Accuracy of magnetic resonance imaging in predicting dentate line invasion in low rectal cancer
Shota Tatsumoto1; Takahiro Itoh1; Junko Takahama1; Nagaaki Marugami1; Kiyoyuki Minamiguchi1; Toshihiro Tanaka1; Fumikazu Koyama2; Kohei Morita3; and Kimihiko Kichikawa1
1 Department of Radiology, Nara Medical University, 840 Shijo-cho, Kashihara 634-8522, Japan
2 Department of Surgery, Nara Medical University, 840 Shijo-cho, Kashihara 634-8522, Japan
3 Department of Diagnostic Pathology, Nara Medical University, 840 Shijo-cho, Kashihara 634-8522, Japan
Corresponding author:
Shota Tatsumoto, M.D.
Department of Radiology, Nara Medical University 840 Shijo-cho, Kashihara 634-8522, Japan Tel: +81-744-22-3051
Fax: +81-744-25-7657
E-mail: [email protected]
Funding:
None
Conflict of Interest:
The authors declare that they have no conflict of interest.
Ethical Statement:
The Ethics Committee of our institution approved this retrospective study (Approval No. 2219) and waived the requirement to obtain informed consent. Information about this study is presented on our institutional home page. All participants were given the opportunity to opt out of this study.
Manuscript type:
Original Article
Word count:
3214
E-mail:
Takahiro Itoh: [email protected] Junko Takahama: [email protected] Nagaaki Marugami: [email protected] Kiyoyuki Minamiguchi: [email protected] Toshihiro Tanaka: [email protected] Fumikazu Koyama: [email protected] Kohei Morita: [email protected] Kimihiko Kichikawa: [email protected]
Abstract Purpose
To retrospectively assess the accuracy of magnetic resonance imaging (MRI) in predicting dentate line invasion in low rectal cancer.
Materials and methods
Eighty-one patients with primary rectal cancer were assessed by dynamic contrast-enhanced MRI. The location of the dentate line was assessed on MRI in 27 patients with upper-mid rectal cancer. Two observers independently evaluated the distance between the distal tumor edge and the MRI-defined dentate line in 54 patients with low rectal cancer, and the imaging and histological findings were compared.
Results
