Thermal modelling using discrete vasculature for thermal therapy: A review

Figures & data

Table I. Overview of the categories of discrete vessel models and the corresponding applications. The pyramid at the left indicates that the number of models decreases with increasing complexity.

Figure 1. (A) A blood vessel embedded in a tissue voxel with surrounding tissue voxels 1–8. The tissue voxel around the vessel has been divided into four boundary elements. The dotted lines indicate the lines along which the conductive heat flow in the tissue is calculated in the model. (B) shows the geometry around a vessel for two different vessel radii [37]. This picture has been reproduced from Lagendijk JJ et al. (A three-dimensional description of heating patterns in vascularised tissues during hyperthermic treatment. Phys Med Biol 1984;29:495–507. http://dx.doi.org/10.1088/0031-9155/29/5/002). © Institute of Physics and Engineering in Medicine. Published on behalf of IPEM by IOP Publishing Ltd. Reproduced by permission of IOP Publishing. All rights reserved.

Figure 2. Projection of a vessel segment (A) and a vessel cross-section (B) onto a tissue grid, together with the associated estimation and exchange sets. (A) shows three discrete vessel samples, which are labelled as ‘buckets’ [39]. Heat flow towards the vessel is withdrawn from the tissue in the exchange set voxels. The estimation set voxels are used to calculate the thermal interaction between the vessel and surrounding tissue. This picture has been reproduced from Kotte et al. (A description of discrete vessel segments in thermal modelling of tissues. Phys Med Biol 1996;41:865–84. http://dx.doi.org/10.1088/0031-9155/41/5/004). © Institute of Physics and Engineering in Medicine. Published on behalf of IPEM by IOP Publishing Ltd. Reproduced by permission of IOP Publishing. All rights reserved.

Figure 3. The vessel network in a prostate, together with the simulated 40.5 °C iso-temperature surface for a homogenous SAR level of 20 W kg⁻¹. Pre-heating of the prostate vessels differs from vessel to vessel [44]. This picture has been reproduced from Van den Berg et al. (Towards patient specific thermal modelling of the prostate. Phys Med Biol 2006;51:809–25. http://dx.doi.org/10.1088/0031-9155/51/4/004). © Institute of Physics and Engineering in Medicine. Published on behalf of IPEM by IOP Publishing Ltd. Reproduced by permission of IOP Publishing. All rights reserved.

Figure 4. (A) Large arteries (red) and veins (blue) reconstructed from a CT angiogram of a human pelvis, together with the bony structures. (B) Expanded vasculature using the vessel generation algorithm devised by Van Leeuwen et al. [43].

Lagendijk JJ, Schellekens M, Schipper J, van der Linden PM. A three-dimensional description of heating patterns in vascularised tissues during hyperthermic treatment. Phys Med Biol 1984;29:495–507 . http://dx.doi.org/10.1088/0031-9155/29/5/002

 PubMed Web of Science ®Google Scholar

Kotte ANTJ, van Leeuwen GMJ, de Bree J, van der Koijk JF, Crezee J, Lagendijk JJW. A description of discrete vessel segments in thermal modelling of tissues. Phys Med Biol 1996;41:865–84 . http://dx.doi.org/10.1088/0031-9155/41/5/004

 PubMed Web of Science ®Google Scholar

Van den Berg CAT, van de Kamer JB, De Leeuw AAC, Jeukens CRLPN, Raaymakers BW, Van Vulpen M, et al. Towards patient specific thermal modelling of the prostate. Phys Med Biol 2006;51:809–25 . http://dx.doi.org/10.1088/0031-9155/51/4/004

 PubMed Web of Science ®Google Scholar

van Leeuwen GM, Kotte AN, Lagendijk JJ. A flexible algorithm for construction of 3-D vessel networks for use in thermal modeling. IEEE Trans Biomed Eng 1998;45:596–604

 PubMed Web of Science ®Google Scholar