General non-Cartesian gradient waveform calculation method, system and device based on g space

Abstract

The invention provides a g-space-based general non-Cartesian gradient waveform calculation method, system and device, and the method comprises the steps: mapping a generated non-Cartesian sampling track to a g space, and carrying out the solving of each sampling point through a bidirectional traversal mechanism, so as to obtain a final track parameter sequence; and then parameterizing the final trajectory parameter sequence to obtain a gradient waveform sequence of the non-Cartesian sampling trajectory. The method is used for solving the problems of long calculation time and inaccurate switching rate control caused by the fact that the gradient waveform is calculated by adopting a bidirectional traversal mechanism for any non-Cartesian trajectory in the prior art and depends on an arc length parameter equation. Parameter conversion is not needed, dependence on an arc length parameter equation is avoided, and the calculation time is greatly shortened; in addition, when the obtained trajectory parameter sequence is re-parameterized, the problem of arc length direction time interpolation does not exist, so that the problem of inaccurate switching rate control does not exist, and the application of the non-Cartesian sampling trajectory in a clinical scene is facilitated.

Description

Technical Field

[0001] This invention relates to the field of magnetic resonance imaging, and in particular to a method, system, and apparatus for calculating general non-Cartesian gradient waveforms based on g-space. Background Technology

[0002] Non-Cartesian imaging techniques, due to their advantages such as efficient sampling trajectories, robustness to motion, high signal-to-noise ratio, and randomization of undersampling artifacts, have been widely applied in fields such as parameter quantification, downsampling reconstruction, silent imaging, and magnetic resonance spectroscopy. A key technical challenge in non-Cartesian imaging is designing gradient waveforms based on a given sampling trajectory. These waveforms must not only meet hardware constraints but also ensure temporal optimality. In the early stages, when only a few non-Cartesian trajectories existed, optimal gradient waveforms were typically developed for specific trajectories, such as spiral or rose trajectories. The basic idea was to model the switching rate using trajectory parameters and solve for the trajectory parameters at the desired switching rate amplitude.

[0003] To address this, Meyer et al. proposed a fast recursive method for designing helical trajectories, which projects the gradient waveform into a vector space where the switching rate is represented by the distance between adjacent gradient sampling points. This method simplifies switching rate control and ensures accurate execution of hardware constraints. However, the Meyer method is limited to helical trajectories because relying solely on forward solving cannot predict upcoming curvature maxima. Furthermore, simply constraining gradient sampling points to be parallel to the current trajectory derivative does not fully guarantee that the sampling points fall exactly on the trajectory. Subsequently, Lustig et al. proposed an optimal control-based method that simultaneously constrains both gradient magnitude and switching rate magnitude. The Lustig method is non-iterative and applicable to arbitrary non-Cartesian trajectories. Compared to the Meyer method, the Lustig method employs a bidirectional traversal mechanism, which solves for gradient values ​​in both forward and backward directions and uses the minimum of the forward and backward solutions as the final result to ensure deceleration at the appropriate time before the curvature maxima. This mechanism can handle arbitrary trajectories with non-monotonic curvature and has been widely adopted in non-Cartesian imaging.

[0004] However, the optimal control algorithm used in the Lustig method only accepts arc-length parametric equations as trajectories. Since existing sampling trajectories in MRI are not represented by arc-length parametric equations, the Lustig method requires additional arc-length integration and numerical solutions to its inverse function to transform arbitrary parametric equations into arc-length parametric equations. The step size of the arc length also needs to be traded off based on the requirements of computational speed and accuracy (decreasing the step size will inevitably lead to a significant reduction in speed, while increasing the step size will inevitably lead to a significant reduction in accuracy). The consequence of this is that MRI, being a speed-sensitive application, will consume a significant amount of computation time when using the Lustig method. Another limitation of the Lustig method is inaccurate switching rate control. This is because during the interpolation of arc length with time, the gradient magnitude is initially small, resulting in far more time sampling points required per unit arc length than when the gradient is larger, leading to inaccurate switching rate control. Furthermore, MRI switching rates have hardware limitations. When the preset input switching rate approaches the hardware limit due to insufficient switching rate accuracy, the scan will fail, which is a serious problem in clinical settings. Summary of the Invention

[0005] In view of the shortcomings of the prior art described above, the purpose of this invention is to provide a general non-Cartesian gradient waveform calculation method, system and device based on g-space, to solve the problems of long calculation time and inaccurate switching rate control caused by the use of bidirectional traversal mechanism to calculate gradient waveforms for arbitrary non-Cartesian trajectories based on g-space and the dependence on arc length parameter equations.

[0006] To achieve the above and other related objectives, a first aspect of the present invention provides a general non-Cartesian gradient waveform calculation method based on g-space, the method comprising: generating a non-Cartesian sampling trajectory; sequentially solving for the final trajectory parameter sequence by using a bidirectional traversal mechanism on each sampling point of the non-Cartesian sampling trajectory mapped in g-space; and re-parameterizing the final trajectory parameter sequence to obtain the gradient waveform sequence of the non-Cartesian sampling trajectory.

[0007] In some embodiments of the first aspect of the present invention, the step of sequentially solving the sampling points of the non-Cartesian sampling trajectory mapped in space g using a bidirectional traversal mechanism to obtain the final trajectory parameter sequence includes: sequentially determining the sampling points of the non-Cartesian sampling trajectory mapped in space g using a bidirectional traversal mechanism, and obtaining the gradient vector and trajectory parameters of each sampling point to form a gradient vector sequence and a trajectory parameter sequence.

