Accurate Prostate Volume Estimation Using Multifeature Active Shape Models on T2-weighted MRI

Rationale and Objectives

Accurate prostate volume estimation is useful for calculating prostate-specific antigen density and in evaluating posttreatment response. In the clinic, prostate volume estimation involves modeling the prostate as an ellipsoid or a spheroid from transrectal ultrasound, or T2-weighted magnetic resonance imaging (MRI). However, this requires some degree of manual intervention, and may not always yield accurate estimates. In this article, we present a multifeature active shape model (MFA) based segmentation scheme for estimating prostate volume from in vivo T2-weighted MRI.

Materials and Methods

We aim to automatically determine the location of the prostate boundary on in vivo T2-weighted MRI, and subsequently determine the area of the prostate on each slice. The resulting planimetric areas are aggregated to yield the volume of the prostate for a given patient. Using a set of training images, the MFA learns the most discriminating statistical texture descriptors of the prostate boundary via a forward feature selection algorithm. After identification of the optimal image features, the MFA is deformed to accurately fit the prostate border. An expert radiologist segmented the prostate boundary on each slice and the planimetric aggregation of the enclosed areas yielded the ground truth prostate volume estimate. The volume estimation obtained via the MFA was then compared against volume estimations obtained via the ellipsoidal, Myschetzky, and prolated spheroids models.

Results

We evaluated our MFA volume estimation method on a total 45 T2-weighted in vivo MRI studies, corresponding to both 1.5 Tesla and 3.0 Tesla field strengths. The results revealed that the ellipsoidal, Myschetzky, and prolate spheroid models overestimated prostate volumes, with volume fractions of 1.14, 1.53, and 1.96, respectively. By comparison, the MFA yielded a mean volume fraction of 1.05, evaluated using a fivefold cross-validation scheme. A correlation with the ground truth volume estimations showed that the MFA had an r 2 value of 0.82, whereas the clinical volume estimation schemes had a maximum value of 0.70.

Conclusions

Our MFA scheme involves minimal user intervention, is computationally efficient and results in volume estimations more accurate than state of the art clinical models.

Prostate volume has been shown to be a strong predictor of treatment outcome for patients with prostate cancer , especially when combined with a baseline prostate-specific antigen (PSA) level . Prostate volume has also been shown to be useful in determining PSA density . The most common method for estimating the prostate volume involves modeling the prostate as a simple geometric shape based on manually estimated measurements of the anteroposterior, transverse, and craniocaudal lengths of the prostate.

The most common models for approximating the prostate shape are the ellipsoid model and the prolate spheroid model . It is important to note that the ellipsoidal model has been a clinical standard for comparisons from at least 1991 to the present day . Some researchers have reported that in several cases the ellipsoid model underestimated the prostate volume . Tewari et al and Eri et al both found that the ellipsoid model underestimated the prostate volume by about 10%. Matthews et al found that the ellipsoid model from transrectal ultrasound (TRUS) imagery underestimated the volume for large prostates (>50 mL), but overestimated the volume for small prostates (<30 mL). Myschetzky et al overcame this underestimation by proposing a new formula in which the ellipsoid volume estimation is multiplied by a factor of 1.34 . Additionally, methods involving manual intervention are typically subject to inter- and intraobserver variability and these volume estimations are not highly reproducible.

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Materials and methods

Data Description and Notation

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Table 1

Data Description

Dataset Field Strength Total Studies Slice ( M ) per Study_X-Y_ Dimensions_T_ (mm) Pixels mm D 1 1.5 Tesla 19 10 ≤ M ≤ 17 256 × 256 140 × 140 3.0 D 2 3.0 Tesla 26 8 ≤ M ≤ 20 512 × 512 140 × 140 2.2

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Ground Truth Estimations of Prostate Volume

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VEx=T⋅∑Mm=1Am. V

∑

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Clinically Employed Prostate Volume Estimation Models

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Table 2

Enumeration of Prostate Volume Estimation Techniques Employed in this Article with Corresponding Formulae

