Radial k-space Trajectory Using Prime Number Angular Increments
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Solution Overview
Problem
Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) faces challenges in achieving optimal temporal and spatial resolution due to the higher number of spokes required by the golden angle scheme, leading to increased undersampling and artifacts, which are worse compared to schemes with constant angular increments.
Innovation Solution
A method that selectively chooses prime numbers for determining the angular increments in a radial k-space trajectory, allowing for isotropically resolved images at arbitrary time instants with fewer sampled spokes, thereby fulfilling the Nyquist-Shannon sampling theorem and minimizing undersampling artifacts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the golden angle scheme is used for radial acquisition, then isotropically resolved images can be calculated at arbitrary time instants, but the number of spokes required increases substantially, leading to greater undersampling and worse artifacts
Solution Approach 1:
The patent changes the angular increment parameter from the golden angle (111.25°) to a constant angular increment of 180°/N, where N is the number of spokes. This parameter change reduces the number of spokes required while maintaining the ability to calculate isotropically resolved images at arbitrary time instants, thereby reducing undersampling artifacts and improving image quality
2Measurement precision
If the number of spokes N is chosen to just sufficiently cover k-space according to the Nyquist-Shannon sampling theorem, then the temporal resolution decreases when using the golden angle scheme
Solution Approach 1:
The patent changes the angular increment parameter from the golden angle to a constant angular increment of 180°/N. This allows for a reduction in the number of spokes N required to cover k-space sufficiently, thereby improving temporal resolution while maintaining spatial resolution according to the Nyquist-Shannon sampling theorem
3Manufacturing precision
If a constant angular increment dΦ=π/N is used between adjacent spokes in k-space, then k-space is uniformly covered after precisely N profiles, but the full flexibility of the golden scheme in respect of the choice of time windows is not achieved
Solution Approach 1:
The patent uses a constant angular increment of 180°/N (which is 2×π/N) instead of the golden angle. This parameter change maintains uniform k-space coverage after precisely N profiles while still allowing for flexible choice of time windows, as images can be calculated from any number of sequentially measured spokes
Data Source
AI summary
In method for determining a radial k-space trajectory, having multiple spokes, of an MR control sequence, a first whole number (N) is selected from a first subset of whole numbers. A first constant angular increment (dΦ) between respective spokes of the radial k-space trajectory that are spatially adjacent in k-space is determined as the quotient of π and the first whole number N. Subsequently, a second constant angular increment (Δk*dΦ) between spokes of the radial k-space trajectory that are measured sequentially in time is determined as the product from a second whole number (Δk) and the first constant angular increment dΦ, wherein the second whole number Δk is determined from a second subset of whole numbers. The first subset of whole numbers and/or the second subset of whole numbers are/is the set of prime numbers.