CN101216956A - Heart 3D representation method based on NURBS - Google Patents

Abstract

A heart 3D representation method based on NURBS comprises the following steps of: 1) obtaining and processing data as follows: obtaining the 3D points on the heart surface from a plurality of given heart medical images; 2) carrying out NURBS surface fitting with the 3D point cloud as the control points by using an arithmetic formula (1), wherein, pi,j (i is equal to 0,1,ellipsis,n;j is equal to 0,1,ellipsis,m) are the surface control points(i.e. point cloud with boundary from the heart)in a topological rectangular array, omega i,j are weight factors relating to the control points; and Ni,k1(u) and N j,k2(v) are k1 and k2 degree standard rational B-spline basis function respectively. The invention provides a heart 3D representation method based on NURBS with high calculation accuracy, rapid calculation speed, and conformance to the requirements of clinical diagnosis.

Description

Heart three dimensional representation method based on NURBS

Technical field

The present invention relates to a kind of three dimensional representation method of heart.

Background technology

Heart is extremely complicated system ensembles such as current collection physiology, dynamics, hemodynamics and nerve, biochemical control.Modeling and simulating is the effective means of research complex biological knowledge topic.In the past few years, people have had deep understanding to the physiological significance of cardiac structure and function, and have set up many mathematical models, make great efforts to quantize viewed myocardium mechanical behavior, conductivity behavior and biological chemistry behavior.But because the complicacy of heart physiological pathology system, generally speaking these models are separate development, and still nobody can integrate research to the various mechanism of heart at present.

The virtual heart research of rising in recent years is incorporated into the thought of virtual reality the research field of the such complexity of cardiovascular system, it is to utilize computing machine powerful computing ability and graphics process display capabilities, sets up virtual cardiac module and provides possibility for further investigation cardiomotility mechanism.Model not only will be from emulation heart on the form, and the motion process that should be able to simulate true heart, mechanical characteristics, the characteristics of electrical conductivity of heart and the hydrodynamic characteristic of chambers of the heart inner blood of the cardiac muscle of emulation heart, valve and chambers of the heart motion, and can emulation heart pathological state, for clinical diagnosis disease is given information.

There are some scholars to propose some methods at present, are used to obtain the body of heart and the description of motion based on model.Kyoungju Park, scholars such as Dimitris Metaxas have proposed the new theory of a kind of cardiac function analysis.Set up a basic cardiac module with the image of MRI, the method that has proposed finite element analysis is calculated whole and local functional parameter.Experiment shows, the structure that draws based on such model can characterize the motion and the dynamic rule of heart wall.Taratorin and Sideman then are divided into a large amount of cube infinitesimal sheets to myocardium and carry out modeling and analysis, and it is more satisfactory to obtain effect.

Yet because method itself, some does not also reach the required requirement of clinical diagnosis on computational accuracy based on the heart method for expressing of model for these, and some arithmetic speed is slow.

Summary of the invention

Clinical diagnosis requires, the deficiency of poor practicability for the computational accuracy that overcomes existing heart movement analytical approach or speed do not reach, and the invention provides a kind of computational accuracy height, fast operation, meets the heart three dimensional representation method based on NURBS of the required requirement of clinical diagnosis.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of heart three dimensional representation method based on NURBS, described heart three dimensional representation method may further comprise the steps:

1), the obtaining and handling of data:

Given a large amount of heart medical image obtains the three-dimensional point of heart surface from these images, comprising:

(1.1), carry out smoothing processing with image filtering method, the removal noise;

(1.2), by given index file sectioning image is adjusted to correct order;

(1.3), the definition area-of-interest, the method by the gray scale thresholding is partitioned into the target area from former CT image;

(1.4), obtain the gray-scale value of image, calculate the changing value of gray scale, get the cardiac boundary that is of grey scale change maximum;

(1.5), extract the three-dimensional point cloud of heart;

2), the three-dimensional point cloud of getting above-mentioned heart is as the reference mark, carries out the nurbs surface match, its formula is (1):

$s(u,v)=\frac{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}\underset{j=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ω}}_{i,j}{p}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}\underset{j=0}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\ω}}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}---\left(1\right)$

In the following formula, p _{I, j}(i=0,1 ... n; J=0,1 ... m) be the reference mark of curved surface, promptly take from the frontier point cloud of heart, be topological rectangular array, ω _{I, j}Be the weight factor that interrelates with the reference mark; N _{I, k1}(u) and N _{J, k2}(v) be respectively k1 and k2 the reasonable B spline base function of standard;

The de Boor-Cox recursion formula of reasonable B spline base function, it is defined as follows:

In the following formula, B batten N _{I, k}(u) though be defined on the entire parameter u axle B batten N _{I, k}(u) by interior nodes u between its supporting area _i, u _I+1... .u _I+k+1Decision.

