DE102011081480A1 - Method for determining e.g. fiber directions of muscle fibers of blood vessel in left ventricle of human heart, involves comparing local elongations and elongation portions to determine intrinsic anisotropy of tissue - Google Patents

Abstract

The method involves reading data of a detected three-dimensional (3D) movement of predetermined positions (P1, P2) of a hollow body wall (6). 3D local elongations of the predetermined positions are determined from the detected movement. Geometrically defined elongation portions in the predetermined positions are calculated by simulation. A compensated 3D elongation state is calculated by correction of the 3D local elongations with the elongation portions. The 3D local elongations and the elongation portions are compared for determining intrinsic anisotropy of a tissue. An independent claim is also included for a computer program product comprising a set of instructions for performing a method for determining an intrinsic anisotropy of a wall material of a flexible hollow body.

Description

The present invention relates to a method for determining the intrinsic anisotropy of the wall material of a pressurized flexible hollow body, for example the fiber directions and material properties of fibers of a fabric. In particular, the present invention relates to a method for visualization of the fiber progressions of muscle bundles on hollow bodies or hollow organs of man, such. B. certain blood vessels, especially the heart. The invention thus makes possible a novel, anatomical analysis and visualization of hollow organs that can be integrated into existing representations, such as, for example, surface models or parameter maps (cf. WO 2007 141 038 A1 ) can be introduced.

In the conventional visualization or calculation of pressurized hollow bodies, such as the heart, models of the hollow body are visualized in a two-dimensional (2D), three-dimensional (3D) or temporally resolved, ie four-dimensional (4D) representation on the screen of a corresponding computer system, usually two-dimensional slice images from CT, MR or ultrasound images are used for their reconstruction, for example to reconstruct a surface model of the heart. To determine functional parameters such as strains, strain changes, displacements or wall speeds of the hollow body wall then either 3D or 4D image data sets, or 2D image data sets, such. B. so-called Kurzachsschnitte or long axis sections of a heart, in particular of the left ventricle of a heart, used for this purpose, the 2D or 3D image data sets are aligned on the basis of a global coordinate system, as for example in 1 is shown.

The global coordinate system GK is characterized z. B. as a right-handed coordinate system, wherein the z-axis, for example, the left ventricle of a heart of the base 4 in the direction of the apex 3 shows. Corresponding long-axis sections are parallel to the z-axis, while the short-axis sections are then parallel to the xy plane.

However, the calculation and presentation of the functional parameters of a heart then takes place on the basis of a heart-specific coordinate system, which generally corresponds to a polar or local coordinate system, i. H. with radial, longitudinal and circumference components (in each case with respect to the heart axis, which is usually along the z axis, but often also curved, which is why local coordinate systems are usually recommended).

The prior art thus results in values or functional parameters related to the cardiac coordinate system, since the corresponding measurements are always projected onto the cardiac axes (longitudinal, radial and rotational (circumferential)). However, this system does not take into account the tissue morphology such as the heart muscle fiber pathways.

The skeletal muscle-like structure of the heart muscle is characterized by special muscle fiber strands of different directions and orientation. Each muscle fiber contracts only along its fiber direction. If several muscle fibers with individually different fiber orientation are involved, a correspondingly superimposed movement arises. The contraction direction of the heart wall then corresponds first to the mean fiber direction of the muscle bundles involved.

Different cardiac loads and diseases now have an impact on the contraction-involved muscle bundles and thus on the shape and pattern of contraction of the heart. Heart functions can therefore also be measured by means of a division or determination of muscle fibers (the so-called "single muscle band" theory).

A disadvantage of the representation and corresponding measurement methods in the right-handed, global coordinate system is that tangential movements, such as a torsional movement of the hollow body wall, are not necessarily immediately recognizable as such, since they are quantitatively divided along the main direction components of the coordinate system used and visualized accordingly. The physiological structure of the muscle fibers remains partially unconsidered. For medical interventions, for example for the localization of the attachment points of electrodes of a cardiac pacemaker, it is desirable to determine the exact location and direction of the muscle fiber strands. Oriented the doctor z. As in the present in a cardiac coordinate system maps and the calculated there functional parameters, he usually can not see in which direction the muscle fiber strands run and what physiology they have (strength of the strands, direction, location and thickness). It would be better, To detect the relevant for the contraction of a heart directions of the muscle fibers, as these can then be targeted.

In the prior art, there are two further disadvantages: Since in the contraction of muscle bundles at the heart of an elongation usually only along the muscle fibers, the elongation of the hollow body wall but calculated only on the basis of the standard directions (longitudinal, radial and circumference), and results an absolutely homogeneous cardiac muscle contracting along its fiber direction in all conventionally used standard cards an inhomogeneous distribution of the measured values, since only a projection of the actual strain on the respective measuring direction is detected, but not the strain along the muscle fibers themselves.