The MRI-defined dentate line was 24.0 ± 3.8 mm above the anal verge in patients with upper-mid rectal cancer. The dentate line invasion status agreed with the histological findings in 49/54 (91%) patients (κ = 0.72 [95% CI 0.50–0.95]) for observer 1, and in 51/54 (94%) patients (κ = 0.83 [0.65–1.00]) for observer 2 in patients with low rectal cancer. Interobserver agreement was good (κ = 0.83 [0.65–1.00]). The MRI- derived distance between the distal tumor edge and the dentate line had significant correlation with the histological distance (r = 0.86 for reader 1, 0.75 for observer 2).
Conclusion
MRI demonstrates high accuracy in predicting dentate line invasion in low rectal cancer.
Keywords:
Anal canal; Dentate line; Magnetic resonance imaging; Rectal cancer; Rectum
,QWURGXFWLRQ
$ORQJ ZLWK DGYDQFHV LQ SUHRSHUDWLYH VWDJLQJ VXUJLFDO WUHDWPHQW DQG QHRDGMXYDQW WKHUDS\ VSKLQFWHU SUHVHUYLQJ UHVHFWLRQ IRU ORZ UHFWDO FDQFHU KDV EHHQ SHUIRUPHG H[WHQVLYHO\ LQ UHFHQW \HDUV LQVWHDG RI DEGRPLQRSHULQHDO UHVHFWLRQ >@7KH PRVW OLPLWLQJ IDFWRURI VSKLQFWHUSUHVHUYLQJ VXUJHU\ LV WKH ORZHU HGJHRIWKHWXPRUDQGWKHRSWLPDOODQGPDUNLVSUREDEO\WKHGHQWDWHOLQH>@,QSDUWLFXODULQWHUVSKLQFWHULF UHVHFWLRQZLWKFRORDQDODQDVWRPRVLVKDVEHHQDGRSWHGDVWKHXOWLPDWHVSKLQFWHUSUHVHUYLQJSURFHGXUHWKH UHVHFWLRQOLQHIRUWKLVVXUJHU\YDULHVGHSHQGLQJRQWKHGLVWDQFHRIWKHWXPRUIURPWKHGHQWDWHOLQH>@
7KHGHQWDWHOLQHLVWKHPRVWVLJQLILFDQWDQDWRPLFDOODQGPDUNRIWKHDQDOFDQDO7KHDQDWRPLFDODQDOFDQDO EHJLQVFUDQLDOO\DWWKHGHQWDWHOLQHZKLFKLVWKHIXVLRQSRLQWRIWKHHQGRGHUPDODQGHFWRGHUPDOFRQWULEXWLRQV WRWKHKLQGJXWDQGHQGVFDXGDOO\DWWKHDQDO YHUJH,QFRQWUDVWWKHVXUJLFDO DQDOFDQDO LVGHILQHGDVWKH SRUWLRQ RI WKH WHUPLQDO LQWHVWLQH H[WHQGLQJ IURP WKH OHYHO ZKHUH WKH UHFWXP SDVVHV WKURXJK WKH SHOYLF YLVFHUDODSHUWXUHWKHDQRUHFWDOULQJWRWKHDQDOYHUJH7KHDQDOFDQDODERYHWKHGHQWDWHOLQHLVOLQHGPRVWO\
E\ FROXPQDU RU WUDQVLWLRQDO HSLWKHOLXP ZKHUHDV WKH DQDO FDQDO EHORZ WKH GHQWDWH OLQH LV FRYHUHG E\
VTXDPRXVHSLWKHOLXP>@,QDGGLWLRQWKHGHQWDWHOLQHLVDQLPSRUWDQWVXUJLFDOODQGPDUNIRUGLIIHUHQWLDWLQJ WKHYDVFXODWXUHQHUYHVXSSO\DQGO\PSKDWLFGUDLQDJH>@
0DQ\ VWXGLHV KDYH UHSRUWHG WKH DFFXUDF\ RI PDJQHWLF UHVRQDQFH LPDJLQJ 05, LQ VWDJLQJ IRU ORFDO H[WHQVLRQRIUHFWDOFDQFHU>@+RZHYHUWRWKHEHVWRIRXUNQRZOHGJHQRUHSRUWKDVGHILQHGWKHGHQWDWH OLQHRQ05,RUDVVHVVHGWKHDFFXUDF\RI05,IRUSUHGLFWLQJGHQWDWHOLQHLQYDVLRQDQG IRUPHDVXULQJWKH GLVWDQFHEHWZHHQWKHWXPRUPDUJLQDQGWKHGHQWDWHOLQHLQORZUHFWDOFDQFHU7KHDLPRIRXUVWXG\ZDVWR DVVHVVWKHDFFXUDF\RISUHRSHUDWLYH05,IRUSUHGLFWLQJGHQWDWHOLQHLQYDVLRQDQGIRUPHDVXULQJWKHGLVWDQFH EHWZHHQWKHWXPRUDQGWKHGHQWDWHOLQH