The nurbs surface match of cylindrical coordinates is as preferred a kind of scheme: in described step 2) in, with (n+1) * (m+1) reference mark array (x _Ij, y _Ij, z _Ij) (i=0,1...n, j=0,1...m) translation causes to such an extent that curved surface is the center with the z axle, Cartesian coordinates is represented a little to convert to then point (the r under the cylindrical coordinates _Ij, θ _Ij, z _Ij) (i=0,1...n, j=0,1...m), its conversion formula following (3):

$r_{\mathrm{ij}}=\sqrt{x_{\mathrm{<figure-callout\; id="2"\; label="ij"\; filenames="S2007103072497E00011.png"\; state="\{\{state\}\}">ij</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="y\; ij"\; filenames="S2007103072497E00011.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{ij}}^{}},$

${\mathrm{\&theta;}}_{\mathrm{ij}}=\left\{\begin{array}{ccccc}\mathrm{\&pi;}/2& \mathrm{if}& x_{\mathrm{ij}}=0& \mathrm{and}& y_{\mathrm{ij}}>0\\ 3\mathrm{\&pi;}/2& \mathrm{if}& x_{\mathrm{ij}}=0& \mathrm{and}& y_{\mathrm{ij}}<0\\ a\tan (y_{\mathrm{ij}}/x_{\mathrm{ij}})& \mathrm{if}& x_{\mathrm{ij}}>0& \mathrm{and}& y_{\mathrm{ij}}\&GreaterEqual;0\\ \mathrm{\&pi;}+a\tan (y_{\mathrm{ij}}/x_{\mathrm{ij}})& & & \mathrm{if}& x_{\mathrm{ij}}<0\\ 2\mathrm{\&pi;}+a\tan (y_{\mathrm{ij}}/x_{\mathrm{ij}})& \mathrm{if}& x_{\mathrm{ij}}>0& \mathrm{and}& y_{\mathrm{ij}}<0\end{array}\right.---\left(3\right)$

z _ij＝z _ij

The formula of the nurbs surface match of cylindrical coordinate is (4):

$[r(u,v),\mathrm{\&theta;}(u,v),z(u,v)]=\frac{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{p}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}---\left(4\right)$

Wherein, p _{I, j}=[r _{I, j}, θ _{I, j}, z _{I, j}].

In described step 1), medical image adopts SPECT medical image, nuclear magnetic resonance image, CT image, spiral CT image, ultrasonoscopy or PET image.

Described heart is left ventricle, right ventricle, atrium sinistrum, atrium dextrum, the surfaces externally and internally of heart partly or completely.

Technical conceive of the present invention is: NURBS claims non-uniform rational B-spline again, and it also has lot of advantages except the characteristics that possess the B batten: 1) both resolve shape for standard and also provide a public mathematical form for the accurate expression of free type curved surface with design; 2) not only can utilize weight factor again, therefore have bigger dirigibility by adjusting the shape that the reference mark changes curve and surface; 3) the suitable popularization of right and wrong reasonable B batten form and your form of reasonable and non-reasonable Betsy etc.

Nurbs curve: a k nurbs curve can be expressed as one section rational polynominal vector function:

$c_i\left(t\right)=\frac{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{p}_i{N}_{i,k}\left(u\right)}{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{N}_{i,k}\left(u\right)}---\left(5\right)$

Wherein, ω _i(i=0,1 ... n) be called weight factor, respectively with control vertex p _i(i=0,1 ... n) interrelate.First and last weight factor ω ₀, ω _n＞0, all the other ω _i〉=0, and k weight factor of order be not zero simultaneously, with prevent that denominator from being zero, reservation convex closure character and curve not the reason weight factor deteriorate to a bit.N _{I, k}(u) be k standard B spline base function.

