Quantitative Prediction of Stone Fragility From Routine Dual Energy CT

Rationale and Objectives

Previous studies have demonstrated a qualitative relationship between stone fragility and internal stone morphology. The goal of this study was to quantify morphologic features from dual-energy computed tomography (CT) images and assess their relationship to stone fragility.

Materials and Methods

Thirty-three calcified urinary stones were scanned with micro-CT. Next, they were placed within torso-shaped water phantoms and scanned with the dual-energy CT stone composition protocol in routine use at our institution. Mixed low- and high-energy images were used to measure volume, surface roughness, and 12 metrics describing internal morphology for each stone. The ratios of low- to high-energy CT numbers were also measured. Subsequent to imaging, stone fragility was measured by disintegrating each stone in a controlled ex vivo experiment using an ultrasonic lithotripter and recording the time to comminution. A multivariable linear regression model was developed to predict time to comminution.

Results

The average stone volume was 300 mm 3 (range: 134–674 mm 3 ). The average comminution time measured ex vivo was 32 seconds (range: 7–115 seconds). Stone volume, dual-energy CT number ratio, and surface roughness were found to have the best combined predictive ability to estimate comminution time (adjusted R 2 = 0.58). The predictive ability of mixed dual-energy CT images, without use of the dual-energy CT number ratio, to estimate comminution time was slightly inferior, with an adjusted R 2 of 0.54.

Conclusions

Dual-energy CT number ratios, volume, and morphologic metrics may provide a method for predicting stone fragility, as measured by time to comminution from ultrasonic lithotripsy.

Introduction

Symptomatic urinary stone disease affects approximately 900,000 persons in the United States each year, resulting in an estimated annual medical expenditure of over $1 billion in 2007 among Medicare beneficiaries alone . The prevalence of kidney stones in the United States rose by 37% between 1976–1980 and 1988–1994 in both genders . Due to the effects of global warming, it has been predicted that there could be an increase of 1.6–2.2 million lifetime cases of urinary stones by 2050 in the United States alone, as kidney stones tend to form more frequently in states where dehydration is common .

Several surgical options are available for the 10%–20% of symptomatic stone formers who fail to pass their stones spontaneously . Larger, harder kidney stones and those located in the lower pole of the kidney tend to be more easily fragmented and removed by percutaneous nephrolithotripsy (PCNL), a minimally invasive procedure whereby the stone is accessed through a small flank incision which allows direct visualization and intracorporeal ultrasonic lithotripsy for stone disruption and removal of fragments . Stone fragility, which we define as the time to comminution by a given surgical procedure, is affected by the extent of the stone burden (ie, the size and number of stones) as well as its mineral composition .

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Materials and Methods

Micro-CT Imaging

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Whole-body CT Imaging

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Texture Analysis of Stone Morphology

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coocΔx,Δy,Δz(i,j)=∑np=1∑mq=1∑or=1{1,0,ifI(p,q,r)=iandI(p+Δx,q+Δy,r+Δz)=jotherwise c

(

)

∑

{

(

)

(

)

otherwise

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TABLE 1

Haralick Features Describing Stone Internal Morphology and Features Describing Stone Surface ; cooc = co-occurrence matrix

Variable Formula Interpretation 1. Energy

∑numlevelsi=1∑numlevelsj=1cooc(i,j)2 ∑

levels

∑

levels

cooc

(

)

Uniformity of the image 2. Entropy

∑numlevelsi=1∑numlevelsj=1cooc(i,j)log10(cooc(i,j)) ∑

levels

∑

levels

cooc

(

)

(

cooc

(

)

Randomness of the image 3. Correlation

∑numlevelsi=1∑numlevelsj=1((i−μx)×(j−μy)×(cooc(i,j)/(σx×σy)) ∑

levels

∑

levels

(

−

)

(

−

)

(

cooc

(

)

(

)

Local gray level linear dependency of the image 4. Contrast

∑numlevelsi=1∑numlevelsj=1cooc(i,j)×|i−j|2 ∑

levels

∑

levels

cooc

(

)