Furthermore, one reason for a spatially inhomogeneous distribution of the strain in the geometry of the examined hollow body is itself justified, even assuming an isotropic material for the hollow body wall, on which a certain internal pressure acts. Thus, due to the geometric shape already different strains in different main directions and distributed over the wall thickness of the hollow body. Consider, for example, an ideal, elastic, thick-walled cylinder, which is under a certain internal pressure, it can be seen that this pressure changes not only radially but also longitudinally in a different ratio, so that even here, in pressure changes, strains and thus also movements in more than one main direction arise.

The present invention is therefore based on the object of determining the intrinsic anisotropy of the tissue from the three-dimensional movement or contraction pattern of the hollow body wall, that is to say the intrinsic anisotropy of the tissue. H. to extract the shape-corrected, local contraction direction, so that thereby the fiber directions of the fibers involved can be obtained. The direction of contraction can represent a new additional factor in the evaluation of pathologies that can be used for diagnostic purposes. In addition, by means of a calculation of the direction of contraction, the amount of contraction can also be better evaluated, since no projection into corresponding standard directions (longitudinal, circumference, radial) takes place, which as a rule is uncorrelated to the respective muscle fiber direction.

The present invention solves this problem by the features of claim 1. Advantageous embodiments of the invention and particular embodiments are characterized in the dependent claims and claimed there. The inventive method is used to determine the intrinsic anisotropy of a wall material of a pressurized flexible hollow body. The hollow body is preferably a hollow organ of the human or animal body, for. B. a blood vessel, in particular a heart chamber. The wall material is preferably made of fabric, for. From muscle tissue containing elongated muscle fibers and strands. In particular, the local, shape-corrected (ie taking into account the geometry of the hollow body) anisotropic expansion of the wall material of the hollow body is determined. For this purpose, either the three-dimensional movement of predeterminable positions of the hollow body wall, for example by a known in the art three-dimensional "feature tracking method" detected, or data of the already detected movement of the predeterminable positions of the hollow body wall are read. However, this three-dimensional movement of the hollow body wall does not correspond to the fiber direction of the cardiac muscle fibers, which is why, starting from this movement, the three-dimensional, local strain of these predeterminable positions (P) is first determined from the detected movement.

Thereafter, geometrically determined expansion portions are calculated at these predeterminable positions by modeling or simulation, the simulation or the model being based on information about the geometry and material properties of the hollow body. By "geometrically determined expansion fractions" are here preferably understood those expansion fractions resulting from the internal pressure and the geometry of the hollow body, as well as possibly material properties of the hollow body wall, in particular according to a model calculation. This z. B. in each case on a standard model of the hollow body, in particular of the human heart, are used. The intrinsic anisotropy of the tissue is then determined from the comparison between the three-dimensional, local strains and the geometrically determined strain fractions. According to a preferred embodiment, a compensated 3D strain state is calculated in which the three-dimensional, local strains are corrected with the geometrically determined strain fractions, for. B. by subtraction of the respective strain tensors or 3D-strain states. From the compensated 3D strain states, it is possible in each case to calculate a local main strain vector, which in some embodiments corresponds directly to the contraction direction or the respective mean fiber direction.

According to a first preferred embodiment of the present invention, a symmetrical strain tensor for each of the detected predeterminable positions from this detected motion is determined for determining the three-dimensional, local strain of the predeterminable positions (P).

Subsequently, these local, symmetric strain tensors are compensated or normalized by taking into account (eg, subtracted) the geometrically determined strain fractions. Subsequently, the respective compensated strain tensors (ε →) are converted by means of a coordinate transformation to determine the direction of the greatest strain, wherein the direction of the greatest strain also corresponds to the direction of the respective local main strain vector (V _H ), which is used to determine the respective mean fiber direction (FIG. 9 ) serves. The greatest strain then also corresponds to the local principal strain at the predeterminable position.

For the coordinate transformation, the respective compensated or normalized strain tensor is preferably decomposed into its eigenvectors and eigenvalues. Finally, the respective local principal strain vectors are calculated from the eigenvectors and eigenvalues, with the local principal strain vectors indicating the mean fiber direction at this location or region. In particular, the local principal strain vectors yield a vector field that reflects the local orientation of the contraction directions. These thus correspond to the mean fiber direction of the acting muscle fibers.

Preferably, by means of calculating the regionally resolved, three-dimensional strain tensor, it is thus possible to determine the average myocardial fiber orientation in space. The above-mentioned disadvantages of the prior art are eliminated, in particular by estimating the expansion parts determined by the geometry and subtracting them from the detected local strain, so that the muscle action or contraction underlying the local stretching can be separated therefrom. The three-dimensional deformation of the hollow body thus becomes physiologically meaningful.