Nurbs curve has the local property adjusted, convex closure, character such as geometric invariance.In addition, owing to introduced weight factor, make that the adjustment of curve is more flexible.

Nurbs surface a: k ₁* k ₂The rational fraction of inferior nurbs surface is represented:

$s(u,v)=\frac{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{p}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}---\left(6\right)$

P wherein _{I, j}(i=0,1 ... n; J=0,1 ..m) be topological rectangular array, form a Control Network.ω _{I, j}Be the weight factor that interrelates with the reference mark.N _{I, k1}(u) and N _{J, k2}(v) be respectively k ₁And k ₂The reasonable B spline base function of inferior standard.

Reasonable B-spline surface has and the similar geometric properties of non-reasonable B-spline surface.And, being similar to nurbs curve, its weight factor can be used to adjust the shape of curved surface.

Another advantage that nurbs surface is different from B-spline surface is exactly that its accurately expression standard is resolved body (as cylinder, circular cone, ball, surface of revolution etc.).

The NURBS technology has been introduced weight factor, thereby solve the problem that B-spline surface can not accurately be represented elementary analytic surface, yet, for the free type curved surface, the weight factor of nurbs surface is not brought into play very big effect yet, and weight factor adjust unreasonable, will cause very bad parametrization, even destroy curved-surface structure subsequently.So we are difficult to accurately represent by weight factor the body of heart, left ventricle, owing to heart, left ventricle likeness in form column body, therefore, introduce the nurbs surface of cylindrical coordinate in addition.The nurbs surface of cylindrical coordinate is fit to expression heart, left ventricle more than the nurbs surface of cartesian coordinate system, especially, is providing under the situation of a small amount of marginal point, and the advantage of the nurbs surface of cylindrical coordinate is more obvious.

Beneficial effect of the present invention mainly shows:

1) nurbs surface is represented convenience very, and given reference mark is used than low order NURBS just can obtain a desirable curved surface, and this cardiac module compares based on simple geometric body or the cardiac module that utilizes simple mathematical to represent truer;

2) heart represented of NURBS is smooth, a continuous model, for the static state that is subsequently applied to and the analysis of dynamic function parameter provide the foundation;

3) local modification of nurbs surface can be done local modification to the heart body under the situation that does not change global shape;

4) nurbs surface has very strong dirigibility, changes the heart body by changing reference mark or weight factor, for the research of heart deformation provides possibility.

Description of drawings

Fig. 1 is the area-of-interest synoptic diagram that obtains from the CT section.

Fig. 2 is the synoptic diagram of the point of the heart surface that extracts.

Fig. 3 is the synoptic diagram of nurbs surface match plastics heart.

Fig. 4 is a synoptic diagram of playing up nurbs surface match plastics heart.

Fig. 5 is the left ventricle inside and outside wall nurbs surface match synoptic diagram of seven states in the cardiac cycle.

Embodiment

Below in conjunction with accompanying drawing the present invention is further described.

With reference to Fig. 1～Fig. 5, a kind of heart three dimensional representation method based on NURBS may further comprise the steps:

1), the obtaining and handling of data:

Given a large amount of heart medical image obtains the three-dimensional point of heart surface from these images, comprising:

(1.1), carry out smoothing processing with image filtering method, the removal noise;

(1.2), by given index file sectioning image is adjusted to correct order;

(1.3), the definition area-of-interest, the method by the gray scale thresholding is partitioned into the target area from former CT image;

(1.4), obtain the gray-scale value of image, calculate the changing value of gray scale, get the cardiac boundary that is of grey scale change maximum;

(1.5), extract the three-dimensional point cloud of heart;

2), the three-dimensional point cloud of getting above-mentioned heart is as the reference mark, carries out the nurbs surface match, its formula is (1):

$s(u,v)=\frac{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{p}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}---\left(1\right)$

In the following formula, p _{I, j}(i=0,1 ... n; J=0,1 ... m) be the reference mark of curved surface, promptly take from the frontier point cloud of heart, be topological rectangular array, ω _{I, j}Be the weight factor that interrelates with the reference mark; N _{I, k1}(u) and N _{J, k2}(v) be respectively k1 and k2 the reasonable B spline base function of standard;

The de Boor-Cox recursion formula of reasonable B spline base function, it is defined as follows:

In the following formula, B batten N _{I, k}(u) though be defined on the entire parameter u axle B batten N _{I, k}(u) by interior nodes u between its supporting area _i, u _I+1... .u _I+k+1Decision.

