Dynamic-Threshold Level Set Method for Volumetry of Porcine Kidney in CT Images

Rationale and Objective

We sought to assess the accuracy of a novel computerized volumetry method, called dynamic-thresholding (DT) level set, in determining the renal volume of pigs in CT images on the basis of in vivo and ex vivo reference standards.

Methods and Materials

Eight Yorkshire breed anesthetized pigs (weight range 45–50 kg) were scanned on a 64-slice multidetector CT scanner (Sensation 64; Siemens) after injection of an iodinated (300 mg I/ml) contrast agent through an IV cannula. The kidneys of the pigs were then surgically resected and scanned by CT in the same manner. Both in vivo and ex vivo CT images were subjected to our computerized volumetry using DT level set method. The resulting volumes of the kidneys were compared with in vivo and ex vivo reference standards: the former was established by manual contouring of the kidneys on the CT images by an experienced radiologist, and the latter was established as the water displacement volume of the resected kidney.

Results

The comparisons of the in vivo and ex vivo measurements by our volumetric scheme with the associated reference standards yielded a mean difference of 1.73 ± 1.24% and 3.38 ± 2.51%, respectively. The correlation coefficients were 0.981 and 0.973 for in vivo and ex vivo comparisons, respectively. The mean difference between in vivo and ex vivo reference standards was 5.79 ± 4.26%, and the correlation coefficient between the two standards was 0.760.

Conclusion

Our computerized volumetry using the DT level set method can provide accurate in vivo and ex vivo measurements of kidney volume, despite a large difference between the two reference standards. This technique can be employed in human subjects for the determination of renal volume for preoperative surgical planning and assessment of oncology treatment.

Precise organ volumetry is gaining significance in various clinical settings for patient selection for an appropriate management, surgery planning, and monitoring a disease status ( ). Traditionally, kidney size/diameter measurement on imaging has been used as a surrogate to supplement these clinical needs. However, the kidney size measurement is an imperfect measure of overall organ volume. Three-dimensional kidney volumetry is more preferred in living kidney donors ( ), in assessing progression of polycystic renal disease ( ), and for tumor burden and treatment response evaluation ( ). With the recent introduction of MDCT scanners, there has been astronomical increase in the use of image postprocessing and three-dimensional services. Therefore, organ volumetry, although more desirable, is not routinely performed in lieu of the expertise required and substantial processing time. In addition, there is no known scientifically validated commercially available software that enables the organ volumetry in an automated fashion.

Segmentation of the kidney from CT images is an essential step for renal volumetry. However, manual segmentation of a kidney requires contouring of the kidney boundary on each renal CT image, which is labor intensive and prone to interoperator variability. Computerized volumetry (CV), on the other hand, relies on an efficient and accurate segmentation method, which is a subject of active research in medical image processing ( ). To reduce the labor of manual contouring, it is common to use a two-dimensional deformable model, i.e., a closed deformable curve, often called a snake ( ), to assist in user contouring. This model requires initialization of the curve on each axial image.

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Materials and methods

Study Design

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Dynamic-Threshold Level Set Method

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S={x|(x)=k}}, S

{

(

)

}

where k is an arbitrary scalar value (often zero, called zero-level set). Detailed descriptions of the level set method can be found in Refs. and .

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∙∙t=FDT(x)|∇|+CCurvature∇⋅(∇|∇|)|∇|+CSM∇2, •

•

(

)

∇

⋅

(

∇

)

∇

where C Curvature and C SM are two control parameters smoothing the segmentation results. In this study, C Curvature and C SM were empirically set to 0.5 and 0.2, respectively.

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Threshold shift

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Pf⋅Pf(Topt)=Pb⋅Pb(Topt), P

⋅

(

)

⋅

(

)

where P f and P b are the a priori probabilities of each material, which satisfy P f + P b = 1. P f and P b correspond to the percentages of the volume of each material in the images. P f and P b are the PDF functions of the foreground and background.

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Topt∣∣FtB<1>Topt|FtB=1(Ttheory)>Topt|FtB>1, T

(

)

where FtB = v f /v b , which is the volumetric ratio of the foreground material to the background material in the histogram. In other words, the optimal threshold that separates two materials shifts toward the small region in a histogram relative to the theoretic threshold value. The threshold shift, T opt − T theory , is negative when v f > v b , whereas it is positive when v f < v b . Only when FtB = 1 ( v f = v b ), i.e., the histogram is balanced, is T opt equal to T theory .

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Dynamic-thresholding speed function

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FDT(x;Iopt)=sign(ΔI(x))⋅|ΔI(x)|n, F

(

;

)

(

)

⋅

(

)

where sign(x) is a sign function (also known as an indicator function), which is 1 if x is positive and −1 if x is negative; and n is often set to 2 or 3. ΔI(x) is defined by;

ΔI⎛⎝⎜⎜⎜⎜x⎞⎠⎟⎟⎟⎟=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪−1(I(x)−Iopt)/ΔB(I(x)−Iopt)/ΔF1ifI(x)≤Iopt−ΔBifI(x)≤IoptifI(x)≤Iopt+ΔFifI(x)>Iopt+ΔF, Δ

(

)

{

−

(

)

≤

−

(

)

−

)

(

)

≤

(

)

−

)

(

)

≤

(

)

where Δ B and Δ F are the distance between the peak of the background in the histogram and the optimal threshold I opt , and the peak of foreground in the histogram to optimal threshold I opt , respectively ( Fig. 2 ).

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Results

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In Vivo and Ex Vivo Comparison

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Diff(VR,VX)=|VX−VR|VR⋅100%, D

(

)

−

⋅

100

where V R is the volume of the RS, and V X is the measured experimental volume. Six groups of comparison were performed, including the comparison between in vivo CV and in vivo RS, the comparison between ex vivo CV and ex vivo RS, the comparison between in vivo RS and ex vivo RS, the comparison between ex vivo RS and in vivo CV, the comparison between ex vivo RS and ex vivo manual volumetry (MV), and the comparison between ex vivo MV and ex vivo CV. We calculated the difference of the volume for each individual kidney in each comparison group. The statistical results are summarized in Table 1 .

Table 1

Statistical Results of Comparison Among In Vivo Reference Standard (RS), Ex Vivo RS, In Vivo Computerized Volumetry (CV), Ex Vivo CV, and Ex Vivo Manual Volumetry (MV)

Diff ( V R , V X ) Mean Difference (%) SD (%) Median Difference (%) Correlation Coefficient In vivo RS, in vivo CV 1.73 1.24 1.45 0.981 Ex vivo RS, ex vivo CV 3.36 2.54 2.75 0.972 In vivo RS, ex vivo RS 5.79 4.26 4.91 0.760 Ex vivo RS, in vivo CV 4.71 4.14 3.06 0.835 Ex vivo RS, ex vivo MV 14.77 2.20 15.19 0.913 Ex vivo MV, ex vivo CV 13.42 3.32 13.29 0.934

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Discussion

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Conclusion

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References

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Dynamic-Threshold Level Set Method for Volumetry of Porcine Kidney in CT Images

Rationale and Objective

Methods and Materials

Results

Conclusion

Materials and methods

Study Design

Dynamic-Threshold Level Set Method

Threshold shift

Dynamic-thresholding speed function

Results

In Vivo and Ex Vivo Comparison

Discussion

Conclusion

References

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