To determine the three-dimensional movement, a time series of 2D or 3D images of the hollow body recorded by means of ultrasound or another imaging method, such as CT or MRI, is preferably used. On these images, it is preferred to use certain features first of all by means of a feature tracking method. H. Predeterminable positions of the hollow body wall, the pressurized flexible hollow body in space three-dimensional tracked. From this three-dimensional movement of the wall material points (in the case of the heart: myocardial points), a symmetrical second order strain tensor can then be determined locally. This determination is made directly from the imaging method by measurement.

If one also wishes to determine the stress tensor which exists at every predeterminable position of the hollow body wall, the following procedure can be adopted: A stress tensor can be represented in the following form, with reference to a global, right-handed coordinate system GK:

Thus, at each point of the hollow body wall there are three stresses σ in the principal stress directions (for example in the x, y and z directions) and six shear stress components τ at the respective side surfaces of an infinitesimally small volume element. If the hollow body wall is then approximated as an isotropic, elastic material, then starting from the previously measured strain tensor at every predeterminable position of the hollow body wall, taking into account the detected three-dimensional strain, a symmetrical stress tensor can be determined by linking the strain and the resulting stress via the material constant (σ = kε).

In the first embodiment, for. B. compensates the local, symmetric strain tensor by correcting the geometrically determined expansion components. These geometrically determined expansion parts hang u. a. from the geometric structure of the hollow body, since depending on the geometry of the hollow body different (resulting from the pressure change) expansions of the hollow body wall arise when pressure changes, for example by contraction movements result.

Thereafter, the compensated strain tensors are decomposed locally, e.g. In their eigenvectors and eigenvalues. When decomposing the respective corrected strain tensors into their eigenvectors and eigenvalues, for example, an eigenvalue decomposition is performed using a right-handed coordinate system. The eigenvectors then indicate the respective main strain directions and the eigenvalues the respective major strains at the respective position (cf. Doppler myocardial imaging; George R. Sutherland, Liv Hatle, Frank E. Rademakers, Piet Claus, Jan D'hooge, Bart H. Bijnens; January 27, 2005 ). The decomposition of the respective corrected strain tensors into their eigenvectors and eigenvalues preferably takes place by means of a diagonalization of the corrected strain tensor, ie by transformation into a right-handed orthonormal system (OS (a, b, c)):

Alternatively, singular value decomposition (SVD) may also be used to obtain the diagonalized strain tensor.

The right-handed orthonormal system (OS (a, b, c)) should be oriented so that the greatest strain ε _a in the direction of the unit vector e → _a he follows. Thus, the strain ε _{a can} also be understood as the principal strain ε _H and the associated direction vector e → _a as the main stretch direction V → _H ,

Since the diagonalization of the strain tensor only corresponds to a respective local rotation of the coordinate system, the main strain direction V → _H also be represented in a common global coordinate system.

The vector field of all main strain directions V → _H thus indicates the local orientation of the resulting contraction directions of the individual muscle fibers and thus the mean fiber direction.

An alternative calculation method is described below. In each case, the three-dimensional, local strains from the detected movement in each coordinate system are determined here. Then, a singular value decomposition (SVD) of the three-dimensional local strains is performed to determine the respective principal strain directions. These decomposed local strains are then compared again with the geometrically determined strain rates. Furthermore, it is also possible likewise to subject the geometrically determined expansion components to a singular value decomposition in order to determine the respective main expansion directions here as well. Both the three-dimensional local strains, as well as the geometrically determined strain fractions, as well as both singular-value decomposition can be decomposed. The SVD is a type of principal component analysis that allows the comparison of two strain states no matter in which coordinate system they have been determined. The SVD is used here as a tool to obtain a local, standardized coordinate system. In this type of calculation, the strain states (three-dimensional, local strains and / or the geometrically determined strain fractions) are not described as strain tensor, but as a matrix containing strain components in different directions.

According to a preferred embodiment of the present invention, the three-dimensional movement of predeterminable positions of the hollow body wall is detected by means of a 3D feature tracking method. In particular, certain points of a myocardial tissue of a flexible heart under pressure are tracked and their 3D position determined on different, possibly temporally successive, images.

According to one embodiment, the simulation or modeling is based on the assumption that the hollow body wall consists of an isotropic, elastic material. As a result, the geometrically determined expansion components can be calculated relatively easily, solely from a geometric model (expansion model). A precise knowledge of the internal pressure is not required, since in an ideal elastic material, the strain in each case is proportional to the internal pressure. Incidentally, an assumption about the internal pressure can also be made, or it is iteratively set so that the geometrically determined expansion components come closest to the detected three-dimensional local strains.

In the embodiment described above, in which the model is based on the assumption that the hollow body wall consists of an isotropic, elastic material, the intrinsic anisotropy is determined directly from the difference or the difference between the three-dimensional, local strains and the geometrically determined expansion parts , If this difference is zero, the tissue is apparently isotropic. If local differential directions or differential amounts result, they provide information about the fiber course of the muscle strands in the tissue. Preferably, the internal pressure for the simulation is adjusted so that the local amounts of the local strains and the geometrically determined expansion portions are as similar as possible.