0DWHULDOVDQGPHWKRGV 3DWLHQWV
7KLVUHWURVSHFWLYHVWXG\ZDVDSSURYHGE\WKHORFDO,QVWLWXWLRQDO5HYLHZ%RDUG$SSURYDO1RDQG WKHUHTXLUHPHQWIRULQIRUPHGSDWLHQWFRQVHQWZDVZDLYHG7XPRUVZLWKWKHGLVWDOHGJHZLWKLQFPIURP WKH DQDO YHUJH ZHUH GHILQHG DV ORZ UHFWDO FDQFHU >@ )URP WKH LQVWLWXWLRQDO UDGLRORJ\ GDWDEDVHV ZH
LGHQWLILHG FRQVHFXWLYH SDWLHQWV ZLWK DGHQRFDUFLQRPD RI WKH ORZ UHFWXP DQG XSSHUPLG UHFWXP ZKR ZHUHWUHDWHGDWRXULQVWLWXWLRQEHWZHHQ)HEUXDU\DQG0DUFKDQGZKRPHWWKHIROORZLQJLQFOXVLRQ FULWHULDDG\QDPLFFRQWUDVWHQKDQFHG05,ZDVSHUIRUPHGEHIRUHVXUJHU\DQGEVXUJHU\ZDVSHUIRUPHG DW RXU LQVWLWXWLRQ ZLWKLQ PRQWKV RI 05, :H H[FOXGHG SDWLHQWV ZKR KDG SUHYLRXVO\ XQGHUJRQH FKHPRWKHUDS\UDGLRWKHUDS\IRUUHFWDOFDQFHURUZKRVH05LPDJHVZHUHWHFKQLFDOO\LQDGHTXDWHLQWHUPVRI FRQWUDVWPHGLXPEROXVVFDQUDQJHRUPRWLRQDUWLIDFW2YHUDOORXU05,GDWDVHWLQFOXGHGSDWLHQWVZLWK ORZUHFWDOFDQFHURUXSSHUPLGUHFWDOFDQFHU
0DJQHWLFUHVRQDQFHLPDJLQJ
$OO 05, H[DPLQDWLRQV ZHUH SHUIRUPHG ZLWK D 7 05, 0$*1(720$YDQWR 6LHPHQV )RUFKKHLP
*HUPDQ\DQG705,0$*1(7209HULR0$*1(7206N\UD6LHPHQV1RERZHOSUHSDUDWLRQ ZDVJLYHQ3DWLHQWVZHUHLQMHFWHGLQWUDYHQRXVO\ZLWKPJRIVFRSRODPLQHEXW\OEURPLGHWRUHGXFHFRORQLF PRWLOLW\5RXWLQHSHOYLF05,DQGG\QDPLFFRQWUDVWHQKDQFHG05,'&(05,ZHUHDFTXLUHG'&(05, ZDVREWDLQHGZLWKWKH IROORZLQJSDUDPHWHUVLQMHFWLRQVSHHGPOVGRVHPPRONJDQGVFDQWLPLQJ ILUVWVHFRQGDQGWKLUGSKDVHVDQGV6XEVHTXHQWDQDO\VLVZDVSHUIRUPHGRQWKHDQGV SRVWFRQWUDVW LPDJHV 7KH GHWDLOV RI WKH VHTXHQFHV DUH VKRZQ LQ (OHFWURQLF 6XSSOHPHQWDU\ 0DWHULDO 6XSSOHPHQWDU\7DEOH
,PDJHLQWHUSUHWDWLRQ
(YDOXDWLRQRIWKH05,GHILQHGGHQWDWHOLQH
:HSHUIRUPHGDQLQLWLDODQDO\VLVWRHYDOXDWHWKHGHQWDWHOLQHRQ05,LQSDWLHQWVPHDQDJH\HDUV UDQJH±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
WKHYDULRXVHQKDQFHPHQWSDWWHUQVRIWKHDQDOFDQDO PXFRVDEHORZWKH05,GHILQHGGHQWDWHOLQHRQD[LDO FRQWUDVWHQKDQFHGIDWVDWXUDWHG7ZHLJKWHGLPDJLQJ
$VLQJOHUDGLRORJLVWZLWK\HDUVRIH[SHULHQFHLQUHDGLQJSHOYLF05,LQYHVWLJDWHGWKHORFDWLRQRIWKHGHQWDWH OLQHRQ05,DQGPHDVXUHGWKHOHQJWKRIWKHDQDWRPLFDODQDOFDQDOIURPWKHGHQWDWHOLQHWRWKHDQDOYHUJH RQ05,7KHOHQJWKRIWKHDQDWRPLFDODQDOFDQDOZDVPHDVXUHGE\DVVHVVLQJWKHSRVLWLRQRIWKHGHQWDWHOLQH RQDQD[LDOFRQWUDVWHQKDQFHGIDWVDWXUDWHG7ZHLJKWHGLPDJHDQGWKHQPHDVXULQJWKHVKRUWHVWGLVWDQFH IURPWKLVOLQHWRWKHDQDOYHUJHRQDVDJLWWDOLPDJH)LJ
0HDVXUHPHQWRIWKHGLVWDQFHEHWZHHQWKHGLVWDOWXPRUHGJHDQGWKHGHQWDWHOLQH