[0008] In some embodiments of the first aspect of the present invention, the bidirectional traversal mechanism includes: a backward traversal phase operation and a forward traversal phase operation; wherein, the backward traversal phase operation includes: starting from the end point of the non-Cartesian sampling trajectory, solving along the parameter decreasing direction to obtain a gradient vector sequence and a trajectory parameter sequence, and obtaining a functional relationship between the two sequences; the forward traversal phase operation includes: after the backward traversal phase operation is completed, starting from the start point of the non-Cartesian sampling trajectory, solving along the parameter increasing direction to obtain a gradient vector sequence and a trajectory parameter sequence that conform to the functional relationship between the two sequences obtained by the backward traversal phase operation.

[0009] In some embodiments of the first aspect of the present invention, the backward traversal stage operation includes: taking the endpoint of the non-Cartesian sampling trajectory as the initial point, obtaining the gradient vector of the initial point, the current trajectory tangent direction, and trajectory parameters; taking the endpoint as the current sampling point, drawing a first curve, a second curve, and a straight line based on the gradient vector of the current sampling point, the current trajectory tangent direction, and a preset limit value; determining the gradient vector and trajectory tangent direction of the next sampling point with the parameter decreasing direction through selected key points, calculating the trajectory parameters of the next sampling point, and using the sampling point as the current sampling point to calculate the next sampling point, until the gradient vectors and trajectory parameters of all sampling points are obtained, forming a gradient vector sequence and a trajectory parameter sequence, and obtaining the functional relationship between the two sequences through interpolation processing.

[0010] In some embodiments of the first aspect of the present invention, the forward traversal phase operation includes: taking the starting point of the non-Cartesian sampling trajectory as the initial point, obtaining the gradient vector of the initial point, the current trajectory tangent direction, and trajectory parameters; taking the starting point as the current sampling point, drawing a first curve, a second curve, and a straight line based on the gradient vector of the current sampling point, the current trajectory tangent direction, and a preset limit value, and determining the gradient vector trajectory tangent direction of the next sampling point with the parameter increment direction through selected key points and calculating the trajectory parameters of the next sampling point, so that the obtained trajectory parameters and gradient vector conform to the functional relationship between the two sequences obtained by the backward traversal phase operation, and using the sampling point as the current sampling point to calculate the next sampling point, until the gradient vectors and trajectory parameters of all sampling points are obtained, forming the final trajectory parameter sequence.

[0011] In some embodiments of the first aspect of the present invention, the step of reparameterizing the final trajectory parameter sequence to obtain the gradient waveform sequence of the non-Cartesian sampled trajectory includes: inputting a preset trajectory function into the final trajectory parameter sequence to obtain a trajectory sampling point sequence; and performing numerical differentiation on the trajectory sampling point sequence to obtain the gradient waveform sequence.

[0012] In some embodiments of the first aspect of the present invention, the step of drawing a first curve, a second curve, and a straight line based on the gradient vector of the current sampling point, the current trajectory tangent direction, and a preset limit value includes: drawing a circle with the gradient vector of the current sampling point as the center and the product of the switching rate limit value and the time step as the radius to obtain the first curve; drawing a circle with the origin of g-space as the center and the gradient magnitude limit value as the radius to obtain the second curve; and drawing a straight line with an intercept of 0 and parallel to the current trajectory tangent direction.

[0013] In some embodiments of the first aspect of the present invention, the method of selecting key points includes: selecting the intersection point of a second curve and a straight line within the circular range formed by the first curve as the key point; wherein, the gradient vector of the key point is constrained by the switching rate constraint value in the preset constraint value, and the magnitude of the gradient vector of the key point is constrained by the gradient magnitude constraint value and the escape velocity constraint value in the preset constraint value.

[0014] To achieve the above and other related objectives, a second aspect of the present invention provides a general non-Cartesian gradient waveform calculation system based on g-space. The system includes: a trajectory generation module, a mapping module, a bidirectional traversal calculation module, and a reparameterization module. The trajectory generation module is used to generate the non-Cartesian sampled trajectory. The mapping module, connected to the trajectory generation module, is used to map the non-Cartesian sampled trajectory onto g-space through a function transformation. The bidirectional traversal calculation module, connected to the mapping module, is used to sequentially solve for each sampling point mapped onto g-space using a bidirectional traversal mechanism to obtain the final trajectory parameter sequence. The reparameterization module, connected to the bidirectional traversal calculation module, is used to reparameterize the final trajectory parameter sequence to obtain the gradient waveform sequence of the non-Cartesian sampled trajectory.

[0015] To achieve the above and other related objectives, a third aspect of the present invention provides a general non-Cartesian gradient waveform calculation device based on g-space. The device includes a memory, a processor, and a computer program stored in the memory.

[0016] As described above, the present invention provides a general non-Cartesian gradient waveform calculation method, system, and apparatus based on g-space, which has the following beneficial effects: by mapping the generated non-Cartesian sampling trajectory onto g-space, the final trajectory parameter sequence is obtained by sequentially applying a bidirectional traversal mechanism to each sampling point, and then the final trajectory parameter sequence is re-parameterized to obtain the gradient waveform sequence of the non-Cartesian sampling trajectory. This invention addresses the problems of long computation time and inaccurate switching rate control caused by the dependence of the arc length parameter equation on the arc length parameter equation when calculating the gradient waveform of arbitrary non-Cartesian trajectories based on g-space using a bidirectional traversal mechanism. This invention eliminates the need for any parameter transformation, avoids dependence on the arc length parameter equation, and significantly shortens the scanning time; furthermore, there is no arc length-to-time interpolation problem when re-parameterizing the obtained trajectory parameter sequence to obtain the gradient waveform sequence, thus eliminating the problem of inaccurate switching rate control and effectively promoting the application of non-Cartesian sampling trajectories in clinical scenarios. Attached Figure Description

[0017] Figure 1 The diagram shown is a flowchart illustrating a general non-Cartesian gradient waveform calculation method based on g-space in one embodiment of the present invention.