According to another embodiment, the simulation is based on a model of the hollow body in which the hollow body wall consists of an anisotropic material. For this purpose, z. B. a 3D trained model of the fiber directions of the heart muscle can be used, which does not accept the heart muscle as isotropic, but already includes an empirically derived model of the fiber progressions. In this case, a comparison between the three-dimensional, local strains and the geometrically determined strain parts respectively provides the deviation of the heart examined from the standard heart. This can already be a very interesting size, the exact calculation of the fiber gradients may not be necessary.

In particular, in this embodiment, the model of the hollow body can be iteratively changed until there is a high agreement with the detected three-dimensional, local strains. It can then be assumed that the intrinsic anisotropy of the tissue corresponds to the anisotropy of the model underlying the simulation.

In general, it is possible from the intrinsic anisotropy, in particular from the compensated 3D strain state, to determine the respective mean fiber direction of fibers of the tissue of the hollow body wall. In particular, the respective local principal strain direction, in particular a main strain vector, can be determined from the compensated 3D strain state.

When the hollow body is a ventricle, the three-dimensional local strains are preferably calculated from a comparison of the predeterminable positions that move over time at two different times in the cardiac cycle. Preferably, the predeterminable positions are compared at a time of large or maximum heart contraction with the corresponding positions at a time of relaxation of the heart, and determined from the respective movement of the heart chamber wall between these two points in time, the respective local strain.

The invention can also be used dynamically, ie calculate the strains between two successive images over a time series of images. All other features described herein can also be applied to this embodiment, in each case then a dynamic consideration of the elongation is possible.

The correction or compensation of the 3D strain states by determining the geometrically determined strain fractions is done by means of mathematical models. For this purpose, according to one embodiment, an isotropic, elastic material for the tissue of the hollow body wall is used as the basis and a specific load is simulated by internal pressure. The resulting strains are proportional to the simulated pressure. Thus one obtains the size ratios of the strains caused by pressure and geometry and can thus normalize or correct the local strains of the predeterminable positions.

The internal pressure can be estimated or measured. A precise knowledge of the internal pressure is not required, since the ratio of the strains is known, and the elongation, at least in the following simple example, is always proportional to the internal pressure.

A mathematical model is explained in more detail by the following example:
If the left ventricle of a heart is modeled by ending a long, thick-walled cylinder at the end with a spherical half-shell, the following results, also with reference to the attached 3 closer relationships shown:
Assuming that the hollow body wall consists of an isotropic, elastic material and sets this hollow body under an internal pressure p _i , the following material stresses result, whereby the edge effects in the cylindrical part are disregarded, ie it is assumed that the cylinder is very long and you only consider the tensions far away from the edge:

It can be seen that the ratio of the rotational or circumference direction to the longitudinal direction (k _{φ, l} (r)) is always not equal to 1, and increases within the hollow body wall from outside to inside (~ 1 / r ² ). On the outer wall, this ratio is always 2, so regardless of the inner radius:

The corresponding formulas for the thick-walled ball half shell are:

The transition between the cylinder and the ball half shell is not continuous. For a more accurate calculation, in particular in any ventricular geometry, therefore, a numerical solution using appropriate differential equation systems is necessary, for. B. FEM or the finite element method. Nevertheless, this simplified example allows an overview of the geometrically caused expansion parts and the corresponding size ratios.

In the case of a pressure change, the resulting strains result from the stresses via the material constants. Considering, for example, the main direction of elongation in the cylindrical part, it can be seen on the basis of the ratio k _φ1 (r), which already results in different strains in the different directions for an isotropic, elastic material.

This example shows that the local dilation of the heart wall is determined both by the direction of the muscle fiber and by a geometric effect that has to be taken into account. In particular, it is not possible to deduce the muscle fiber runs from the local main directions of the expansion since the deviation of the geometry-related expansion of the hollow body wall must be taken into account. To correct the three-dimensional, local elongation of the left ventricle of a heart, geometrically determined expansion components are therefore preferably calculated, which are calculated numerically. For this purpose, z. B. Methods of Finite Element Analysis (FEA). Furthermore, a strain model can be used to calculate the geometrically determined expansion components, which approximates the hollow body wall as an isotropic, elastic material.

Alternatively, a model can be used which takes into account anisotropic material properties, in particular a model of the main fiber directions in the hollow body.