The nurbs surface match of cylindrical coordinates is as preferred a kind of scheme: in described step 2) in, with (n+1) * (m+1) reference mark array (x _Ij, y _Ij, z _Ij) (i=0,1...n, j=0,1...m) translation causes to such an extent that curved surface is the center with the z axle, Cartesian coordinates is represented a little to convert to then point (the r under the cylindrical coordinates _Ij, θ _Ij, z _Ij) (i=0,1...n, j=0,1...m), its conversion formula following (3):

$r_{\mathrm{ij}}=\sqrt{x_{\mathrm{ij}}^2+y_{\mathrm{ij}}^2},$

${\mathrm{\&theta;}}_{\mathrm{ij}}=\left\{\begin{array}{ccccc}\mathrm{\&pi;}/2& \mathrm{if}& x_{\mathrm{ij}}=0& \mathrm{and}& y_{\mathrm{ij}}>0\\ 3\mathrm{\&pi;}/2& \mathrm{if}& x_{\mathrm{ij}}=0& \mathrm{and}& y_{\mathrm{ij}}<0\\ a\tan (y_{\mathrm{ij}}/x_{\mathrm{ij}})& \mathrm{if}& x_{\mathrm{ij}}>0& \mathrm{and}& y_{\mathrm{ij}}\&GreaterEqual;0\\ \mathrm{\&pi;}+a\tan (y_{\mathrm{ij}}/x_{\mathrm{ij}})& & & \mathrm{if}& x_{\mathrm{ij}}<0\\ 2\mathrm{\&pi;}+a\tan (y_{\mathrm{ij}}/x_{\mathrm{ij}})& \mathrm{if}& x_{\mathrm{ij}}>0& \mathrm{and}& y_{\mathrm{ij}}<0\end{array}\right.---\left(3\right)$

z _ij＝z _ij

The formula of the nurbs surface match of cylindrical coordinate is (4):

$[r(u,v),\mathrm{\&theta;}(u,v),z(u,v)]=\frac{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{p}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}---\left(4\right)$

Wherein, p _{I, j}=[r _{I, j}, θ _{I, j}, z _{I, j}].

In described step 1), medical image adopts SPECT medical image, nuclear magnetic resonance image, CT image, spiral CT image, ultrasonoscopy or PET image.

Described heart is left ventricle, right ventricle, atrium sinistrum, atrium dextrum, the surfaces externally and internally of heart partly or completely.

In the present embodiment, at first, the CT slice map of given a large amount of plastic cement heart, this plastic cement heart is placed on the wooden support, and the syringe that oil is housed on the support is used for heart deformation.The plastic cement heart of this experiment under the nurbs surface match state.

Secondly, from the CT slice map, obtain the three-dimensional point of plastic cement heart surface.This process is divided into 6 steps:

1) with filtering picture is carried out smoothing processing, remove some noises;

2) by given index file the CT section is adjusted into correct order;

3) area-of-interest of definition, purpose is to be partitioned into this process of target area (Fig. 1) to be partitioned into heart surface based on the brightness thresholding;

4) gray-scale value of acquisition image, the changing value of calculating gray scale is got the cardiac boundary that is of grey scale change maximum;

5) extract three-dimensional point cloud, manually delete some obvious noise points;

6) show these points (Fig. 2).

Get 30 * 35 points among Fig. 4 as reference mark (wherein 30 for counting on every layer, and 35 for obtaining the number of plies), heart such as Fig. 3 and 4 after 3 * 3 rank nurbs surface matches.

In order to obtain some functional parameters of heart, heart wall inside and outside the left ventricle of 7 states in the cardiac cycle is carried out nurbs surface match (Fig. 5).Being divided into 7 time intervals a cardiac cycle, each is 100ms at interval, so the left ventricle of each at interval corresponding state.