%DVHGRQWKHDERYHPHDVXUHPHQWUHVXOWVGHQWDWHOLQHLQYDVLRQZDVHYDOXDWHGDQGWKHGLVWDQFHEHWZHHQWKH WXPRUPDUJLQDQGWKHGHQWDWHOLQHZDVPHDVXUHGLQSDWLHQWVZLWKORZUHFWDOFDQFHUPHDQDJH\HDUV UDQJH±\HDUV7KHFKDUDFWHULVWLFVRIWKHORZUHFWDOFDQFHUSDWLHQWVDUHOLVWHGLQ7DEOH7KHPHGLDQ WLPH IURP 05, WR VXUJHU\ ZDV GD\V UDQJH ±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
3DWKRORJLFDOLQWHUSUHWDWLRQ
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
6WDWLVWLFDODQDO\VLV
7KHKLVWRORJLFDOGLVWDQFHWRWKHGHQWDWHOLQHZDVWDNHQDVWKHJROGVWDQGDUGDJDLQVWZKLFKWKH05,ILQGLQJV ZHUHFRPSDUHG$JUHHPHQWEHWZHHQWKH05,ILQGLQJVDQGKLVWRORJLFDOLQYDVLRQVWDWXVDQGWKDWEHWZHHQ REVHUYHUVZHUHPHDVXUHGZLWKWKHțVWDWLVWLF>@:LWKUHJDUGWRGHQWDWHOLQHLQYDVLRQWKHVHQVLWLYLW\
VSHFLILFLW\SRVLWLYHSUHGLFWLYHYDOXH339DQGQHJDWLYHSUHGLFWLYHYDOXH139ZHUHDOVRDVVHVVHG,QDOO SDWLHQWVZKRXQGHUZHQWDEGRPLQRSHULWRQHDOUHVHFWLRQ3HDUVRQ¶VFRUUHODWLRQDQDO\VLVZDVSHUIRUPHGRQWKH 05,GHWHUPLQHG DQG KLVWRORJLFDOO\ GHWHUPLQHG GLVWDQFH EHWZHHQ WKH WXPRU DQG WKH GHQWDWH OLQH 6FDWWHUSORWVRIWKH05,DQGKLVWRORJLFDOGLVWDQFHVZHUHDQDO\]HGXVLQJWKHOLQHDUUHJUHVVLRQPHWKRGZLWK FRQILGHQFHLQWHUYDO>@$SYDOXH 0.ZDVFRQVLGHUHGVWDWLVWLFDOO\VLJQLILFDQW6WDWLVWLFDODQDO\VLV ZDV SHUIRUPHG XVLQJ 0HG&DOF 6WDWLVWLFDO 6RIWZDUH YHUVLRQ 0HG&DOF 6RIWZDUH EYED 2VWHQG
%HOJLXPKWWSZZZPHGFDOFRUJ
5HVXOWV
'HWHUPLQDWLRQRIWKHEDVHOLQH05,GHILQHGGHQWDWHOLQH
7KH05,GHILQHGGHQWDWHOLQHZDVORFDWHGPPVWDQGDUGGHYLDWLRQDERYHWKHDQDOYHUJH7KH GLVWDQFHIURPWKH05,GHILQHGGHQWDWHOLQHWRWKHDQDOYHUJHZDVVLJQLILFDQWO\VKRUWHULQIHPDOHVWKDQLQ PDOHVYVPP p
$FFXUDF\RISUHGLFWLQJGHQWDWHOLQHLQYDVLRQRQSUHRSHUDWLYH05,
)RUREVHUYHUWKH05,GHQWDWHOLQHLQYDVLRQVWDWXVDJUHHGZLWKWKHKLVWRORJLFDOILQGLQJVLQSDWLHQWV ț >&,±@7KHVHQVLWLYLW\VSHFLILFLW\339DQG139IRUWKHSUHGLFWLRQRIGHQWDWH OLQHLQYDVLRQZHUHDQG)RUREVHUYHUWKH05,GHQWDWHOLQHLQYDVLRQVWDWXVDJUHHG ZLWK WKH KLVWRORJLFDO ILQGLQJV LQ SDWLHQWV ț > &, ±@ 7KH VHQVLWLYLW\
VSHFLILFLW\ 339 DQG 139 IRU WKH SUHGLFWLRQ RI GHQWDWH OLQH LQYDVLRQ ZHUH DQG UHVSHFWLYHO\ ,QWHUREVHUYHU DJUHHPHQW ZDV JRRG ț > &, ±@7KH PHDQ KLVWRORJLFDO GLVWDQFHEHWZHHQWKHWXPRUDQGWKHGHQWDWHOLQHZDVPPUDQJH±PP7KHPHDQUDGLRORJLFDO GLVWDQFHEHWZHHQWKHWXPRUDQGWKHGHQWDWHOLQHDVPHDVXUHGRQG\QDPLFFRQWUDVWHQKDQFHG7ZHLJKWHG 05,ZDVPPIRUREVHUYHUUDQJH±PPDQGPPIRUREVHUYHUUDQJH±PP)LJXUHV
