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The Tei index, an important indicator of heart function, lacks a direct method to compute because it is difficult to directly evaluate the isovolumic contraction time (ICT) and isovolumic relaxation time (IRT) from which the Tei index can be obtained. In this paper, based on the proposed method of accurately measuring the cardiac cycle physical phase, a direct method of calculating the Tei index is presented. The experiments based on real heart medical images show the effectiveness of this method. Moreover, a new method of calculating left ventricular wall motion amplitude is proposed and the experiments show its satisfactory performance.

Cardiovascular diseases have become the top factor causing human death in both western and eastern world. People hope that these diseases can be traced before they onset. A simple, reproducible, non-invasive test for determinants of prognosis is therefore necessary. For this kind of test, doctors need to observe the current status of hearts and have some effective measurement rules to decide if hearts is normal or not. For non-invasive check methods, there are several heart medical imaging technologies, such as MR, CT, SPECT and Ultrasound, widely used for heart diseases diagnosis, from which doctors can observe patients heart status without invasion.

Myocardial motion that is directly related to cardiac vascular supply is widely studied based on heart medical images to analyze the heart condition, especially the left ventricular function, for diagnosing heart abnormalities [

In the myocardial motion analysis, the cardiac cycle is a complicated time-varying process and is generally partitioned into several phases based on time to simplify the process. According to clinical diagnosis, however, the phase should be definitely based on LV deformation and stress since the dynamics of heart is caused by that deformation. This definition is called cardiac physical phase. In this paper, a method of cardiac cycle physical phase (CPP) division according to the LV anatomy is proposed first based on B-spline represented heart model, of which the initial work [

Moreover, LV wall motion amplitude (LVMA) can also be computed to analyze the LV wall movement based on the accurate CPP partitions in this study. The movement of LV wall is another very important index of the LV function [

The organization of this paper is as follows. In the next section, the matrix representation of B-spline is introduced and the volumetric measurement of B-spline is given. The method of CPP partition and calculation of Tei and LVMA are explained in Section 3. The proposed methods are evaluated by experiments on a real human data in Section 4 and the results are also analyzed.

A B-spline curve consists of segments, with each segment of degree k constructed by k+1 sequential control points. Let _{i}_{i}_{+1} –_{i}_{i}_{i}_{+1}]:

The whole curve can thus be represented as:

Equally, a part of the B-spline surface in the nonempty area [_{i},u_{i}_{+1}) × [_{i}_{i}_{+1}) can be represented as:
_{k}_{1} = [1 ^{2} ⋯ ^{k1}] and
_{i}_{i}_{+1} –_{i}_{i}_{i}_{+1} –_{i}_{i}_{i}_{+1}) × [_{i}_{i}_{+1}).
_{i}_{i}_{+1}) and [_{i}_{i}_{+1}), respectively.

The whole surface is then represented as follow:

The volume can be expressed as [

As the equations given by

The computation of the area of a slice at depth

The volume of B-spline surface of orders _{1} × _{2} is:
_{i}_{,} _{j}_{1} × 3_{2} which is the product of the three polynomials

Cardiac cycle is a very complicated physical process. Traditional researches used to divide the cycle into two major parts as systole and diastole. During systole, LV contracts thus the blood in LV can be ejected out. On the opposite, during diastole LV bulges and imbibes blood in. The function of heart is achieved by the repeatedly alternating systole and diastole. As the LV motion is not uniform neither in systole nor in diastole, this rough partition can hardly express the true feature of LV motion. In fact it is shown by anatomy knowledge that the whole cardiac cycle contains 7 CPPs based on different LV shape and function. These CPPs are Isovolumic Systolic (IS), Rapid Ejection Period (REP), Slow Down Ejection Period (SDEP), Isovolumic Relaxation Period (IRP), Rapid Filling Period (RFP), Slow Down Filling Period (SDFP) and Atrial Systole (AS) [

The shape of LV shows various features in different CPP, and the changing of these shapes is the main basis of CPP partition. To divide the CPP phases, two shape factors are necessary. The first shape factor is the volume of LV (LVV). Assume that the LVV curve during whole cardiac cycle is already known and denoted with

Fortunately, there is another shape factor, called LV long-axis length (LVLL), that can provide the complement information. LVLL is defined as the height from the base to the apical of LV. Assuming the LVLL curve is

In the beginning of systole and diastole, the shape of LV sharply changes while the LVV stays invariant. These periods are called isovolumetric contraction (IC) and isovolumetric relaxation (IR). Medical research shows that the biggest stress and displacement of LV occur in these two periods. When some diseases occur, the LV would need longer time to achieve the deformation and displacement, thus the length of IC and IR are very important index for evaluating LV functions. Based on that Tei-index is raised by Japanese researcher Tei in 1995 [

Tei index is also called myocardial performance index (MPI). This new index can generally evaluate the heart function in both diastole and systole. It has been widely used in heart disease diagnosis. Based on the CPP partition, a direct method of calculating Tei index can be deduced.