By eigenvalue decomposition or singular value decomposition of the strain tensor or of the compensated strain state, one then obtains three eigenvectors in each case, the so-called main strain directions, and as eigenvalues the respective associated major strains. If one then forces a right-handed coordinate system for the eigenvectors and, for example, uses an isotropic, incompressible material as a model, for example for the heart muscle, then the information obtained can be mapped as a local main strain vector with four parameters:
The main strain vector thus results from the direction vector of the magnitude-greatest strain and from the signed strain itself: V → _H = (v _x, v _y, v _z), ε _H (9)

The vector field of the local principal strain vectors V _H thus represents the local orientation of the contraction directions, which can not be explained from geometry and internal pressure, and corresponds essentially to the mean fiber direction of the muscle fibers involved in the contraction. According to a preferred embodiment of the present invention, this model concept can also be utilized by spatially regularizing the vector field.

The main expansion vectors at corresponding determinable positions of the hollow body wall represent exactly this muscle fiber contraction at those points where only one muscle fiber direction occurs in the muscle in each case, ie. H. This results in a homogeneous measured value. Only at the points where different muscle bundles with different fiber directions come together does the mean fiber direction replace the local fiber directions of the individual muscle bundles involved. However, this represents a significantly improved physiological model, for example of the heart, as compared to the standard prior art directions.

The comparison between the determined three-dimensional, local strains and the geometrically determined strain fractions can be visualized in various ways, in particular as a representation of a vector field or a field line representation in a surface model or a parameter map of the hollow body. Basically, such two-dimensional representations of a ventricle wall are known, for. As a so-called bag presentation, in which the surface of the ventricle inner wall is shown in a perspective view as a "bag", or the polar plot, in which the heart chamber wall is spread like a map. In these known representations, the results of the method according to the invention can then be entered by color coding or line representations.

Preferably, the difference between the three-dimensional, local strains and the geometrically determined strain fractions is represented as a vector field. Depending on the model used, this difference can correspond to the compensated 3D strain state and the vector vectors of the vector field then represent the main strain direction. Thus, the length or thickness of the illustrated arrows correspond to the strength of the contractions, while z. B. the color corresponds to the sign (contraction or relaxation). However, in a model that already takes into account the grain directions, the difference can simply represent the difference to a standard heart. In addition, a field line representation can also be used which, like a height map, reproduces the amount of the 3D strain state in each case. Again, the sign of the strain (contraction or relaxation) can be reproduced by the color, if necessary.

According to a still further preferred embodiment, the compensated 3D strain state is represented as a vector field, wherein the direction of the arrows and lines respectively corresponds to the main strain direction and the color of either the lines or the background corresponds to the amount of strain and thus the magnitude of the contraction.

The invention also relates to a computer program product for carrying out the method described above. This computer program product, z. B. in the form of a stored on a memory computer program is preferably used on a computer, the z. B. from an ultrasound device corresponding data of the three-dimensional movement predeterminable positions of the hollow body wall receives. The first step of the method according to the invention can therefore also be omitted if the data are already present or have been detected in advance in a separate step.

A preferred embodiment of the present invention will be explained in more detail with reference to the accompanying drawings. Showing:

1 the schematic view of a left ventricle of the heart with some muscle fibers,

2 a short axis incision through the ventricle 1 with two local, usually non-cylindrical cardiac coordinate systems,

3 the schematic view of a left ventricle of a heart with local heart coordinate system and geometric model,

4 schematic representations of a muscle fiber with schematically represented eigenvectors of the diagonalized strain tensor,

5 the directions of the main strain vectors as texture on a surface model,

6 a direction vector field on a parameter map, and

7 the schematic view of a left Herzventrikels with a partial element of the hollow body wall, shown enlarged (eg for finite element method)

1 shows the schematic representation of a hollow body 2 , such as the left ventricle of a heart, with a global coordinate system GK whose xy plane is approximately parallel to the base 4 of the heart and its z-axis from the base 4 of the heart to the apex 3 directed. In other hollow bodies, such as the lungs, this coordinate system can also be oriented differently. The hollow body 2 itself is being affected by muscle fibers 1 surrounded, for example, in the form of a large loop from the base 4 down to the apex 3 , on the front of the hollow body 2 and from the apex 3 back to the base 4 on the side facing away from the observer, ie the back of the hollow body 2 , pass.

An in 1 illustrated short-axis section 5 is in 2 shown schematically. Here is the hollow body wall 6 in the short-axis section 5 represented as a thick wall covering the muscle fibers 1 as a muscle fiber strand, these muscle fibers 1 in the short-axis section 5 are shown only in section, so that a tangential movement of a predeterminable position P in the short-axis section 5 only partially and a longitudinal movement, ie out of the image plane, a predeterminable position P in the short-axis section 5 not visible at all. In the short-axis section 5 are only radial movements 7 or circumference movements 8th representable, ie a first predeterminable position P1 can be tracked in a first radial direction R1 and a first circumferential direction C1. The same applies to a second predeterminable position P2, which changes both in a second radial direction R2 and a second circumference direction C2, ie longitudinal movement components can not be detected or represented in this representation. The same applies mutatis mutandis to corresponding long-axis sections of the left ventricle, ie sections parallel to the z-axis, in which longitudinal and radial, but not circumference movements are recognizable.