DQGVKRZWKH05,DSSHDUDQFHVRIWKUHHRIWKHVHFDVHV+LVWRORJLFVOLFHVZHUHREWDLQHGDWWKHDQDO FDQDOIRUWKHFRUUHODWLRQEHWZHHQWKHGHQWDWHOLQHDQGWKH05,GHILQHGGHQWDWHOLQH)LJ)LJXUHVKRZV VFDWWHUSORWVRIWKHUDGLRORJLFDOO\GHWHUPLQHGGLVWDQFH EHWZHHQWKHWXPRUDQGWKHGHQWDWHOLQHDJDLQVWWKH KLVWRORJLFDOO\GHWHUPLQHGGLVWDQFHIRUERWKREVHUYHUV7KHOHDVWVTXDUHVUHJUHVVLRQHTXDWLRQZDV\
[IRUREVHUYHUDQG\ [IRUREVHUYHU3HDUVRQ¶VFRUUHODWLRQDQDO\VLVVKRZHGD VWDWLVWLFDOO\ VLJQLILFDQW FRUUHODWLRQ EHWZHHQ WKH 05,SUHGLFWHG DQG KLVWRORJLFDO GLVWDQFHV REVHUYHU FRUUHODWLRQFRHIILFLHQWU pREVHUYHUU p
'LVFXVVLRQ
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
>@$VDQDGGLWLRQDOILQGLQJRIG\QDPLFFRQWUDVWHQKDQFHG05,WKHOXPLQDOVXUIDFHEHORZWKH05, GHILQHGGHQWDWHOLQHZDVEHWWHUGHSLFWHGLQWKHDUWHULDOSKDVHWKDQLQWKHGHOD\HGSKDVH7KHVSKLQFWHUPXVFOH YHQRXVSOH[XVDQG PXFRVDOHSLWKHOLXPDOOVKRZHQKDQFHPHQWLQWKHGHOD\HGSKDVHWKXVGHFUHDVLQJWKH FRQWUDVWEHWZHHQWKHVHWLVVXHV>@:LWKH[SHULHQFHZH IRXQGWKDWG\QDPLF FRQWUDVWHQKDQFHG 05, ZDV EHWWHU DEOH WR GLIIHUHQWLDWH WKH HSLWKHOLXP RI WKH DQDO FDQDO PRUSKRORJLFDOO\ 8QIRUWXQDWHO\ WKH
WUDQVLWLRQ ]RQH ZDV QRW DOZD\V GHSLFWHG FOHDUO\ RQ FRQWUDVWHQKDQFHG 05, :H VSHFXODWH WKDW WKH DQDO YDOYHVDQGVLQXVHVRIWKLV]RQHDUHSDUWLFXODUO\SURPLQHQWLQFKLOGUHQEXWEHFRPHOHVVSURQRXQFHGZLWKDJH
>@
,Q WKH SUHVHQW VWXG\ WKH 05,GHILQHG GHQWDWH OLQH ZDV ORFDWHG PP DERYH WKH DQDO YHUJH DQG WKH GLVWDQFHEHWZHHQWKHOLQHDQGWKHDQDOYHUJHZDVVLJQLILFDQWO\VKRUWHULQIHPDOHVWKDQLQPDOHV7KHVHUHVXOWV DUHVLPLODUWRWKRVHDVVHVVHGE\SURFWRVFRSHLQSUHYLRXVVWXGLHVLQPHQWKHDYHUDJHOHQJWKZDVFP ZKHUHDVLQZRPHQWKHDYHUDJHOHQJWKZDVFP>@
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a RI FDVHV RI DGYDQFHG UHFWDO FDQFHU DQG LV UHJDUGHG DV WKH PDMRU VRXUFH RI ORFDO UHFXUUHQFH LV GLIILFXOW WR DVVHVV HQGRVFRSLFDOO\ >@ ,Q FRQWUDVW WHFKQLFDODGYDQFHVLQ05,KDYHUHVXOWHGLQGUDPDWLFLPSURYHPHQWVLQVSDWLDOUHVROXWLRQDQG05,KDVEHHQ VKRZQ WR VDWLVIDFWRULO\ GHSLFW WKH QRUPDO JDVWURLQWHVWLQDO VWUXFWXUHV ZLWK JRRG GLIIHUHQWLDWLRQ EHWZHHQ PXFRVD VXEPXFRVD DQG PXVFOH >@ ,Q WKH SUHVHQW VWXG\ 05, SUHGLFWHG GHQWDWH OLQH LQYDVLRQ DFFXUDWHO\DQGWKHUDGLRORJLFDOO\GHWHUPLQHGGLVWDQFHEHWZHHQWKHWXPRUDQGWKHGHQWDWHOLQHDVPHDVXUHG RQG\QDPLFFRQWUDVWHQKDQFHG05,KDGDSRVLWLYHFRUUHODWLRQZLWKWKHKLVWRORJLFDOO\GHWHUPLQHGGLVWDQFH 7KHUHIRUH05,LVDYDOLGPHWKRGIRUGHVFULELQJWKHVSDWLDOUHODWLRQVKLSEHWZHHQWKHGLVWDOWXPRUHGJHRI ORZUHFWDOFDQFHUDQGWKHGHQWDWHOLQHLQFOXGLQJWKHLQWUDPXUDOVSDFH
,QRXUVWXG\WKHPHDQGLVWDQFHEHWZHHQWKHWXPRUDQGWKH05,GHILQHGGHQWDWHOLQHZDVPPVKRUWHU