[0018] Figure 2 (a) Shows a graph of the relationship between gradient intensity and time for a non-Cartesian sampling trajectory according to an embodiment of the present invention;

[0019] Figure 2 (b) shows a two-dimensional g-space coordinate diagram according to an embodiment of the present invention.

[0020] Figure 3 The diagram shown is a schematic representation of a bidirectional traversal mechanism in one embodiment of the present invention.

[0021] Figure 4 The diagram shown is a schematic representation of key point coordinates based on g-space in one embodiment of the present invention.

[0022] Figure 5 The diagram shown is a connection schematic of a general non-Cartesian gradient waveform calculation system based on g-space according to an embodiment of the present invention.

[0023] Figure 6 The diagram shows a comparison of the sampling trajectory gradient waveform in one embodiment of the present invention with the calculation results of the prior art and the present invention.

[0024] Figure 7 The diagram shown is a schematic representation of a general non-Cartesian gradient waveform calculation device based on g-space in one embodiment of the present invention. Detailed Implementation

[0025] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0026] It should be noted that in the following description, reference is made to the accompanying drawings, which illustrate several embodiments of the invention. It should be understood that other embodiments may also be used, and changes in mechanical composition, electrical structure, and operation may be made without departing from the spirit and scope of the invention. The following detailed description should not be considered limiting, and the scope of the embodiments of the invention is defined only by the claims of the published patents. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. Spatially related terms, such as “upper,” “lower,” “left,” “right,” “below,” “below,” “lower part,” “above,” “upper part,” etc., may be used herein to illustrate the relationship between one element or feature shown in the figures and another element or feature.

[0027] Throughout this specification, when it is said that a part is "connected" to another part, this includes not only "direct connection" but also "indirect connection" by placing other elements in between. Furthermore, when it is said that a part "includes" a certain constituent element, unless otherwise stated otherwise, this does not exclude other constituent elements, but rather means that other constituent elements may also be included.

[0028] The terms "first," "second," and "third," etc., used herein are for the purpose of describing various parts, components, regions, layers, and / or segments, but are not limiting. These terms are used only to distinguish one part, component, region, layer, or segment from others. Therefore, the "first part," "component," "region," "layer," or "segment" described below may refer to a "second part," "component," "region," "layer," or "segment" without departing from the scope of this invention.

[0029] Furthermore, as used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context indicates otherwise. It should be further understood that the terms “comprising,” “including,” indicate the presence of the stated feature, operation, element, component, item, kind, and / or group, but do not preclude the presence, occurrence, or addition of one or more other features, operations, elements, components, items, kinds, and / or groups. The terms “or” and “and / or” as used herein are interpreted as inclusive, or mean any one or any combination thereof. Thus, “A, B, or C” or “A, B, and / or C” means “any one of: A; B; C; A and B; A and C; B and C; A, B, and C.” Exceptions to this definition arise only when combinations of elements, functions, or operations are inherently mutually exclusive in some manner.

[0030] This invention provides a general non-Cartesian gradient waveform calculation method, system, and apparatus based on g-space. It maps the generated non-Cartesian sampling trajectory onto g-space, and sequentially uses a bidirectional traversal mechanism to solve for each sampling point to obtain the final trajectory parameter sequence. Then, it re-parameterizes the final trajectory parameter sequence to obtain the gradient waveform sequence of the non-Cartesian sampling trajectory. This invention addresses the problems of long computation time and inaccurate switching rate control in existing technologies that rely on arc length parameter equations when calculating gradient waveforms for arbitrary non-Cartesian trajectories using a bidirectional traversal mechanism in g-space. This invention eliminates the need for any parameter transformation, avoids dependence on arc length parameter equations, and significantly reduces scanning time. Furthermore, it avoids the problem of arc length-to-time interpolation when re-parameterizing the obtained trajectory parameter sequence to obtain the gradient waveform sequence, thus eliminating the problem of inaccurate switching rate control and effectively promoting the application of non-Cartesian sampling trajectories in clinical scenarios.

[0031] The present invention will now be described in detail with reference to the accompanying drawings, so that those skilled in the art can readily implement it. The present invention can be embodied in many different forms and is not limited to the embodiments described herein.

[0032] like Figure 1 The illustration shows a flowchart of a general non-Cartesian gradient waveform calculation method based on g-space in an embodiment of the present invention.

[0033] The method includes:

[0034] S11: Generate a non-Cartesian sampling trajectory;

[0035] S12: The final trajectory parameter sequence is obtained by sequentially solving the bidirectional traversal mechanism for each sampling point of the non-Cartesian sampling trajectory mapped in the g space;

[0036] S13: The final trajectory parameter sequence is reparameterized to obtain the gradient waveform sequence of the non-Cartesian sampled trajectory.

[0037] The non-Cartesian sampling trajectories include, but are not limited to, spiral sampling, rose-shaped sampling, conical sampling, and golden angle rotation trajectories; the g-space is the gradient magnetic field space, used to describe the magnetic field changes generated by gradient coils in MRI.

[0038] In one embodiment, the step of sequentially solving the sampling points of the non-Cartesian sampling trajectory mapped onto the g space using a bidirectional traversal mechanism to obtain the final trajectory parameter sequence includes: sequentially determining the sampling points of the non-Cartesian sampling trajectory mapped onto the g space using a bidirectional traversal mechanism, and obtaining the gradient vector and trajectory parameters of each sampling point to form a gradient vector sequence and a trajectory parameter sequence.