According to the invention, so-called 3D feature tracking methods track specific points of the myocardial tissue of a flexible heart under pressure in three-dimensional space, so that the three-dimensional movement of predeterminable positions of the hollow body wall can be measured. From this the local, three-dimensional strain can be determined. This can be represented according to an embodiment as a symmetrical strain tensor.

Subsequently, for example, the normalization or compensation of the strain tensor by means of determining the geometrically determined strain fractions using mathematical models. For this purpose, z. B. an isotropic, elastic material for the tissue of the hollow body wall 6 and simulated a certain load by internal pressure. The resulting strains are proportional to the simulated pressure. Thus one obtains the size ratios of the strains caused by pressure and geometry and can thus normalize or correct the local strain tensors of the predeterminable positions.

To illustrate the geometric compensation, the following is explained in more detail with reference to a simple geometric model:

3 shows the schematic representation of a thick-walled hollow body 2 with an inner radius r _i and an outer radius r _a , which is under an internal pressure p _i . A heart is at the base 4 usually completed by appropriate flaps, so that due to the internal pressure a certain elongation established. Also shown schematically is a substantially thick-walled cylinder Z, which lies on a ball half-shell H. Every point P on or in the cave body wall 6 In particular, in the case of a heart, a local coordinate system carries a cardiac coordinate system with a radial direction R, a longitudinal direction L, and a circumference direction C, which will also be denoted by φ below.

If one now takes the aforementioned equations (3) - (5) for the calculation of the geometric stress fractions and takes, for example, an inner diameter of 4 cm and a wall thickness of 1 cm for the left ventricle of a heart, the following values result: r _i = 2 cm (10) r _a = 3 cm (11)

The following voltage values thus result for the cylindrical part: σ _l = 0.8 p _i (12) σ _{tube φ} (r _i ) = 2.6p _i (13) σ _tubeφ (r _a ) = 1.6p _i (14) σ _tuber (r _i ) = -p _i (15) σ _tuber (r _a ) = 0 (16)

For the hemisphere, the following values result: σ _{sphere φ} (r _i ) = σ _spherel (r _i ) = 1.13 p _i (17) σ _{sphere φ} (r _a ) = σ _spherel (r _a ) = 0.63 p _i (18) σ _spherer (r _i ) = -p _i (19) σ _spherer (r _a ) = 0 (20)

From the present numerical example and equation (6) it follows that the circumference component of the stress in the cylinder - depending on the radius - is 2 to 3.25 times greater than the longitudinal component.

Using the assumptions of the isotropic material constants Elastic modulus E and Transverse contraction number v, the corresponding strains can be calculated from the thus determined stresses.
Elongation of the thick-walled hollow cylinder: ε _r (r) = 1 / E [σ _r (r) - υ (σ _φ (r) + σ _l (r))] (21) ε _φ (r) = 1 / E [σ _φ (r) - υ (σ _r (r) + σ _l (r))] (22) ε _l (r) = 1 / E [σ _l (r) - υ (σ _r (r) + σ _φ (r))] (23)

Elongation of the thick-walled spherical shell: ε _r (r) = 1 / E [σ _r (r) - 2υσ _φ (r)] (24) ε _φ (r) = 1 / E [(1-υ) σ _φ (r) -υσ _r (r)] (25)

4 shows the schematic view of a muscle fiber 1 having at a predetermined position P a normalized or compensated strain tensor ε → (or also referred to as T), from the gem. Formula (9) lets calculate the local principal strain vector V _H. This then gives the fiber direction of the muscle fiber 1 at the position P on. This local main strain vector V _{H is} calculated from the eigenvectors (ε _a , ε _b , ε _c ) of the diagonalized, symmetric strain tensor ε → 2nd order, these eigenvectors being in 4 are shown schematically in a right-handed orthonormal system OS. This Orthonormal System OS can be located locally in any point of the hollow body wall 6 by rotating the local cardiac coordinate system accordingly. Thus can be at any point of the hollow body wall 6 Eliminate shear stress components so that only the principal strain components remain in the diagonal of the corresponding tensor matrix (see Equation (2)).

According to another preferred embodiment, the strains are not each represented as a strain tensor, but in a more general three-dimensional (matrix) representation. In order to simplify the handling of the strains, it is preferable to subject the detected three-dimensional, local strains and / or the geometrically determined strain parts to a singular value decomposition. As a result, the main expansion direction is easily read from the representation of the respective three-dimensional strain state. Also from this can be read in each case the main strain vectors V _H.

According to 5 can be z. B. the main strain vectors V _H as a texture 11 in a surface model of the hollow body, this texture then indicating the mean fiber directions of the involved muscle fibers. Optionally, these mean fiber directions can also be reproduced in a parameter card 6 register, these from the WO 2007 141 038 A1 known parameter map can be provided in such a way with the main strain vectors V _H , that they indicate the contraction direction of the muscle fibers by means of arrow representations.