WKDQWKHKLVWRORJLFDOO\GHWHUPLQHGGLVWDQFH7KHSRVVLEOHFDXVHVRIWKLVGLVFUHSDQF\PD\EHGXHWRGLIILFXOW\
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
>@ )RXUWK EHFDXVH WKH 05 LPDJHV ZHUH UHYLHZHG UHWURVSHFWLYHO\ WKH LPDJLQJ WHFKQLTXHV ZHUH QRW VWDQGDUGL]HG ,Q SDUWLFXODU ZH DVVHVVHG WKH DFFXUDF\ RI SUHRSHUDWLYH 05, IRU SUHGLFWLQJ GHQWDWH OLQH LQYDVLRQXVLQJ7DQG7V\VWHPV'LIIHUHQFHVLQWHFKQLFDOSDUDPHWHUVEHWZHHQWKHWZRV\VWHPVPD\
KDYHFDXVHGYDULDWLRQLQLPDJHTXDOLW\
,QFRQFOXVLRQ05,GHPRQVWUDWHVKLJKDFFXUDF\LQSUHGLFWLQJGHQWDWHOLQHLQYDVLRQLQORZUHFWDOFDQFHUDQG FDQDVVLVW LQGHFLGLQJWKHH[WHQWRIVXUJHU\DQGWKHQHHG IRUSUHRSHUDWLYHFKHPRUDGLRWKHUDS\ LQSDWLHQWV ZLWKORZUHFWDOFDQFHU
$FNQRZOHGJHPHQWV
7KH DXWKRUV DFNQRZOHGJH WKH FRQWULEXWLRQ RI 0U <RVKLPDVD 0DL WHFKQLFDO DVVLVWDQW 'HSDUWPHQW RI
&HQWUDO5DGLRORJ\IRUSURFHVVLQJWKHYROXPHUHQGHUHGLPDJHV
5HIHUHQFHV
+HDOG 5- 6PHGK 5. .DOG$ 6H[WRQ 5 0RUDQ %-$EGRPLQRSHULQHDO H[FLVLRQ RI WKH UHFWXP±DQ HQGDQJHUHGRSHUDWLRQ1RUPDQ1LJUR/HFWXUHVKLS'LV&RORQ5HFWXP±
%HHWV7DQ5%HHWV9OLHJHQ5HWDO$FFXUDF\RIPDJQHWLFUHVRQDQFHLPDJLQJLQSUHGLFWLRQRIWXPRXU IUHHUHVHFWLRQPDUJLQLQUHFWDOFDQFHUVXUJHU\/DQFHW±
6DXHU5%HFNHU++RKHQEHUJHU:HWDO3UHRSHUDWLYHYHUVXVSRVWRSHUDWLYHFKHPRUDGLRWKHUDS\IRUUHFWDO FDQFHU1(QJO-0HG±
7HUDPRWR7:DWDQDEH0.LWDMLPD03HU$QXPLQWHUVSKLQFWHULFUHFWDOGLVVHFWLRQZLWKGLUHFWFRORDQDO DQDVWRPRVLV IRU ORZHU UHFWDO FDQFHU 7KH XOWLPDWH VSKLQFWHUSUHVHUYLQJ RSHUDWLRQ 'LV &RORQ 5HFWXP 6±6
5XOOLHU ( *RIIUH % %RQQHO & =HUELE ) &DXGU\ 0 6DULF - 3UHRSHUDWLYH UDGLRFKHPRWKHUDS\ DQG VSKLQFWHUVDYLQJUHVHFWLRQIRU7FDUFLQRPDVRIWKHORZHUWKLUGRIWKHUHFWXP$QQ6XUJ±
8HQR+0RFKL]XNL++DVKLJXFKL<,VKLNDZD.)XMLPRWR+6KLQWR(HWDO3UHRSHUDWLYHSDUDPHWHUV H[SDQGLQJWKHLQGLFDWLRQRIVSKLQFWHUSUHVHUYLQJVXUJHU\LQSDWLHQWVZLWKDGYDQFHGORZUHFWDOFDQFHU$QQ 6XUJ
6FKLHVVHO5.DUQHUဨ+DQXVFK-+HUEVW)7HOHN\%:XQGHUOLFK0,QWHUVSKLQFWHULFUHVHFWLRQ IRUORZ UHFWDOWXPRUV%U-6XUJ±
<DPDGD . 2JDWD 6 6DLNL< )XNXQDJD 07VXML<7DNDQR 0 )XQFWLRQDO UHVXOWV RI LQWHUVSKLQFWHULF UHVHFWLRQIRUORZUHFWDOFDQFHU%U-6XUJ±
5\DQ'3&RPSWRQ&&0D\HU5-&DUFLQRPDRIWKHDQDOFDQDO1(QJO-0HG
*URXS0([WUDPXUDO'HSWKRI7XPRU,QYDVLRQDW7KLQ6HFWLRQ05 LQ3DWLHQWVZLWK5HFWDO&DQFHU 5HVXOWVRIWKH0(5&85<6WXG\5DGLRORJ\±
%DWWHUVE\1-+RZ30RUDQ%6WHO]QHU6:HVW13%UDQDJDQ*HWDO3URVSHFWLYH9DOLGDWLRQRID/RZ 5HFWDO&DQFHU0DJQHWLF5HVRQDQFH,PDJLQJ6WDJLQJ6\VWHPDQG'HYHORSPHQWRID/RFDO5HFXUUHQFH5LVN 6WUDWLILFDWLRQ0RGHO7KH0(5&85<,,6WXG\$QQ6XUJ
