Mathematical Modeling of Melanoma Cell Migration with an Elastic Continuum Model for the Evaluation of the Influence of Tumor Necrosis Factor-Alpha on Migration

<table>Migration due to deformation. Simulation of the model obtained for the hypothetical situation in which migration would occur exclusively due to deformation. The values of <svg height="7.9499998" id="M92" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.7375002 7.9499998" width="8.7375002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q-12 -27 -36 -158q-44 -7 -77 -15l-5 7l82 349q6 25 -2 25q-16 0 -72 -41l-14 22q44 41 89 69.5t66 28.5q19 0 19 -32q0 -16 -6 -43l-35 -160l146 143q94 92 136 92q20 0 33 -12t13 -30z" id="x1D705"></path></g>
</svg> and <svg height="12.325" id="M93" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 10.0125 12.325" width="10.0125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.825)"><path d="M559 271q0 -109 -83 -187t-189 -89l-36 -213q-16 -30 -86 -43l-7 9q10 36 53 242q-91 11 -139.5 63.5t-48.5 132.5q0 186 242 271l11 -28q-76 -34 -119.5 -91.5t-43.5 -136.5q0 -66 29 -108.5t77 -55.5q39 205 56 260q21 71 65 111t93 40q50 0 88 -45.5t38 -131.5z
M484 273q0 65 -26.5 99t-52.5 34q-37 0 -53 -75l-59 -298q80 5 135.5 74.5t55.5 165.5z" id="x1D711"></path></g>
</svg> used are the ones from Table <a href="../tab1/">1</a>. <svg height="20.275" id="M94" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 62.099998 20.275" width="62.099998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path d="M516 277q0 -126 -140 -231q-36 -27 -75.5 -42.5t-63.5 -15.5q-38 0 -73 43q-10 -44 -18 -106q-18 -134 -32 -151q-12 -16 -40 -25t-46 -10l-5 14q22 38 84 406q16 92 44.5 146.5t88.5 95.5q68 47 136 47q63 0 101.5 -47.5t38.5 -123.5zM432 259q0 61 -27 101t-79 40
t-82 -49t-49 -148l-24 -127q42 -36 88 -36q79 0 126 61.5t47 157.5z" id="x1D70C"></path></g><g transform="matrix(.017,-0,0,-.017,13.933,15.775)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,28.637,15.775)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,39.636,15.775)"><path d="M513 0h-211v26q44 5 55 17t11 60v166q0 123 -98 123q-59 0 -104 -51v-238q0 -48 10 -60.5t55 -16.5v-26h-213l1 26q46 4 57 16t11 61v477q0 48 -9.5 58.5t-58.5 14.5v24q63 9 147 35v-336q73 73 143 73q64 0 101 -42t37 -129v-175q0 -49 11 -61t55 -16v-26z" id="x68"></path></g>
<g transform="matrix(.012,-0,0,-.012,48.712,7.613)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.012,-0,0,-.012,55.697,7.613)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg> for both situations: control and TNF-<i>α</i>.</table>

Journal of Computational Medicine

fig2

Figure 2

Figure 2: Mathematical Modeling of Melanoma Cell Migration with an Elastic Continuum Model for the Evaluation of the Influence of Tumor Necrosis Factor-Alpha on Migration 

Figure 2 | Mathematical Modeling of Melanoma Cell Migration with an Elastic Continuum Model for the Evaluation of the Influence of Tumor Necrosis Factor-Alpha on Migration 