[0039] Specifically, such as Figure 2 As shown, the curves depicting the gradient intensity and time generated by the magnetic field varying with the x and y coordinates through the x and y channels of a non-Cartesian sampling trajectory are as follows: Figure 2 (a) Two curves g x (t), g y (t) represents the relationship between the gradient intensity and time of the non-Cartesian sampling trajectory through the x and y channels, respectively. Taking two-dimensional imaging as an example... Figure 2 As shown in (b), space g is based on g x g is the horizontal axis of the coordinate system. y The space formed by the Cartesian coordinate system established with the vertical axis of the coordinate system will... Figure 2 In (a), the gradient of the x-channel and the gradient of the y-channel of any non-Cartesian sampling trajectory at the same time can be mapped to the g-space to obtain a gradient waveform sampling point in the g-space. All the gradient waveform sampling points constitute the g-space curve corresponding to the gradient curve of the non-Cartesian sampling trajectory.

[0040] In one embodiment, the bidirectional traversal mechanism includes a backward traversal phase operation and a forward traversal phase operation; wherein, the backward traversal phase operation includes: starting from the end point of the non-Cartesian sampling trajectory, solving along the parameter decreasing direction to obtain a gradient vector sequence and a trajectory parameter sequence, and obtaining the functional relationship between the two sequences; the forward traversal phase operation includes: after the backward traversal phase operation is completed, starting from the start point of the non-Cartesian sampling trajectory, solving along the parameter increasing direction to obtain a gradient vector sequence and a trajectory parameter sequence that conform to the functional relationship between the two sequences obtained by the backward traversal phase operation.

[0041] like Figure 3As shown, in a k-space, the illustrated trajectory is composed of two line segment trajectories and a 1 / 4 circular curve segment trajectories. The k-space is the spectral space of the non-Cartesian sampled trajectory image after Fourier transform, used to represent the spatial distribution of the non-Cartesian sampled trajectory. The relationship between the k-space and the g-space can be expressed as:

[0042] k(t)=γ∫G(t)dt; (Formula 1)

[0043] Since γ is the gyromagnetic ratio constant, k(t) and G(t) are in a simple differential relationship, that is, the k space and g space are in a differential relationship. The spatial trajectory of the k space is controlled by gradient control in the g space.

[0044] In k-space, the bidirectional traversal mechanism employs a "solve backward before solve forward" strategy, meaning it solves backward before verifying forward. The backward traversal phase begins at the end of the non-Cartesian sampling trajectory and proceeds along the parameter decreasing direction. The gradient magnitude must be less than the user-input preset gradient and escape velocity limits. After differential transformation in k-space, this can be represented as:

[0045] ∣g(τ1)∣=min{∣gforw(τ1)∣,∣gback(τ1)∣}=G esc ;(Formula 2)

[0046] Where g(τ1) represents the gradient vector of the key point in g space, and the direction from k(τ0) to k(τ1) represents the forward traversal direction of the trajectory, then the direction from k(τ1) to k(τ0) represents the backward traversal direction of the trajectory. k(τ1) represents the forward arc entry point on the 1 / 4 circular curve segment trajectory. The maximum deceleration gradient vector gback(τ1) is derived and calculated from this point in the backward traversal direction. The forward traversal stage operation is performed after the backward traversal stage operation, starting from the starting point k(τ0) of the non-Cartesian sampling trajectory, and solving along the parameter increasing direction. As can be seen from Formula 1... Figure 3 In G, `decelerate(limited by |gback|)` means that the magnitude of the maximum acceptable gradient vector g(τ1) should be limited to |gback|; this yields the maximum accelerated gradient vector gforw(τ1) during the forward traversal phase. esc The escape velocity of the 1 / 4 circular curve segment trajectory is expressed as g(τ1), which means that the magnitude of g(τ1) should be the minimum of the magnitude of the gradient vector gforw(τ1) and the gradient vector gback(τ1), and should not exceed the maximum escape velocity value G. escThat is, the magnitude of the gradient vector in the backward traversal phase, |gback|, is used to limit the excessively large magnitude of the gradient vector in the forward traversal phase, |gforw|, so that the sampling point decelerates in advance on the straight segment in the forward traversal phase, ensuring that the speed is maximum G when entering the circular arc. esc To avoid escape. It is worth noting that this only applies if the sampling point's velocity does not exceed G when entering the circular arc. esc Only when the sampling point's velocity exceeds G when entering the arc can key points exist. esc If the condition is not met, the key point will escape and there will be no key point in the space g that meets the condition. Repeat the above steps to obtain the gradient vector sequence and trajectory parameter sequence in the space g that conform to the functional relationship between the two sequences obtained by the backward traversal stage operation.

[0047] In one embodiment, the backward traversal phase includes: taking the endpoint of the non-Cartesian sampling trajectory as the initial point, obtaining the gradient vector of the initial point, the current trajectory tangent direction, and trajectory parameters; at this time, the gradient vector of the initial point is a unit vector of the endpoint gradient magnitude multiplied by the trajectory derivative, where the endpoint gradient magnitude is a preset value input by the user, usually preset to 0, and the direction of the gradient vector is the same as the direction parallel to the tangent of the trajectory endpoint, while the unit vector of the trajectory derivative is a unit vector parallel to the trajectory. Taking the endpoint as the current sampling point, based on the gradient vector of the current sampling point, the current trajectory tangent direction, and preset limit values, a first curve, a second curve, and a straight line in g-space are drawn, and the gradient vector and trajectory tangent direction of the next sampling point in the parameter decreasing direction are determined by selecting key points, and the trajectory parameters of the next sampling point are calculated.

