.5_mLs_Ԁsequentiallytoeachofthenext4tubes.YOUTHENADD0.5_mLs_Ԁof < % _RBCs_Ԁtoeachtube.Whatisthefinaldilutionofeachtube?$3V,W݌(&(#(# Ќ  *9_:ddFdd Fdd dd Fdd FFdd Fdd 5_6(#(#,Sdd ,dd ,9dd ,edd ,edd ,'dd +  * Tube =3 <+  ?1?=@@  1 dZ0<,"  ?1 ?  @2@d2 dZ0<-"  @2 @  @3@d3 dZ0<."  @3 @  @4@d4 dZ0</"  @4 @  @5@d5 <20<0"  @5 @ <Aliquot  t1  't2" ' 't3" ' 't4" ' 't5" ' #t6" V#Diluent  <7  '<8" ' '<9" ' '<:" ' '<;" ' #<<" V #Math  t=  't>" ' 't?" 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