Claims (4)

1. heart three dimensional representation method based on NURBS, it is characterized in that: described heart three dimensional representation method may further comprise the steps:

1), the obtaining and handling of data: given a large amount of heart medical image, from these images, obtain the three-dimensional point of heart surface, comprising:

(1.1), carry out smoothing processing with image filtering method, the removal noise;

(1.2), by given index file sectioning image is adjusted to correct order;

(1.3), the definition area-of-interest, from image, be partitioned into the target area by the gray scale threshold value method;

(1.4), obtain the gray-scale value of image, the variation of calculating gray scale, the position of getting the grey scale change maximum is a cardiac boundary;

(1.5), extract the three-dimensional point cloud of heart;

2), the three-dimensional point cloud of getting above-mentioned heart is as the reference mark, carries out the nurbs surface match, its formula is (1):

$s(u,v)=\frac{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{p}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}---\left(1\right)$

In the following formula, p _{I, j}(i=0,1 ... n; J=0,1 ... m) be the reference mark of curved surface, promptly take from the frontier point cloud of heart, be topological rectangular array, ω _{I, j}Be the weight factor that interrelates with the reference mark; N _{I, k1}(u) and N _{J, k2}(v) be respectively k ₁And k ₂The reasonable B spline base function of inferior standard; The Boor-Cox recursion formula of reasonable B spline base function is as follows:

In the following formula, B batten N _{I, k}(u) though be defined on the entire parameter u axle B batten N _{I, k}(u) by interior nodes u between its supporting area _i, u _I+1... .u _I+k+1Decision.

2. the heart three dimensional representation method based on NURBS as claimed in claim 1 is characterized in that: in described step 2) in, with (n+1) * (m+1) reference mark array (x _Ij, y _Ij, z _Ij) (i=0,1...n, j=0,1...m) translation causes to such an extent that curved surface is the center with the z axle, and by coordinate system conversion, the point that Cartesian coordinates is represented converts the point (r under the cylindrical coordinates to _Ij, θ _Ij, z _Ij) (i=0,1...n, j=0,1...m), its conversion formula following (3):

$r_{\mathrm{ij}}=\sqrt{x_{\mathrm{ij}}^2+y_{\mathrm{ij}}^2},$

${\mathrm{\&theta;}}_{\mathrm{ij}}=\left\{\begin{array}{ccccc}\mathrm{\&pi;}/2& \mathrm{if}& x_{\mathrm{ij}}=0& \mathrm{and}& y_{\mathrm{ij}}>0\\ 3\mathrm{\&pi;}/2& \mathrm{if}& x_{\mathrm{ij}}=0& \mathrm{and}& y_{\mathrm{ij}}<0\\ a\tan (y_{\mathrm{ij}}/x_{\mathrm{ij}})& \mathrm{if}& x_{\mathrm{ij}}>0& \mathrm{and}& y_{\mathrm{ij}}\&GreaterEqual;0\\ \mathrm{\&pi;}+a\tan (y_{\mathrm{ij}}/x_{\mathrm{ij}})& & & \mathrm{if}& x_{\mathrm{ij}}<0\\ 2\mathrm{\&pi;}+a\tan (y_{\mathrm{ij}}/x_{\mathrm{ij}})& \mathrm{if}& x_{\mathrm{ij}}>0& \mathrm{and}& y_{\mathrm{ij}}<0\end{array}\right.---\left(3\right)$

z _ij＝z _ij

The formula of the nurbs surface match of cylindrical coordinate is (4):

$\left[\right(r(u,v),\mathrm{\&theta;}(u,v),z(u,v)]=\frac{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{p}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{i,j}{N}_{i,k_1}\left(u\right)N_{j,k_2}\left(v\right)}---\left(4\right)$

Wherein, p _{I, j}=[r _{I, j}, θ _{I, j}, z _{I, j}].

3. the heart three dimensional representation method based on NURBS as claimed in claim 1 or 2, it is characterized in that: in described step 1), the heart medical image adopts SPECT medical image, nuclear magnetic resonance image, CT image, spiral CT image, ultrasonoscopy or PET image.

4. the heart three dimensional representation method based on NURBS as claimed in claim 1 or 2 is characterized in that: described heart is left ventricle, right ventricle, atrium sinistrum, atrium dextrum, the surfaces externally and internally of heart partly or completely.

Images