0RUJDQ&17KRPSVRQ+56XUJLFDODQDWRP\RIWKHDQDOFDQDOZLWKVSHFLDOUHIHUHQFHWRWKHVXUJLFDO LPSRUWDQFHRIWKHLQWHUQDOVSKLQFWHUDQGFRQMRLQWORQJLWXGLQDOPXVFOH$QQ5&ROO6XUJ(QJO
6KLD-$QXSGDWHRQWXPRUVRIWKHDQDOFDQDO$UFK3DWKRO/DE0HG
/DQGLV 5- .RFK ** 7KH 0HDVXUHPHQW RI 2EVHUYHU$JUHHPHQW IRU &DWHJRULFDO 'DWD %LRPHWULFV
/DP3$X<HXQJ .0&KHQJ3::HL:,<XHQ$37UHQGHOO6PLWK1HWDO&RUUHODWLQJ05,DQG KLVWRORJLFWXPRUWKLFNQHVVLQWKHDVVHVVPHQWRIRUDOWRQJXHFDQFHU$-5$P-5RHQWJHQRO
6KHHG\63%UXLQLQJ'+'R]RLV(-)DXELRQ:$)OHWFKHU-*05,PDJLQJRI3HULDQDO&URKQ'LVHDVH 5DGLRORJ\
.RVLQVNL/+DEU*DPD$/XGZLJ.3HUH]56KLIWLQJFRQFHSWVLQUHFWDOFDQFHUPDQDJHPHQWDUHYLHZ RIFRQWHPSRUDU\SULPDU\UHFWDOFDQFHUWUHDWPHQWVWUDWHJLHV&$&DQFHU-&OLQ
7D\ORU%0%HDUW5:-U3KLOOLSV6)/RQJLWXGLQDODQGUDGLDOYDULDWLRQVRISUHVVXUHLQWKHKXPDQDQDO VSKLQFWHU*DVWURHQWHURORJ\±
&DUULQJWRQ(96FRWW60%KDUXFKD$0LRQ)5HPHV7URFKH-00DOFROP$HWDO([SHUWFRQVHQVXV GRFXPHQW$GYDQFHVLQWKHHYDOXDWLRQRIDQRUHFWDOIXQFWLRQ1DW5HY*DVWURHQWHURO+HSDWRO
3XQZDQL 6 5RGULJXH]-XVWR 0 %DLQEULGJH $ *UHHQKDOJK 5 'H 9LWD ( %ORRP 6 HW DO 0XUDO LQIODPPDWLRQLQ&URKQGLVHDVHORFDWLRQPDWFKHGKLVWRORJLFYDOLGDWLRQRI05LPDJLQJIHDWXUHV5DGLRORJ\
&KHQ&<-DZ76:X'&.XR<7/HH&++XDQJ:7HWDO0'&7RIJLDQWJDVWULFIROGVGLIIHUHQWLDO GLDJQRVLV$-5$P-5RHQWJHQRO
2G]H5'*ROGEOXP-56XUJLFDO3DWKRORJ\RIWKH*,7UDFW/LYHU%LOLDU\7UDFWDQG3DQFUHDVQGHGQ 6DXQGHUV3KLODGHOSKLDSS
1LYDWYRQJV66WHUQ+6)U\G'67KHOHQJWKRIWKHDQDOFDQDO'LV&RORQ5HFWXP %HHWV7DQ 5*+ /DPEUHJWV '0- 0DDV 0 %LSDW 6 %DUEDUR % &XUYR6HPHGR / HW DO 0DJQHWLF UHVRQDQFH LPDJLQJ IRU FOLQLFDO PDQDJHPHQW RI UHFWDO FDQFHU 8SGDWHG UHFRPPHQGDWLRQV IURP WKH (XURSHDQ6RFLHW\RI*DVWURLQWHVWLQDODQG$EGRPLQDO5DGLRORJ\(6*$5FRQVHQVXVPHHWLQJ(XU5DGLRO
7DQ3/&KDQ&/0RRUH155DGLRORJLFDODSSHDUDQFHVLQWKHSHOYLVIROORZLQJUHFWDOFDQFHUVXUJHU\
&OLQ5DGLRO
0RUULV-6SHQFHU-$$PEURVH1605LPDJLQJFODVVLILFDWLRQRISHULDQDOILVWXODVDQGLWVLPSOLFDWLRQV
IRUSDWLHQWPDQDJHPHQW5DGLRJUDSKLFV
7DEOHVDQG)LJXUH/HJHQGV
7DEOH&OLQLFDODQGKLVWRSDWKRORJLFDOFKDUDFWHULVWLFVRISDWLHQWVZLWKORZUHFWDOFDQFHU
&KDUDFWHULVWLFV 1R9DOXH
*HQGHU
0DOH
)HPDOH
7XPRUVL]HFP
7XPRUGLIIHUHQWLDWLRQ
:HOORUPRGHUDWH
3RRU
6XUJLFDOSURFHGXUHV
$EGRPLQRSHULWRQHDOUHVHFWLRQ
/RZDQWHULRUUHVHFWLRQ
,QWHUVSKLQFWHULFUHVHFWLRQ
2WKHUSURFHGXUHV
D'DWDDUHQXPEHUVRISDWLHQWVZLWKSHUFHQWDJHVLQSDUHQWKHVHV
)LJXUHOHJHQGV