[0048] Specifically, with Figure 4 For example, a space curve of g is plotted based on the gradient vector g(t0) of the current sampling point, the current trajectory tangent direction, and a preset constraint value. Here, the slew rate constraint represents the switching rate constraint, i.e., the coverage area of ​​the first curve; the gradient constraint represents the gradient constraint, i.e., the coverage area of ​​the second curve; and the area covered by both is the feasible solution range, the Allowed region. The straight line dk constraint represents the gradient direction constraint. Within the feasible solution range, the intersection point where the straight line dk constraint passes through the second curve is the next sampling point g(t1). The calculation of the intersection point determines the gradient vector and trajectory tangent direction of the next sampling point in the direction of parameter decrease, and calculates the trajectory parameters of that sampling point. The formula for the gradient vector direction of the next sampling point (expressed as a unit vector) is:

[0049]

[0050] The formula for calculating the gradient magnitude (i.e., the magnitude of the gradient vector) at the next sampling point is:

[0051] a←1

[0052]

[0053] The gradient vector is formed by combining the magnitude and direction of the gradient vector. The formula for calculating the trajectory parameters of the next sampling point is as follows:

[0054]

[0055] In the above formula, g represents the gradient vector, k represents the k-space coordinates, p represents the parameters of any trajectory equation, and s pt The sign represents the derivative of p with respect to time t. The gradient vector, trajectory tangent direction, and trajectory parameters of the intersection point are calculated using the above formula as the next sampling point. This sampling point is then used as the current sampling point for the next sampling point calculation, until the gradient vectors and trajectory parameters of all sampling points are obtained, forming a gradient vector sequence and a trajectory parameter sequence. Interpolation is then performed to obtain the functional relationship between the two sequences. The interpolation process refers to constructing a continuous functional relationship using the known gradient vector sequence and trajectory parameter sequence.

[0056] In one embodiment, the forward traversal phase includes: taking the starting point of the non-Cartesian sampling trajectory as the initial point, obtaining the gradient vector of the initial point, the current trajectory tangent direction, and trajectory parameters; at this time, the gradient vector of the initial point is a unit vector of the starting point gradient magnitude multiplied by the trajectory derivative, where the starting point gradient magnitude is a preset value input by the user, usually preset to 0, and the direction of the gradient vector is the same as the direction parallel to the tangent of the trajectory endpoint, while the unit vector of the trajectory derivative is a unit vector parallel to the trajectory. Taking this starting point as the current sampling point, a first curve, a second curve, and a straight line are drawn based on the gradient vector of the current sampling point, the current trajectory tangent direction, and a preset limit value. The gradient vector and trajectory tangent direction of the next sampling point in the parameter increment direction are determined by selecting key points, and the trajectory parameters of the next sampling point are calculated, so that the obtained trajectory parameters and gradient vector conform to the functional relationship between the two sequences obtained in the backward traversal phase.

[0057] Specifically, with Figure 4For example, a space curve of g is plotted based on the gradient vector g(t0) of the current sampling point, the current trajectory tangent direction, and a preset constraint value. Here, the slew rate constraint represents the switching rate constraint, i.e., the coverage area of ​​the first curve; the gradient constraint represents the gradient constraint, i.e., the coverage area of ​​the second curve; and the area covered by both is the feasible solution range, the Allowed region. The straight line dk constraint represents the gradient direction constraint. Within the feasible solution range, the intersection point of the straight line dk constraint and the second curve is the next sampling point g(t1). The calculation of the intersection point determines the gradient vector and trajectory tangent direction of the next sampling point in the parameter increment direction, and calculates the trajectory parameters of that sampling point. The formula required for this calculation method is the same as that required in the backward traversal stage. It is worth noting that the gradient magnitude of this sampling point must also be limited to the functional relationship between the two sequences obtained in the backward traversal stage. The gradient vector, trajectory tangent direction, and trajectory parameters of this intersection point are calculated using the above formula. Finally, this sampling point is used as the current sampling point for the next sampling point calculation, until the gradient vectors and trajectory parameters of all sampling points are obtained, forming the final trajectory parameter sequence.

[0058] In one embodiment, the step of reparameterizing the final trajectory parameter sequence to obtain the gradient waveform sequence of the non-Cartesian sampled trajectory includes: inputting a preset trajectory function into the final trajectory parameter sequence to obtain a trajectory sampling point sequence; performing numerical differentiation on the trajectory sampling point sequence to obtain the final gradient waveform sequence, which has the following characteristics: when the gradient magnitude does not reach the user-preset gradient magnitude limit, the switching rate magnitude is always the user-input switching rate limit magnitude, and the overshoot rate does not exceed one-thousandth; when the gradient magnitude reaches the user-preset gradient magnitude limit, the actual gradient magnitude is constant at the user-preset gradient magnitude limit, at which point there is no overshoot, and the undershoot rate does not exceed one ten-thousandth, and overall, the switching rate control is precise.

[0059] In one embodiment, the step of drawing the first curve, the second curve, and the straight line based on the gradient vector of the current sampling point, the current trajectory tangent direction, and the preset limit value includes: the preset limit value is a preset value input by the user, including but not limited to a preset switching rate limit value, a preset gradient magnitude limit value, and a preset escape velocity limit value.

[0060] by Figure 4 For example, the drawing method of the first curve, the second curve, and the straight line includes: taking the gradient vector g(t0) of the current sampling point as the center, and using a preset switching rate limit value... A circle is drawn with the product of the time step Δt and the time step Δt as the radius to obtain the first curve; the circle is then drawn with the origin of the g-space as the center and the preset gradient magnitude limit value as the boundary. Draw a circle with a radius to obtain the second curve; draw a straight line with an intercept of 0 and a direction parallel to the tangent of the current k-space trajectory. The slope of this straight line can be obtained by differentiating the sampling points of the current k-space trajectory.

