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user9447
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Since you are wanting to target the arteries you could either open each one up and modify each one. Since you are using Inkscape you would have to duplicate each one and adjust the anchors to their desired area. Either way this will be a timely process. If you want to target a hole section you would have to see how it was built. Such as this is one artery path but not all the arteries:

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Since you are wanting to target the arteries you could either open each one up and modify each one. Since you are using Inkscape you would have to duplicate each one and adjust the anchors to their desired area. Either way this will be a timely process. If you want to target a hole section you would have to see how it was built. Such as this is one artery path but not all the arteries:

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added 249 characters in body
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user9447
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To answer your question: "What's the best way for editing files like that to be able to select different subparts and color them?"

I would open everything in a code editor and manipulate the fill and you can even add styling with CSS to them.

To answer your question: "What's the best way for editing files like that to be able to select different subparts and color them?"

I would open everything in a code editor and manipulate the fill and you can even add styling with CSS to them.

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user9447
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I wouldnt use Inkscape I would use a code editor in this instance. You can open the SVG file and you could pullout and test the paths, in this case:

<path xmlns="http://www.w3.org/2000/svg" id="path351" fill="#ED5D40" d="M357.395,214.812c-2.646-3.05-6.138-7.847-10.553-8.137c-1.53-0.1-3.363,0.666-4.316,1.871    c2.714,1.652-4.842,5.748-6.275,4.082c1.855,2.163-2.439,3.265-3.823,3.567c-1.448,0.317-2.215,0.128-3.587-0.18    c-1.734-0.391-3.451,0.485-4.984,1.179c-6.429,2.912-7.636,10.117-5.79,16.435c1.497,5.132,3.86,10.467,7.753,14.243    c2.068,2.009,4.276,2.552,6.684,3.871c2.48,1.358,4.274,2.92,7.157,3.681c4.021,1.06,7.828-0.449,11.841-0.435    c1.721,0.005,3.318,0.613,5.08,0.688c2.136,0.093,4.279-0.057,6.406,0.173c5.291,0.575,10.852-5.71,10.705-10.759    c-0.067-2.307-1.234-4.621-1.976-6.778c-1.483-4.324-3.636-8.563-6.132-12.375C363.125,222.186,360.369,218.237,357.395,214.812z"/>

Is the heart:

enter image description here

What I did was use Chrome's Inspect Element to tell me it was the heart:

enter image description here

If you notice in the DOCTYPE it tells you how it was created:

<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd" [
    <!ENTITY ns_extend "http://ns.adobe.com/Extensibility/1.0/">
    <!ENTITY ns_ai "http://ns.adobe.com/AdobeIllustrator/10.0/">
    <!ENTITY ns_graphs "http://ns.adobe.com/Graphs/1.0/">
    <!ENTITY ns_vars "http://ns.adobe.com/Variables/1.0/">
    <!ENTITY ns_imrep "http://ns.adobe.com/ImageReplacement/1.0/">
    <!ENTITY ns_sfw "http://ns.adobe.com/SaveForWeb/1.0/">
    <!ENTITY ns_custom "http://ns.adobe.com/GenericCustomNamespace/1.0/">
    <!ENTITY ns_adobe_xpath "http://ns.adobe.com/XPath/1.0/">
]>

Which most of this could be modified to just include that its an SVG.