The local main expansion vectors V _H can also be entered functionally as a vector field in a surface model of the hollow body or in a parameter map such that the direction and intensity of the respective principal strain are represented as direction or as color, length or thickness of the arrow used in a corresponding vector field representation , Optionally, the mean fiber directions can also be compared to a detected, three-dimensional stretching of the hollow body wall. As a result, the differences, in particular the angular difference, between the detected strain and the fiber direction can be visualized. The angular deviation between the main expansion direction resulting from the geometrically induced expansion parts ("expected elongation") and the measured expansion direction can be used as a measure of the position of the muscle fibers, provided that an isotropic material of the hollow body wall is used.

7 shows schematically the hollow body 2 with subelements 13 the hollow body wall, wherein one of these sub-elements is shown enlarged. In order to be able to determine the actual strains and stresses in the wall of the hollow body from the detected movements of the myocardial points, these are expediently calculated numerically according to the prior art with methods of finite element analysis (FEA). For this purpose, the known geometry first, as in 7 shown schematically in a variety of sub-elements 13 disassembled. For each subelement 13 then mathematical approach functions are chosen, which approximate the material behavior in the respective element with sufficient accuracy. For example, it is believed that the material is an isotropic and / or incompressible material. Furthermore, boundary conditions are defined by means of which the forces acting on the hollow body (eg hydrostatic pressure and support) are modeled. The solution over the entire hollow body model is then numerically by calculation of all sub-elements and their linkage over the respective boundary conditions.

According to the present invention, it is now possible to determine the mechanical activity of a heart along the muscle fibers, which leads to a more homogeneous measurement value distribution and to a physiologically adapted interpretation. Even the conventionally used functional parameters such as strain, strain rate, speed, etc. can be better visualized in such a new representation.

Also, one can model a common distribution of muscle fiber directions, which is then adapted to individual patient data. In addition to a more stable determination of the direction vector field of the main strain vectors, a comparison with standard values can thus be carried out. Changing such a directional vector field, for example under load, could be a better parameter for incipient contraction / relaxation perturbations; The involved muscle fibers can be localized and treated as necessary.

The method according to the present invention has further advantages:
For example, if only two out of three possible strain information are available, the missing third value can be determined assuming incompressibility of the matter of the hollow body wall. In the case of the incompressible medium, the sum of the major strains is always 0. Thus, in principle, the radial strain can be calculated from knowledge of the longitudinal and circumference elastic strain. From the Three-dimensional distribution of the strain tensors can be reconstructed by integration then in principle also the underlying three-dimensional stretching of the hollow body wall.

If the main strain vectors are entered functionally as a vector field, for example in a parameter map of the heart, as shown in FIG 6 schematically as a texture 11 is shown, for example, negative strains, ie shortenings, as a thickening of the line and positive expansions can be represented as a dilution. This behavior can then be intuitively interpreted by the viewer as a contraction of, for example, a muscle fiber. The representation of the tangential components of an expansion can be supplemented by a color-coded representation of the radial expansion (wall thickening).

Finally, it is possible to measure the radial inward movement directly from the three-dimensional movement of predeterminable positions of the hollow body wall. An estimation of the local wall thicknesses together with the radial strain also results in a regional shift. From the difference between these two quantities it can be deduced again whether the local contraction also leads to a corresponding inward movement, that is to say in the case of H. radial reduction leads.

In the subendocardial zone of the myocardium there is a partly strong trabecularization. A measurement volume over such an area thus contains both muscle fibers and blood components. The contraction of the heart can no longer be assumed to be an isovolumic contraction. The deviation between the directly measured radial strain, for example, the radial difference between two parallel bag surfaces and the radial strain determined by the tangential movement (via the isovolumetric approach described above) now provides information about the compressibility of the measurement volume. From this comparison, conclusions can be drawn on the thickening of the trabecular muscle fibers. Advantageous uses of the present inventive method are, for example, in the monitoring of surgery after myocardial infarction, a monitoring of changes in muscle fiber contractions under stress but also for general studies of cardiac activity.