[0061] In one embodiment, the method for selecting key points includes: drawing a g-space curve based on the gradient vector g(t0) of the current sampling point, the current trajectory tangent direction, and a preset constraint value; using a Slew rate constraint as the first curve coverage area and a Gradient constraint as the second curve coverage area; and identifying the key point where the straight line dk constraint intersects the second curve Gradient constraint within the shared Allowed region, which is the next sampling point g(t1). Here, the first curve coverage area represents the gradient vector conforming to the switching rate constraint, the second curve coverage area represents the gradient vector conforming to the gradient magnitude constraint, and the shared coverage area represents the gradient vector conforming to both the gradient magnitude constraint and the switching rate constraint. The straight line represents the gradient vector parallel to the trajectory tangent direction. Therefore, the direction of the key point is constrained by the current trajectory tangent direction, the gradient vector of the key point is constrained by the preset switching rate constraint value, and the magnitude of the gradient vector of the key point is constrained by the preset gradient magnitude constraint value. Furthermore, since intersections can only exist in g-space within the escape velocity constraint value, the magnitude of the gradient vector of the key point is constrained by the escape velocity constraint value.

[0062] In one embodiment, the method for calculating the trajectory parameters of the sampling point includes: using the Runge-Kutta second-order method to solve the gradient vector to obtain the trajectory parameters of the sampling point; optionally, the Euler method can also be used to update the parameters.

[0063] Similar in principle to the above embodiments, the present invention provides a general non-Cartesian gradient waveform calculation system 500 based on g-space, such as... Figure 5 As shown. The system includes: a trajectory generation module 501, a mapping module 502, a bidirectional traversal calculation module 503, and a reparameterization module 504; wherein,

[0064] The trajectory generation module 501 is used to generate the non-Cartesian sampling trajectory;

[0065] The mapping module 502 is connected to the trajectory generation module 501 and is used to map the non-Cartesian sampled trajectory onto the g space through function transformation.

[0066] The bidirectional traversal calculation module 503 is connected to the mapping module 502 and is used to solve the final trajectory parameter sequence by sequentially applying the bidirectional traversal mechanism to each sampling point mapped in the g space.

[0067] The reparameterization module 504, connected to the bidirectional traversal calculation module 503, is used to reparameterize the final trajectory parameter sequence to obtain the gradient waveform sequence of the non-Cartesian sampled trajectory.

[0068] It should be noted that the division of modules in the embodiment of the general non-Cartesian gradient waveform calculation system based on g-space is merely a logical functional division. In actual implementation, they can be fully or partially integrated into a single physical entity, or they can be physically separated. Furthermore, these units can be implemented entirely in software via processing element calls, or entirely in hardware; alternatively, some units can be implemented via processing element calls to software, while others are implemented in hardware. Since the implementation principle of this general non-Cartesian gradient waveform calculation system based on g-space has been described in the foregoing embodiments, it will not be repeated here.

[0069] To better illustrate the above-mentioned general non-Cartesian gradient waveform calculation method based on g-space, the present invention provides the following specific embodiments.

[0070] In one embodiment, such as Figure 6 This graph represents a comparison of the gradient waveform of the sampled trajectory with the calculation results of the prior art and the present invention. Where: Trajectory represents a non-Cartesian trajectory type; Mean Exe.Time (MTG) represents the average calculation time of the prior art; Mean Exe.Time (MAG) represents the average calculation time of the present invention; Time Reduction represents the reduction rate of calculation time between the present invention and the prior art; Slew Overshoot (MTG) represents the switching rate overshoot rate of the prior art; SlewOvershoot (MAG) represents the switching rate overshoot rate of the present invention; and Overshoot Reduction represents the overshoot reduction rate between the present invention and the prior art.

[0071] Specifically: in a two-dimensional trajectory,

[0072] In the calculation of the gradient waveform of the Spiral trajectory, the calculation time of this invention is only 23.969ms, while the calculation time of the prior art is 115.264ms, which is a speed-up of 79.205%. At the same time, the switching rate overshoot is reduced from 4.131% to 0.034%, a reduction of 99.177%, proving that the switching rate control of this invention is more stable in the gradient waveform calculation of the Spiral trajectory.

[0073] In the gradient waveform calculation of the Variable Density Spiral trajectory, the calculation time of this invention is 22.109ms, while the calculation time of the prior art is 86.613ms, which is a speed-up of 74.473%. The switching rate overshoot is reduced from 4.069% in the prior art to 0.038% in this invention, a reduction of 99.066%, which proves that the switching rate control of this invention is more stable in the gradient waveform calculation of the Variable Density Spiral trajectory.

[0074] In the calculation of the gradient waveform of the Rosette trajectory, the calculation time of this invention is 48.966ms, while the calculation time of the prior art is 221.729ms, which is a speed-up of 77.916%. The switching rate overshoot is reduced from 4.151% in the prior art to 0.050% in this invention, a reduction of 98.795%, which proves that the switching rate control of this invention is more stable in the gradient waveform calculation of the Rosette trajectory.

[0075] In complex three-dimensional trajectories

[0076] In the gradient waveform calculation of the Yarnball trajectory, the calculation time of this invention is 7,519.904 ms, while the calculation time of the prior art is 24,576.042 ms, which is a speed-up of 69.401%. The switching rate overshoot is reduced from 4.151% in the prior art to 0.035% in this invention, a reduction of 99.157%, proving that the switching rate control of this invention is more stable in the gradient waveform calculation of the Yarnball trajectory.