−

Measure of local variations in the image 5. Homogeneity

∑numlevelsi=1∑numlevelsj=1cooc(i,j)|i−j|+1 ∑

levels

∑

levels

cooc

(

)

−

Local homogeneity of the image 6. Variance

∑numlevelsi=1∑numlevelsj=1((i−μx)2+(j−μy)2)×cooc(i,j) ∑

levels

∑

levels

(

−

)

(

−

)

cooc

(

)

Gray-level variability of the pixel pairs 7. Sum mean

∑numlevelsi=1∑numlevelsj=1cooc(i,j)×(i+j) ∑

levels

∑

levels

cooc

(

)

(

)

N.A. 8. Inertia

∑numlevelsi=1∑numlevelsj=1cooc(i,j)×(i+j)2 ∑

levels

∑

levels

cooc

(

)

(

)

N.A. 9. Cluster shade

∑numlevelsi=1∑numlevelsj=1(i+j−μx−μy)3cooc(i,j) ∑

levels

∑

levels

(

−

)

cooc

(

)

Skewness of the image 10. Cluster tendency

∑numlevelsi=1∑numlevelsj=1(i+j−μx−μy)4cooc(i,j) ∑

levels

∑

levels

(

−

)

cooc

(

)

Another measure of asymmetry of the image 11. Max probability

max(cooc) m

(

cooc

)

N.A. 12. Inverse variance

∑numlevelsi=1∑numlevelsj=1cooc(i,j)|i−j|2 ∑

levels

∑

levels

cooc

(

)

−

Local homogeneity of the image 13. Shape index FWHM of histogram of vertex curvatures Overall surface morphology of a stone

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Ex Vivo Analysis of Stone Fragility

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Statistical Analysis

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Results

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Univariate and Volume-adjusted Models of Stone Fragility

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TABLE 2

Association between DECT-derived Morphology Metrics and Comminution Time, Unadjusted and Adjusted for Volume

Imaging Variable Unadjusted Model Adjusted for Volume P var R 2 P var 1 P vol 2 VIF 3 R 2 adj Volumetric Volume0.00020.37\* Porosity 0.25 0.04 0.12 0.0001 1.00 0.39 Internal morphology Energy 0.24 0.04 0.09 0.0001 1.7 0.39 Entropy 0.24 0.04 0.43 0.0003 1.34 0.35 Correlation 0.34 0.03 0.98 0.0003 1.09 0.33 Contrast 0.55 0.01 0.85 0.0002 1.05 0.33 Homogeneity<0.00010.42 0.12 0.60 5.12 0.38 Variance 0.84 0 0.27 0.0001 1.10 0.36 Sum mean 0.005 0.23 0.50 0.01 1.78 0.34 Inertia 0.55 0.01 0.85 0.0002 1.05 0.33 Cluster shade 0.0002 0.36 0.23 0.15 2.98 0.37 Clusters tendency 0.15 0.07 0.37 0.0004 1.05 0.35 Max probability 0.37 0.030.04<0.00011.660.42\\ Inverse variance 0.047 0.12 0.14 0.0005 1.06 0.38 Surface morphology Shape index 0.27 0.04 0.11 0.0001 1.00 0.39 Peak curvature 0.52 0.01 0.45 0.0002 1.00 0.35 Mean curvature<0.00010.48 0.02 0.53 7.30 0.45 Dual Energy CT CT number ratio 0.25 0.040.002<0.00011.110.52\\\* HU low (90 kVp) 0.004 0.23 0.45 0.01 1.75 0.35 HU high (150 kVp)0.00010.380.020.031.520.44

CT, computed tomography.

Bold means best qualified model among those investigated.