)LJ'\QDPLFFRQWUDVWHQKDQFHGIDWVDWXUDWHG7ZHLJKWHG05LPDJHVRIWKHQRUPDODQDOFDQDOLQWKH DUWHULDOSKDVHLQD\HDUROGPDOHD7KUHHGLPHQVLRQDOPRUSKRORJLFDOYROXPHUHQGHUHGLPDJHRIDQDO FDQDO PXFRVDOHQKDQFHPHQWE±G$[LDO LPDJHV DWWKHFRUUHVSRQGLQJ OHYHOV PDUNHGRQDGHPRQVWUDWH VWURQJPXFRVDOHQKDQFHPHQWDQGVKRZPRUSKRORJLFDOGLIIHUHQFHVRIWKHOXPLQDOVXUIDFHRIWKHDQDOFDQDO DFFRUGLQJWRORFDWLRQ1RWHPXFRVDODOLJQPHQWDORQJWKHORQJD[LVEHWZHHQEDQGGWKDWLVFRQVLVWHQWZLWK WKDWRIWKHDQDOFROXPQV7KHGDVKHGOLQHLVWKHGLVWDQFHEHWZHHQWKH05,GHILQHGGHQWDWHOLQHDQGWKHDQDO YHUJH
)LJ6FKHPDWLFGUDZLQJVDQGFRUUHVSRQGLQJD[LDOG\QDPLFFRQWUDVWHQKDQFHG05LPDJHVVKRZYDULRXV HQKDQFHPHQWSDWWHUQVRIDQDOFDQDOPXFRVDEHORZWKH05,GHILQHGGHQWDWHOLQH:KLWHDUHD DQDOFDQDO PXFRVD
)LJ3KRWRJUDSKRIDKLVWRORJ\VOLGHVKRZLQJORZUHFWDOFDQFHU:HPHDVXUHGWKHGLVWDQFHEHWZHHQWKH GLVWDOWXPRUHGJHDQGWKHGHQWDWHOLQHGDVKHGOLQH
)LJ ,PDJHV RI D \HDUROG PDQ ZLWK ORZ UHFWDO FDQFHU VPDOO DUURZ LQ ZKRP WKH KLVWRORJLFDOO\
GHWHUPLQHG GLVWDQFH EHWZHHQ WKH WXPRU DQG WKH GHQWDWH OLQH ZDV PP D 6DJLWWDO G\QDPLF FRQWUDVW HQKDQFHG7ZHLJKWHG LPDJH7KHGLVWDQFHEHWZHHQWKHGLVWDOWXPRUHGJHDQGWKH05,GHILQHGGHQWDWH OLQHLVPPGDVKHGOLQHE'RXEOHFRQWUDVWEDULXPHQHPDODWHUDOYLHZ
)LJ,PDJHVRID\HDUROGPDQZLWKORZUHFWDOFDQFHULQZKRPWKHKLVWRORJLFDOO\GHWHUPLQHGGLVWDQFH EHWZHHQWKHWXPRUDQGWKHGHQWDWHOLQHZDVPPD&RURQDOG\QDPLFFRQWUDVWHQKDQFHG7ZHLJKWHG LPDJH7KHGLVWDQFHEHWZHHQWKHWXPRUDQGWKH05,GHILQHGGHQWDWHOLQHZDVDVVHVVHGDVPPIRUERWK REVHUYHUVE'RXEOHFRQWUDVWEDULXPHQHPDSRVWHULRU±DQWHULRUYLHZ
)LJ,PDJHVRID\HDUROGPDQZLWKORZUHFWDOFDQFHUDQGLQWHUVSKLQFWHULFILVWXODLQZKRPWKHHQWHULF HQWU\SRLQWRIWKHILVWXODZDVRQWKHGHQWDWHOLQHD&RURQDOG\QDPLFFRQWUDVWHQKDQFHG05LPDJHVKRZV D OHIWVLGHG LQWHUVSKLQFWHULF ILVWXOD 1RWH WKH HQWU\ VLWH LQ WKH PLGGOH WKLUG RI WKH VXUJLFDO DQDO FDQDO
DUURZKHDGEF$[LDOLPDJHVDWWKHFRUUHVSRQGLQJOHYHOVPDUNHGRQDGHPRQVWUDWHLUUHJXODUDQDOFDQDO OXPHQFRYHUHGE\IODWWHQHGPXFRVDEDQGWKHVXSHULRUERUGHURIWKHVPRRWKDQDOFDQDOOXPHQFRYHUHGE\
IODWWHQHGPXFRVDF1RWHWKDWWKH05,GHILQHGGHQWDWHOLQHDQGWKHHQWU\SRLQWRIWKHILVWXODDUURZKHDG DUHWKHUHIRUH ORFDWHGRQWKH VDPH OHYHO G &RUUHVSRQGLQJ PDFURVFRSLF VHFWLRQ VKRZV WKH HQWHULF HQWU\
SRLQWRILQWHUVSKLQFWHULFILVWXODDUURZKHDGRQWKHGHQWDWHOLQH
)LJ6FDWWHUSORWVKRZLQJWKHGLVWDQFHEHWZHHQWKHGLVWDOWXPRUHGJHDQGWKHGHQWDWHOLQHDVGHWHUPLQHG IURPKLVWRORJ\VSHFLPHQVFRPSDUHGZLWKWKHGLVWDQFHEHWZHHQWKHGLVWDOWXPRUHGJHDQGWKHGHQWDWHOLQH DVGHWHUPLQHGE\05,U \ [ IRUUHDGHUDQGU \ [ IRU REVHUYHU