[0077] In the calculation of the gradient waveform of the Cones trajectory, the calculation time of the present invention is 8,707.739 ms, while the calculation time of the prior art is 27,534.991 ms, which is a speed-up of 68.376%. The switching rate overshoot is reduced from 4.151% in the prior art to 0.037% in the present invention, a reduction of 99.109%, which proves that the present invention has more stable switching rate control in the gradient waveform calculation of the Cones trajectory.

[0078] The calculation results show that the calculation time for gradient waveforms of non-Cartesian trajectories in all experiments was reduced by more than 68%, and the overshoot rate was reduced to less than 0.05%. This effectively verifies the universality of the algorithm for gradient waveform calculation of non-Cartesian trajectories and its stability in switching rate control.

[0079] Similar to the above embodiments, the present invention provides a general non-Cartesian gradient waveform calculation device based on g-space.

[0080] The general non-Cartesian gradient waveform calculation method based on g-space provided in this invention can be implemented on the terminal side or the server side. For the hardware structure of an application terminal for the general non-Cartesian gradient waveform calculation method based on g-space, please refer to [link to relevant documentation]. Figure 7 This is a schematic diagram of an optional hardware structure of an application terminal 700 for a general non-Cartesian gradient waveform calculation method based on g-space provided in an embodiment of the present invention. The computer device includes: at least one processor 701, a memory 702, at least one network interface 703, and a user interface 705. The various components in the device are coupled together through a bus system 704. It is understood that the bus system 704 is used to realize the connection and communication between these components. In addition to a data bus, the bus system 704 also includes a power bus, a control bus, and a status signal bus. However, for clarity, in... Figure 7 The general will label all buses as bus systems.

[0081] The user interface 705 may include a monitor, keyboard, mouse, trackball, clicker, button, touchpad, or touch screen.

[0082] It is understood that memory 702 can be volatile memory or non-volatile memory, or both. Non-volatile memory can be read-only memory (ROM) or programmable read-only memory (PROM), used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM) and synchronous static random access memory (SSRAM). The memories described in the embodiments of this invention are intended to include, but are not limited to, these and any other suitable categories of memory.

[0083] In this embodiment of the invention, the memory 702 is used to store various types of data to support the operation of the electronic terminal 700. Examples of this data include: any executable program for operation on the electronic terminal 700, such as the operating system 7021 and application programs 7022; the operating system 7021 contains various system programs, such as the framework layer, core library layer, driver layer, etc., for implementing various basic services and handling hardware-based tasks. The application program 7022 may contain various applications, such as a media player, browser, etc., for implementing various application services. The implementation of the general non-Cartesian gradient waveform calculation method based on g-space provided in this embodiment of the invention can be included in the application program 7022.

[0084] The methods disclosed in the above embodiments of the present invention can be applied to or implemented by processor 701. Processor 701 may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by the integrated logic circuit of the hardware in processor 701 or by instructions in software form. The processor 701 may be a general-purpose processor, a digital signal processor (DSP), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Processor 701 can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. General-purpose processor 701 may be a microprocessor or any conventional processor, etc. The steps of the accessory optimization method provided in the embodiments of the present invention can be directly reflected as being executed by a hardware decoding processor, or being executed by a combination of hardware and software modules in the decoding processor. The software module may be located in a storage medium, which is located in memory. The processor reads the information in the memory and combines it with its hardware to complete the steps of the aforementioned method.

[0085] In an exemplary embodiment, the electronic terminal 700 may be used by one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), or complex programmable logic devices (CPLDs) to execute the aforementioned method.

[0086] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented using computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0087] In the embodiments provided in this application, the computer-readable and writable storage medium may include read-only memory, random access memory, EEPROM, CD-ROM or other optical disc storage devices, disk storage devices or other magnetic storage devices, flash memory, USB flash drive, portable hard drive, or any other medium capable of storing desired program code in the form of instructions or data structures and accessible by a computer. Additionally, any connection may be appropriately referred to as a computer-readable medium. For example, if instructions are transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of the medium. However, it should be understood that computer-readable and writable storage media and data storage media do not include connections, carrier waves, signals, or other transient media, but are intended for non-transient, tangible storage media. The disks and optical discs used in the application include compact discs (CDs), laser discs, optical discs, digital multifunction discs (DVDs), floppy disks, and Blu-ray discs, where disks typically copy data magnetically, while optical discs use lasers to copy data optically.

[0088] In summary, this invention provides a general non-Cartesian gradient waveform calculation method, system, and apparatus based on g-space. It maps the generated non-Cartesian sampling trajectory onto g-space, sequentially employs a bidirectional traversal mechanism to solve for each sampling point to obtain the final trajectory parameter sequence, and then re-parameterizes the final trajectory parameter sequence to obtain the gradient waveform sequence of the non-Cartesian sampling trajectory. This invention addresses the problems of long computation time and inaccurate switching rate control caused by the reliance on arc length parameter equations in existing technologies for calculating gradient waveforms of arbitrary non-Cartesian trajectories based on a bidirectional traversal mechanism in g-space. This invention eliminates the need for any parameter transformation, avoids dependence on arc length parameter equations, and significantly reduces scanning time. Furthermore, it avoids the problem of arc length-to-time interpolation when re-parameterizing the obtained trajectory parameter sequence to obtain the gradient waveform sequence, thus eliminating the problem of inaccurate switching rate control and effectively promoting the application of non-Cartesian sampling trajectories in clinical scenarios.

[0089] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A general non-Cartesian gradient waveform calculation method based on g-space, characterized in that, include: Generate a non-Cartesian sampling trajectory; The final trajectory parameter sequence is obtained by sequentially solving the bidirectional traversal mechanism for each sampling point mapped to the non-Cartesian sampling trajectory in the g space; The final trajectory parameter sequence is then reparameterized to obtain the gradient waveform sequence of the non-Cartesian sampled trajectory.