However, the aforementioned method can also be applied to other imaging methods such as computed tomography or magnetic resonance tomography, which can detect three-dimensional movements of predeterminable positions of the hollow body wall. Likewise, the method is suitable for the determination of non-contracting fibers of a tissue, for example a blood vessel, which contracts or expands under fluctuating pressure. Thus, passive, d. H. detect only supporting fibers or fiber-like types of tissue surrounding hollow bodies that are under a certain pressure.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• WO 2007141038 A1 [0001, 0074]

Cited non-patent literature

• Doppler myocardial imaging; George R. Sutherland, Liv Hatle, Frank E. Rademakers, Piet Claus, Jan D'hooge, Bart H. Bijnens; January 27, 2005 [0022]

Claims (18)

Method for determining the intrinsic anisotropy of the wall material of a flexible hollow body under pressure (p _i ) 2 ), in particular the fiber directions ( 9 ) of fibers of a tissue, by a) reading data of a detected, three-dimensional movement of predeterminable positions (P) of the hollow body wall ( 6 b) determining the three-dimensional, local expansions of these predeterminable positions (P) from the detected movement, c) calculating geometrically determined expansion components at these predeterminable positions (P) by simulation, wherein the simulation is based on assumptions about geometry and material properties of the hollow body ; d) if necessary, calculating a compensated 3D strain state by correcting the three-dimensional local strains with the geometrically determined strain fractions, and e) determining the intrinsic anisotropy of the tissue from the comparison between the three-dimensional local strains and the geometrically determined strain fractions. Method according to claim 1, characterized by the following steps: - Determining the three-dimensional, local strains of these predeterminable positions (P) from the detected movement in any coordinate system; Performing singular value decompositions of the three-dimensional local strains to determine the respective principal strain directions; - Determining the geometrically determined expansion parts; - Comparison of the singular value decomposed three-dimensional, local strains with the geometrically determined strain parts. Method according to claim 1 or 2, characterized by the following steps: - calculating geometrically determined strain rates in any coordinate system; Performing singular value decomposition of the geometrically determined strain proportions to determine the respective principal strain directions; - Comparison of the three-dimensional, local strains with the singular-value-decomposed geometrically determined strain rates. Method according to claim 1, characterized, in that symmetric strain tensors (ε →) are calculated when determining the three-dimensional local strain of the predeterminable positions (P), that the symmetrical strain tensors (ε →) are compensated by correcting the geometrically determined strain fractions, and in that the respective compensated strain tensors (ε →) are converted by means of a coordinate transformation to determine the direction of greatest elongation. Method according to one of the preceding claims, characterized in that the simulation is based on the assumption that the hollow body wall consists of an isotropic, elastic material, and that the intrinsic anisotropy of the difference between the three-dimensional, local strains and the geometrically determined strain rates, in particular from the compensated 3D strain state. Method according to one of the preceding claims, characterized in that the simulation in step c) is based on a model of the hollow body, in which the hollow body wall consists of an anisotropic material, and that the three-dimensional, local strains and the geometrically determined expansion portions are compared with each other, in particular, iteratively, assuming a high degree of agreement that the intrinsic anisotropy of the tissue corresponds to the anisotropy of the simulation-based model. A method according to claim 6, characterized in that the simulation further takes into account actively contracting muscle fibers, and that the comparison in step e) is iteratively repeated in each case after adaptations of the simulation or the underlying model until the difference between the three-dimensional, local strains and the geometrically determined strain rates smaller than a predetermined limit. Method according to one of the preceding claims, characterized in that from the intrinsic anisotropy, in particular from the compensated 3D strain state, the respective mean fiber direction ( 9 ) of fibers of the tissue of the hollow body wall is determined. Method according to one of the preceding claims, characterized in that the respective local principal strain direction, in particular the main strain vector (V _H ), is determined from the compensated 3D strain state. Method according to one of the preceding claims, characterized in that the detection of the three-dimensional movement of predeterminable positions (P) of the hollow body wall ( 6 ) takes place on a time sequence of images of the hollow body by means of a 3D feature tracking method. Method according to one of the preceding claims, characterized in that fiber directions ( 9 ) of muscle fibers of a myocardial tissue of a flexible heart under pressure (p _i ). Method according to one of the preceding claims, characterized in that the hollow body is a heart chamber and that the three-dimensional, local strains from a comparison of the predeterminable positions (P) at the time of maximum cardiac contraction with the corresponding positions (P) at a time of relaxation of Heart are calculated. Method according to one of the preceding claims, characterized in that the geometrically determined expansion components are calculated numerically by means of mathematical models. A method according to claim 8, characterized in that the respective local main strain vectors (V _H ) are calculated by using a numerical model comprising the hollow body wall ( 6 ) modeled using a finite element method. Method according to one of the preceding claims, characterized in that the mean fiber directions ( 9 ) or main strain directions in a surface model of the hollow body ( 2 ) and / or a parameter card. Method according to one of the preceding claims, characterized in that the compensated 3D strain state as a vector field in a surface model of the hollow body ( 2 ) and / or a parameter map is entered, wherein the direction of the arrows shown corresponds to the main expansion direction and the color, strength and / or length of the arrows used corresponds to the magnitude and / or the sign of the contraction. Method according to one of the preceding claims, characterized in that the difference between the three-dimensional, local strains and the geometrically determined strain fractions as a vector field or as a field line representation in a surface model of the hollow body ( 2 ) and / or a parameter card. Computer program product for carrying out a method according to one of the preceding claims.

Images