IC and IR are the periods while the LV shape changes largely and LVV keeps almost invariant. According to the CPP characters listed in

The Tei index can therefore be calculated as:
_{x}

The function of LV is achieved by cycle motion of LV wall. The motion amplitude of LV wall (LVMA) reflect the deformation capability of LV. When some disease occurs, there must be some abnormalities of the LVMA on the sick area, thus LVMA can be used as an important parameter for LV function analysis. Azhari

It is also known that the movement of LV wall is not in a uniform speed, thus the distribution of LVMA differs largely in different CPPs. For example, the LVMA in the beginning of systole and diastole are much larger than it in other time because the main deformation of LV happens in these periods. Due to these causes mentioned above, to study on the LVMA in different CPP is highly necessary.

Assuming that the point _{t}_{t}_{t}^{T}_{x}_{y}_{z}_{1}, _{2}] (0 ≤ _{1} < _{2} ≤

In order to get the displacement of whole LV wall, a large amount of points should be marked and tracked. Assuming such a points set _{1}, _{2}, ⋯, _{n}_{1,2} of each point in

As an elastomer, the motion of LV is continuous and gradually variational so that the displacement of the whole LV wall can be described as a surface. Using the position information of _{1}) (position of all points in _{1}) and _{1}, _{2}] and be denoted by _{1}, _{2}).

In Section 1 the cardiac cycle is divided into 7 CPPs (_{name}_{name}_{name}_{name}

The 3D heart model is built by the Active Shape Models (ASM) [

Our experiment is focused on the left ventricle, about 1000 points have been tracked, and about 400 points are distributing on inside-wall while rests are on outside-wall. These points constitute the whole motion of left ventricle in a cardiac cycle, and the points are labeled in several phases, with 0.1 second apart from each other. In the model we focus on the inside-wall surface since the LVV and LVLL is majorly decided by it.

After the models in all phases are built, the LVV in each moments can be calculated by _{i}_{i}

In each inside-wall surface model, finding the centers at top and bottom layer, the LVLL can be calculated by the distance of these two centers. Assuming that the LVLL values are obtained from _{i}_{i}

With the curves of

Step 1: find the zero-points in

Step 2: find the zero-points in

The final CPP partition result is shown in

The Tei index can be calculated by

The distribution of LVMA in 6 CPPs is shown in

In this paper, a new perspective of myocardial motion analysis, accurate division of cardiac cycle physical phases (CPP), is proposed. Based on this method, an precise and direct calculation of the Tei index is presented. First, several B-spline models of LV inside-wall are built at different time phases. Second, the LVV and LVLL of each model are calculated by B-spline integral and the curves of these two factors are fitted in whole cardiac cycle. Third, the derivative curves of LVV and LVLL are calculated. At last, the CPP partition by finding zero points in them is obtained. The experiment with real human LV data shows the result of this method is very close to the medical statistical values. Tei index is a new heart function index which strongly depends on the CPP. With the accurate CPP division, the accuracy of the direct Tei index calculation method is shown by the experiment result. This paper also proposed a new method to computing LVMA to analyze the myocardial motion. The color figure of LVMA in different CPP shows rules of myocardial motion which are very close to the results of other researches.

This work was supported by the National Natural Science Foundation of China and Microsoft Research Asia (60870002, 60802087), NCET, and the Science and Technology Department of Zhejiang Province (2010R10006, 2010C33095, Y1090592).

An example of the LV endocardium point model at one time phase.

LVV varying cure (solid line) and LVLL varying cure (dash line) in whole cardiac cycle.

CPP partition in cardiac cycle.

LVMA color graph of 6 CPPs. The color band in left column indicates the value of LVMA.

LVV and LVLL Features of Each CPP.

Systolic | IS | Hold on | Reduce | ||

REP | Reduce | Reduce | |||

SDEP | Reduce | Increase | |||

Diastolic | IRP | Hold on | Increase | ||

RFP | Increase | Increase | |||

SDFP | Increase | Reduce | |||

AS | Hold on | Hold on |

CPP Lasting Time.

Phase | Average data | Result |
---|---|---|

IS | 0.06–0.08 | 0.066 |

PRE | 0.11 | 0.128 |

SDEP | 0.14 | 0.132 |

IRP | 0.06–0.08 | 0.057 |

RFP | 0.11 | 0.047 |

SDFP | 0.12 | 0.151 |

AS | 0.1 | 0.119 |