Extraction of the cerebral cortical boundaries from MRI for measurement of cortical thickness

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Extraction of the Cerebral Cortical Boundaries from MRI for Measurement of Cortical Thickness 1 2 3

Transcript of Extraction of the cerebral cortical boundaries from MRI for measurement of cortical thickness

Extraction of the Cerebral Cortical Boundaries from MRI for

Measurement of Cortical Thickness

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GenerationInitial Inner Surface

DeformationInner Surface

DeformationOuter Surface

Cortex ModelMRI Volume Measurements

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Brain ExtractionCerebrum WMIsolation of

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TessellationCorrectionTopology Initial Inner

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12 �

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1

n

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1

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T �

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Einitial = g(|~vinitial − ~vdeforming |),³��7µ

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g(x) =

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��o^V8m`aXuw{^\iV~ehV�V!]^V`Y[dX|w}�_n]nmJe[gva�]E_)jkV�bR}�a�Yyeho^V�bcV`}�aXY[u�ZAehgiaX]Eaf}6ehonV�gv]^]nV`Ysjh_^Yk}�Z�m~Vzg�j �Einner = c1ELaplacian + c2Esquared Laplacian

+c3Egradient + c4Einflation + c5Einitial ,

³��<µ

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jhV!ZXY[mpo,jh{nZXm`V�aX}�V!Z�mpo,WXV!Yke[V~�3�;��onV�W�V`Yhehg�m~V!j�ZfY[V�uwaAWXV�bqgi],ehongij;��Z1|$_^]<e[gv\6ehonV�]7_^u��)V!Y�aX}�WXV!Yke[gim`V!j(u�aAW�V!b,b^_^Yhgi]^dEZf]gvehV!Y[ZfehgiaX]�g�j.��V`\iaA��Z8dXgiWXV`]�e[o^YhV�jkonaX\�b3l��yonV`Y[VsV!�<_^gi\vgi�^Y[gv_nu g�j�Z�jhjh_^uwV!b3����o^V�_njkV�b�jkV�ZfYpmpo�jk{nZ�m~Vyg�j�jh{^o^V!Yhg�m`ZX\nm~a�]<e[Zfgi]^gi]^dQ���b^g��BV`Y[V`]<ey{)a<jkgvehgiaX])j`�

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��«��.« ®'C : @B N C BEDF=HG!@ ¯ @DFOPB � =N:<8�OP7

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Einflation =

{

−(~n(~v) · ~D), if µGM (~v) + µWM (~v) ≥ µCSF ��� � � � ��� �−(−~n(~v) · ~D), otherwise ��� �� ���� �

r�onZfYpbRm`aX]njkehYpZfgi]<e�{^Y[V`W�V`]<e[j�eho^Vzjh_^Yk}�Z�m~V(}�Yha�u�jkV!\�}ê��gv]<e[V`YpjkV�mJehgi]^d8gi]/jk_^\�m~gB�yo^V!YhV�]^aRÀ�UcÁSgij�V!W<g�bcV!]�e�gi]c����V~e���V`V!]Re[o^Vjh_^\�m`Zf\��nZf]^�cj!����ongij�m`Zf_)jkV�j�eho^V�gv]c¿�ZAehgiaX]qV!]^V`Y[dX|RehaHm`aX\i\iZX{njkV���Zf\i\�jyaf}6ehgidXo<e�jh_^\�m`Zf\�}�aX\�b^j(Zfe�Zw{)a<jkgvehgiaX],ZX{^{^Y[a1�cgvu�ZAe[V`\i|V���_ngibcg�jke[Zf]<eweha>e[o^Vqgv]n]^V`YRjh_^Yh}�ZXm~V�l��yo^V!]�]^a½À�UcÁ g�j�V`W7g�bcV`]<e,³�jhV`VE�nd�_^YhV'�<µJ�#¼saA��V`W�V`Y�l�eho^V/gi]c¿)ZfehgiaX]�V`]^V!Yhd�|±u�Z1|V!YhY[aX]^V!aX_njh\i|/m`aX\i\iZX{njhV8ehonVRjk_^Yh}�ZXm`V�gi]Sjku�Zf\i\�m~a�]nm`Z1W7gvehgiV!j!l�Zf]nbO}�aXYzV~�^ZXu�{n\vVwuwacbcV`\�]^a�]c��V~�cgijkehV!]<e�}�a�\ib^jza�],e[aX{>af}�d�|7Yhg���¸]nm`YhV�ZXjhgv]nd+e[o^VOgi]c¿n_nV`]nm`V,af}zehonV,gv]<e[V`Y[]nZf\sV!]^V`Y[dXgiV!jRYhV�jka�\vW�V!j�ehonV!jhV,{^Y[aX�^\iV`u�j!l��n_ceEZX\ijhaSgvuw{nZXgvYpj�e[o^VOZf�ngv\ig�e�|Kaf}ze[o^Vjh_^Yh}�ZXm~V�e[aOm~a�]c}�aXY[u eha,m`_^Y[WXV!b>Y[V`d�gva�]njzaX]>ehonV�aX_ce[V`Y8��aX_^])b^ZfY[|X�E��aqaAW�V`Ypm~aXuwV�eho^g�jze[Y[Z�bcV`aX�6l�Zf]SV`]nV`Y[dX|Obcg�jh{^\iZ�m~gi]^de[o^V�jk_^Yh}�ZXm`V�b^gvY[V!m~eh\i|/ehaA��ZfYpb^jse[o^VR¾z�+ÂXÀ�U^Á�gvu�Zfd�V�V�bcdXV�g�jzgv]nm`\v_)bcV!b+gv]+ehonV�V!]^V`Y[dX|E}�_^])mJehgiaX]�����o^g�j;V`]^V!Yhd�|qonZXj�e[o^VV`��V�mJe�aX}3_^]c}�aX\�bcgi]^d�m`aX]nm!Z1W7g�e[gvV�j�aX]we[o^V�bcV`}�aXY[uwgv]^d�jk_^Yh}�ZXm`Vy�yo^V`]H]^a8aX_^ehV`Y�jk_nYk}�Z�m~Vsm~a�]nm`Z1W7gvehgiV!j�g�j�V`W7gib^V`]<e�gi]�eho^V�gvu�ZXdXVb^Zfe[Znl<ZX]nbweho7_nj�Z1W�aXg�b^j�}�aXY[uwgv]nd�]^a�]c��V`�cgijkehV!]�e�}�aX\�b^j�gi]Re[o^V�jh_^Yh}�ZXm`VX��r{^Y[aX{�V`Y���V`gidXo<ehgi]^d8��V~e���V`V!]�eho^g�j�V`]^V!Yhd�|wZX]nbwe[o^Vgi]c¿)ZfehgiaX]>V`]^V!Yhd�|Om`ZX_njkV�j;ehgidXo<e8jk_n\im!Zf\�}�aX\�b^jze[aqm~aX\i\�Zf{njhV�Zf]nb>jku�ZX\v\�m`aX]nm!Z1W7g�e[gvV�j(e[aq�)V�_n]c}�aX\�bcV!b�l��yo^gi\vVRm!Zf{ce[_^Y[gv]^dEe[o^V¾z�+Â�À�UcÁ�giuwZXdXV�V!bcd�VX�8��o^V�V`]^V!Yhd�|/_njkV�jzZE¾�¾;»;ÁK�nV`\�bO�7| � _OV~e�Zf\��

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e[aA��ZXY[b^j�V!b^dXV!j�gi]qZ�d�gvW�V`]HV�bcdXVzu�Zf{����¸]$a�Y[bcV!Y�e[awV`]njh_^Y[V�e[onZAe�e[o^V�¾�¾;»�ÁS�)V`\�b${�aXgi]<e[j�e[aA��ZXY[b^j�ehonV;a�_cehV!Yy�)a�_^]nb^ZXYh|�le[o^VHV�bcdXVRu�ZX{±gij�m`ZX\im`_^\iZfehV�bS�<|+e[ZX�7gv]^d,eho^VH�nY[jke�b^V`Y[gvWAZAe[gvW�V�af}ye[o^V$jh_^u af}�ehonVH�� ZX]nb½¾z� }�_^t!t`|>uwV`u���V`Ypjho^gv{)j³�jkV!V��)dX_^Y[V��<µJ����o^VH¾�¾;»;ÁV!]^V`Y[dX|qg�jzehonV�gi]^]^V!Y8{^Y[acbc_nmJe���V~e���V`V!]Oe[o^V�]^aXY[u�Zf\igvt!V!b>¾�¾;»�Á@�nV`\�bOW�V!m~ehaXY ~G

Zf]nb+e[o^V]^a�Yhu�ZX\vgit`V�bHbcgiYhV�mJe[gva�]$W�V!mJe[aXY ~D �

EGGV F = −~G(~v) · ~D³��Xµ

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ρ �

EGGV F =

{

−~G(~v) · ~Dl^g�}

|µCSF − µGM | ≥ ρ

−‖~∇I(~v)‖lnafehonV`Y[�ygijhV ³��<µ

��o^V(j[ZfuwV�gi]�e[V`Y[]nZf\nV`]^V!Yhd�gvV�j�gij�_)jkV�b�}�aXY�ehonV(bcV~}�a�Yhu�ZfehgiaX]�af}Beho^Vya�_cehV!Y�jh_^Yk}�Z�m~VyZXj�eho^a<jkVy_njhV!b�}�a�Y�eho^V(gv]^]nV`Y�jh_^Yh}�ZXm~V����o^V8m`aXuw{^\iV~e[V;V!]^V`Y[dX|w}�_n]nmJe[gva�]E_)jkV�bH}�a�Y�eho^V8b^V~}�aXY[u�ZAe[gva�]$aX}�ehonV�aX_ce[V`Ysjh_^Yk}�Z�m~Vzg�j �

Eouter = c6ELaplacian + c7Esquared Laplacian + c8Einflation + c9EGGV F ,³��<µ

�yo^V!YhVc6...c9

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