Fig 1.
Flow chart of the selection of subjects from the seventh Tromsø Study to the current study.
MR = Magnetic resonance, MRI = Magnetic resonance imaging, TOF = Time-of-flight angiography series, T1 = T1-weighted series, FLAIR = T2-weighted fluid-attenuated inversion recovery series.
Fig 2.
3D volume rendering of a time-of-flight image depicting three classification cases within our classification scheme.
Green arrow: The right anterior cerebral artery is present. Yellow arrow: The left posterior cerebral artery is hypoplastic or missing, and just below 1mm in diameter. Red arrow: The right posterior cerebral artery is clearly missing. The configuration itself is of bilateral missing posterior cerebral artery (2P) type. Image follows neurological convention, where left is left and right is right. An orientation cube in the lower right corner show orientation, and its P denotes posterior.
Fig 3.
Complete graphical overview of all Circle of Willis variants observed in the current study.
All variants are sorted first by (descending) frequency and then, in case of equal frequencies, by alphanumerical ordering. Each variant’s name is put together by the missing segments with the following notation: O = Complete variant (no missing arteries), Ac = Anterior communicating artery, A = Anterior cerebral artery, Pc = Posterior communicating artery, P = Posterior cerebral artery, I = Internal carotid artery, M = Middle cerebral artery, B = Basilar artery, while the suffixes “r” and “l” denote right and left lateralization of arteries. The prefix “2” denotes bilateral missing arteries.
Table 1.
Age distributions per sex of subjects.
Table 2.
Frequencies of common Circle of Willis variants for the whole sample, and their frequencies for men and women, and for being below and above mean age [number of cases (percentage of column total)].
Fig 4.
Frequency that each artery is missing independently of Circle of Willis variants and other arteries.
Nominators and denominators are in corresponding parentheses, and represent respectively the number of times an artery is missing and the total number of subjects. ACA: Anterior cerebral artery. ACoA: Anterior communicating artery. PCoA: Posterior communicating artery. PCA: Posterior cerebral artery. ICA: Internal carotid artery. MCA: Middle cerebral Artery. BA: Basilar artery. Hemispheric left and right lateralization are denoted by “L” and “R” respectively.
Fig 5.
Heatmap of conditional probabilities that Y-artery is missing given that X-artery was missing.
Numerators and denominators of conditional probability estimates are provided in the brackets, and represent respectively the number of times two segments are missing at the same time (joint probability) and per column the number of times the artery X is missing (independent probability). The common denominator of the joint probabilities and independent probabilities have cancelled. ACA: Anterior cerebral artery. ACoA: Anterior communicating artery. PCoA: Posterior communicating artery. PCA: Posterior cerebral artery. Left and right lateralization are denoted by “L” and “R” respectively. Each successive heatmap interval increases in size with 0.05.
Fig 6.
Stacked bar plot of the frequencies of the most common Circle of Willis variants divided into age intervals as decades.
Each variant is put together by the missing segments with the following notation: 2P: Missing bilateral posterior cerebral artery. 2Pc: Missing bilateral posterior communicating artery. Ac: Missing anterior communicating artery. Pc: Missing posterior communicating artery. P: Missing proximal posterior cerebral artery. A: Missing proximal anterior cerebral artery. Left and right lateralization are denoted by using “l” or “r” respectively as a suffix for eligible segments. Special cases exempt from the preceding are: O: Complete variant, i.e. no missing segments. Rare/Other: Composite category of other rare variants with one or more missing segments.