Experiment Description Model_V__ϵ 1_ Ellipsoid_Ell__D_ 1 · D 2 · D 3 · π/6ϵ 2 Myschetzky_Mys__D_ 1 · D 2 · D 3 · 0.7ϵ 3 Prolate spheroid_Sph_ ( D 1 ) 2 · D 2 · π/6ϵ 4 Multifeature ASM_MFA_T⋅∑Mm=1Am T

∑

m Expert_Ex_T⋅∑Mm=1Am T

∑

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MFA-based Prostate Volume Estimations (V MFA )

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Generating a statistical shape model

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Feature extraction

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Generate an appearance model

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Forward feature selection

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Segmentation using the MFA

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Experiments Performed

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Results

Pearson’s Correlation Coefficient

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Table 3

Pearson’s Correlation Coefficient ( r 2 ) between V and V Ex over 45 Studies

Model_V Ell__V Mys__V Sph__V MFA__r 2_ 0.700 0.700 0.454 0.823

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Comparison of Volume Fractions

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Table 4

Comparison of V / V Ex in Terms of Mean, Standard Deviation (SD), and Standard Error (STE) over 45 Studies

Experiment_V_ Mean SD STE_ϵ 1_V Ell 1.143 0.252 0.0376ϵ 2 V Mys 1.528 0.337 0.0502ϵ 3 V Sph 1.958 0.587 0.0875ϵ 4 V MFA 1.053 1.207 0.0277

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Statistical Significance Between Volume Fractions

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Table 5

P Values from Each Set of Paired Student t -tests Between V MFA / V Ex and V Ell / V Ex , V Mys / V Ex , V Sph / V Ex over 45 Studies

V Ell /V Ex__V Mys /V Ex__V Sph /V Ex__V Mys /V Ex 4.33 × 10 –2 ∗ 2.01 × 10 –12 ∗∗ 7.85 × 10 –16 ∗∗

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Discussion

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Acknowledgments

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Appendix

Multifeature active shape model

Input Training Images

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Generate a Shape Model

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X=X¯¯¯+P⋅b, X

⋅

where X¯¯¯ X

¯ represents the mean shape, P is a matrix of the first few principal components (Eigenvectors) of the shape obtained via principal component analysis (PCA), and b is a vector defining the shape, where the individual elements of b can range between –3 and +3 standard deviations from the mean shape X¯¯¯ X

¯ . In our training stage, we have equally spaced 100 landmarks ( N = 100) along the prostate boundary in each slice, and have aligned the landmarks by selecting the topmost landmark in each image as landmark #1.

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Extract Features

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k1=⎡⎣⎢5−3−350−35−3−3⎤⎦⎥,k5=⎡⎣⎢10−120−210−1⎤⎦⎥. k

[

−

]

[

−

]

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G(c)={g(c)⊗k1,…,g(c)⊗k14,xc,yc}. G

(

)

{

(

)

⊗

…

(

)

⊗

}

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Generate an Appearance Model

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μ,Σ,w=argmaxμ,Σ,w∑Tt=1(ln∑Qq=1wq⋅p(Gt|μq,∑q)). μ

arg

max

∑

(

∑

(

∑

)

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Segmenting an Image Using the MFA

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b=P′⋅(Xˆi−Xi) b

′

(

−

)

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Xˆ={en|en=argmaxd∈nκ(c)P(G(d)|μ,Σ,w),n∈{1,…,N}} X

{

arg

max

∈

(

)

(

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∈

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Get Radiology Tree app to read full this article<## Forward Feature Selection

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Get Radiology Tree app to read full this article<## References

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Accurate Prostate Volume Estimation Using Multifeature Active Shape Models on T2-weighted MRI

Rationale and Objectives

Materials and Methods

Results

Conclusions

Materials and methods

Data Description and Notation

Ground Truth Estimations of Prostate Volume

Clinically Employed Prostate Volume Estimation Models

MFA-based Prostate Volume Estimations (V MFA )

Generating a statistical shape model

Feature extraction

Generate an appearance model

Forward feature selection

Segmentation using the MFA

Experiments Performed

Results

Pearson’s Correlation Coefficient

Comparison of Volume Fractions

Statistical Significance Between Volume Fractions

Discussion

Acknowledgments

Appendix

Multifeature active shape model

Input Training Images

Generate a Shape Model

Extract Features

Generate an Appearance Model

Segmenting an Image Using the MFA

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