Table 1.

HDMI quantitative biomarkers

Biomarkers	Definition and calculation
Initial HDMI biomarkers
NB	Numbers of branch points: defined as any node that connected to three or more vessel segments [24].
NV	Number of vessel segments
VD	Vessel density: defined as the proportion of vessel area with blood flow over the total area measured [24].
D (mm)	Vessel diameter (Dmean, Dmax): defined as two times of the minimum distance between the vessel centerline and the vessel border ([24].
DM	Distance metric (DMmean, DMmax): defined as the ratio between the actual path length of a meandering curve (vessel) and the linear distance between the two end points [24]. Distance metric measures vascular tortuosity.
Novel HDMI biomarkers
MD	Murray’s deviation: diameter mismatch, defined as the deviation from Murray's law, increases in the vasculature network of malignant tumors Using skeleton image, the diameters of sub-vessels were used to define mother vessel (the sub-vessel with the largest diameter) and daughter vessels (the remaining sub-vessels).MD was Calculated Using MD = $\frac{\mid {\mathrm{D}}_{\text{mother}}^3-\sum {\mathrm{D}}_{\text{daughter}}^3\mid }{{\mathrm{D}}_{\text{mother}}^3}$. If NB = 0, MD = 1 [25; 31; 32].
mvFD	Microvessel fractal dimension: A unit-less geometrical feature is a marker of microvascular complexity. Can be calculated using the Box counting method. Knowing the box size, s, and the number of boxes, Ns, to cover all the vessels, the mvFD can be calculated, mvFD = $\underset{s\to 0}{\text{lim}}\frac{\log {\mathrm{N}}_{\mathrm{s}}}{\log \frac{1}{\mathrm{s}}}$, to identify the structural complexity of tumor vessels [25; 27; 28].
BA (°)	Bifurcation angle: refers to the angle between two daughter vessels Two straight lines were generated by fitting two daughter vessels, and the angle between them is calculated as BA [25; 29; 30]. If NB = 0, BA = 180°.
VDR	Vessel density ratio (VDR): tumor vessel distributions at the periphery (VDR<1), or at the center (VDR>1) or both (VDR ≈ 1) VDR = $\text{VDR}=\frac{{\text{Vessel Density}}_{\text{center}}}{{\text{Vessel Density}}_{\text{peripheral}}}$ [34].
SVP	Spatial vascularity pattern: the distribution pattern of microvessels, either concentrated peripherally (peritumoral vascularization) or inside the lesion (intratumoral vascularization. SVP is calculated by VDR. If VDR < 1, SVP = 0, meaning a more peripherally concentrated vessel. distribution. If VDR > 1, SVP = 1, meaning a more centrally concentrated vessel distribution [25; 33].