2. The general non-Cartesian gradient waveform calculation method based on g-space according to claim 1, characterized in that, The final trajectory parameter sequence obtained by sequentially solving the mapping of the non-Cartesian sampled trajectory to each sampling point in the g-space using a bidirectional traversal mechanism includes: A bidirectional traversal mechanism is used to sequentially determine each sampling point of the non-Cartesian sampling trajectory mapped in the g space, and to obtain the gradient vector and trajectory parameters of each sampling point, forming a gradient vector sequence and a trajectory parameter sequence.

3. The general non-Cartesian gradient waveform calculation method based on g-space according to claim 2, characterized in that, The bidirectional traversal mechanism includes: backward traversal phase operations and forward traversal phase operations; The backward traversal phase operations include: Starting from the end point of the non-Cartesian sampling trajectory, the solution is performed along the decreasing direction of the parameters to obtain the gradient vector sequence and the trajectory parameter sequence, and the functional relationship between the two sequences is obtained. The forward traversal phase operations include: After the backward traversal phase is completed, starting from the starting point of the non-Cartesian sampling trajectory, the solution is performed along the parameter increment direction to obtain the gradient vector sequence and trajectory parameter sequence that conform to the functional relationship between the two sequences obtained in the backward traversal phase.

4. The general non-Cartesian gradient waveform calculation method based on g-space according to claim 3, characterized in that, The backward traversal phase operations include: Using the endpoint of the non-Cartesian sampled trajectory as the initial point, the gradient vector of the initial point, the tangent direction of the current trajectory, and the trajectory parameters are obtained. The endpoint is taken as the current sampling point. Based on the gradient vector of the current sampling point, the current trajectory tangent direction, and the preset limit value, the first curve, the second curve, and the straight line are drawn. The gradient vector and trajectory tangent direction of the next sampling point in the parameter decreasing direction are determined by the selected key points, and the trajectory parameters of the next sampling point are calculated. The sampling point is taken as the current sampling point and the calculation of the next sampling point is performed until the gradient vector and trajectory parameters of all sampling points are obtained, forming a gradient vector sequence and a trajectory parameter sequence. The functional relationship between the two sequences is obtained through interpolation.

5. The general non-Cartesian gradient waveform calculation method based on g-space according to claim 4, characterized in that, The forward traversal phase operations include: Using the starting point of the non-Cartesian sampling trajectory as the initial point, the gradient vector of the initial point, the current trajectory tangent direction, and the trajectory parameters are obtained. Using the starting point as the current sampling point, the first curve, the second curve, and the straight line are drawn based on the gradient vector of the current sampling point, the current trajectory tangent direction, and the preset limit value. The gradient vector and trajectory tangent direction of the next sampling point in the parameter increment direction are determined by the selected key points, and the trajectory parameters of the next sampling point are calculated. The obtained trajectory parameters and gradient vectors conform to the functional relationship between the two sequences obtained by the backward traversal stage operation. The sampling point is used as the current sampling point to calculate the next sampling point until the gradient vectors and trajectory parameters of all sampling points are obtained, forming the final trajectory parameter sequence.

6. The general non-Cartesian gradient waveform calculation method based on g-space according to claim 1, characterized in that, The reparameterization of the final trajectory parameter sequence to obtain the gradient waveform sequence of the non-Cartesian sampled trajectory includes: A preset trajectory function is input into the final trajectory parameter sequence to obtain the trajectory sampling point sequence; The gradient waveform sequence is obtained by numerically differentiating the sequence of trajectory sampling points.

7. A general non-Cartesian gradient waveform calculation method based on g-space according to claim 4 or 5, characterized in that, The step of drawing the first curve, the second curve, and the straight line based on the gradient vector of the current sampling point, the current trajectory tangent direction, and preset limit values ​​includes: A circle is drawn with the gradient vector of the current sampling point as the center and the product of the switching rate limit and the time step as the radius to obtain the first curve. A circle is drawn with the origin of the g-space as the center and the gradient magnitude limit value among the preset limit values ​​as the radius to obtain the second curve; Draw a straight line with an intercept of 0 that is parallel to the tangent direction of the current trajectory.

8. A general non-Cartesian gradient waveform calculation method based on g-space according to claim 4 or 5, characterized in that, The method for selecting key points includes: selecting the intersection point of the second curve and the straight line within the circular range formed by the first curve as the key point; wherein, the gradient vector of the key point is constrained by the switching rate limit value in the preset limit value, and the magnitude of the gradient vector of the key point is constrained by the gradient magnitude limit value and the escape velocity limit value in the preset limit value.

9. A general non-Cartesian gradient waveform calculation system based on g-space, applied to the general non-Cartesian gradient waveform calculation method based on g-space as described in any one of claims 1 to 8, the system comprising: The system includes a trajectory generation module, a mapping module, a bidirectional traversal calculation module, and a reparameterization module; among which, The trajectory generation module is used to generate the non-Cartesian sampling trajectory; The mapping module is connected to the trajectory generation module and is used to map the non-Cartesian sampled trajectory onto the g-space through a function transformation. The bidirectional traversal calculation module is connected to the mapping module and is used to solve the final trajectory parameter sequence by sequentially applying the bidirectional traversal mechanism to each sampling point mapped in the g space. The reparameterization module, connected to the bidirectional traversal calculation module, is used to reparameterize the final trajectory parameter sequence to obtain the gradient waveform sequence of the non-Cartesian sampled trajectory.

10. A universal non-Cartesian gradient waveform calculation device based on g-space, applied to the universal non-Cartesian gradient waveform calculation method and system based on g-space as described in any one of claims 1 to 9, the device comprising: Memory, processor, and computer programs stored in memory.

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