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Best Multivariable “Single-energy” CT Models of Stone Fragility

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TABLE 3

Multivariable, Single-energy Models

Imaging Variable Adjusted for Volume and Max Probability P var 1 P vol 2 P MaxProb 3 VIF var 4 VIF vol 5 VIF MaxProb 6 R 2 adj Volumetric Volume Porosity 0.15 <0.0001 0.052 1.01 1.67 1.68 0.44 Internal morphology Energy 0.65 0.0001 0.21 10.4 1.72 10.2 0.41 Entropy 0.59 <0.0001 0.051 2.07 1.68 2.58 0.41 Correlation 0.38 <0.0001 0.03 1.26 2.08 1.93 0.42 Contrast 0.23 <0.0001 0.02 1.27 2.05 2.02 0.43 Homogeneity 0.0002 0.95 0.0001 7.36 5.25 2.39 0.63 Variance0.01<0.00010.0021.402.292.110.52 Sum mean0.0060.00030.00082.911.892.720.54\* Inertia 0.23 <0.0001 0.02 1.27 2.05 2.02 0.43 Cluster shade <0.0001 0.13 <0.0001 5.43 3.01 3.03 0.68 Clusters tendency 0.12 <0.0001 0.02 1.12 1.66 1.77 0.45 Max probability Inverse variance 1.00 0.002 0.16 2.27 3.16 3.56 0.40 Surface morphology Shape index0.02<0.00010.0081.061.731.760.50 Peak curvature 0.63 <0.0001 0.051 1.02 1.68 1.70 0.41 Mean curvature 0.003 0.81 0.006 7.49 7.49 1.71 0.57

VIF, variance inflation factor.

Bold means best qualified model among those investigated.

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Best Multivariable Dual-energy CT Models of Stone Fragility

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TABLE 4

Multivariable, Dual-energy Models

Imaging Variable Adjusted for Volume and CT Ratio P var 1 P vol 2 P CTR 3 VIF var 4 VIF vol 5 VIF CTR 6 R 2 adj Volumetric Volume Porosity 0.13 <0.0001 0.002 1.01 1.11 1.12 0.54 Internal morphology Energy 0.78 <0.0001 0.009 2.26 1.71 1.47 0.51 Entropy 0.90 <0.0001 0.003 1.41 1.38 1.18 0.51 Correlation 0.92 <0.0001 0.002 1.09 1.2 1.12 0.51 Contrast 0.84 <0.0001 0.002 1.05 1.16 1.11 0.51 Homogeneity 0.03 0.40 0.0005 5.18 5.13 1.13 0.59 Variance 0.21 <0.0001 0.002 1.1 1.22 1.11 0.53 Sum mean 0.24 0.0006 0.001 1.8 1.84 1.13 0.53 Inertia 0.84 <0.0001 0.002 1.05 1.16 1.11 0.51 Cluster shade 0.03 0.057 0.0003 3.11 2.98 1.16 0.59 Clusters tendency 0.20 <0.0001 0.001 1.05 1.15 1.12 0.53 Max probability 0.70 <0.0001 0.02 2.57 1.7 1.72 0.51 Inverse variance 0.87 <0.0001 0.006 1.34 1.31 1.41 0.51 Surface morphology Shape index0.03<0.00010.00061.011.121.120.58\* Peak curvature 0.56 <0.0001 0.002 1.01 1.12 1.12 0.51 Mean curvature 0.03 0.84 0.003 7.53 7.91 1.15 0.58 DECT CT number ratio HU low (90 kVp)0.040.0010.00031.921.761.220.57 HU high (150 kVp)0.040.0010.0031.571.741.150.57

CT, computed tomography.

Bold means best qualified model among those investigated.

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Discussion

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Conclusions

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Acknowledgments

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Supplementary Data

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Figure S1

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References

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Quantitative Prediction of Stone Fragility From Routine Dual Energy CT

Rationale and Objectives

Materials and Methods

Results

Conclusions

Introduction

Materials and Methods

Micro-CT Imaging

Whole-body CT Imaging

Texture Analysis of Stone Morphology

Ex Vivo Analysis of Stone Fragility

Statistical Analysis

Results

Univariate and Volume-adjusted Models of Stone Fragility

Best Multivariable “Single-energy” CT Models of Stone Fragility

Best Multivariable Dual-energy CT Models of Stone Fragility

Discussion

Conclusions

Acknowledgments

Supplementary Data

References

Further Reading

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Associations Between Academic Rank and Advanced Bibliometric Indices Among United States Academic Radiologists