GEOMETRIC SYSTEMATIC PROSTATE BIOPSY

Doyoung Chang, Xue Chong, Chunwoo Kim, Changhan Jun, Doru Petrisor,

Misop Han, Dan Stoianovici

Robotics Laboratory, Urology Department, School of Medicine,

Johns Hopkins University, Baltimore, MD 21224, USA

Corresponding author: D. Stoianovici (dss@jhu.edu)

ABSTRACT

Objective: The distribution of cores in the common sextant prostate biopsy schema is

defined pictorially and lacks a 3-dimensional (3D) geometric definition. The objective of the

study was to determine the influence of the geometric distribution of the cores on the

probability of detection of prostate cancer (PCa), independent of other factors in a well-

controlled simulation study. Methods: The detection probability of significant (>0.5cm3) and

insignificant (<0.2cm3) tumors were quantified based on a novel three-dimensional (3D)

capsule model of the biopsy sample and anatomical constraints of the needle access. The

pelvic anatomy of the Visible Human Project (National Library of Medicine) was used. The

geometric distribution of the cores was optimized to maximize the probability of detecting

significant cancer. Biopsy schemata were calculated for various prostate sizes (20 to 100cm3),

number of biopsy cores (6 to 40 cores) and biopsy core lengths (14 to 40mm) for transrectal

and transperineal biopsies. Results: The probability of detection of significant cancer can be

improved by geometric optimization. With the current extended sextant biopsy, up to 20% of

tumors may be missed at biopsy in a 20 cm3 prostate due to the schema. Higher number and

longer biopsy cores are required to sample with an equal detection probability in larger

prostates. The detection probability of both significant and insignificant tumors are directly

correlated to the number of biopsy cores. But a higher number of cores increases

predominantly the detection of insignificant tumors. Conclusion: The study demonstrates

mathematically that the geometric biopsy schema plays an important clinical role. It also

demonstrates that increasing the number of systematic biopsy cores is not necessarily helpful.

Keywords: Prostate cancer, systematic biopsy, biopsy optimization, probability of detection,

significant, insignificant tumor.

Introduction

In 2016, an estimated 180,890 new PCa will be diagnosed in the US alone [1]. While studies

have shown that significant overtreatment exists [2], PCa will still cause 26,120 mortalities

[1]. These underscore the need for more reliable PCa diagnosis and patient stratification [3,

4].

The classic prostate biopsy method is guided by transrectal ultrasound (TRUS). Yet, standard

gray-scale ultrasound is unreliable in differentiating PCa from normal gland tissues; therefore

needle guidance is cancer blind [3] and systematic sextant biopsy schemata are used to

uniformly sample the gland instead of actually targeting the tumors.

To address this problem targeted methods have been developed [5], such as the Fusion

biopsy. This uses pre-acquired Magnetic Resonance Imaging (MRI) to depict cancer

suspicious regions (CSR) within the prostate, registered (fused) to the TRUS which is used to

guide the procedure in real time [6]. Numerous clinical studies have already shown higher

PCa detection than traditional untargeted methods [7, 8].

AUTHOR’S COPY

Minimally Invasive Therapy & Allied Technologies. Nov 11 2016

http://www.tandfonline.com/doi/full/10.1080/13645706.2016.1249890

However, the fusion is not normally performed for primary biopsy patients, but in high-risk

and active surveillance patients [9], typically for selected repeat biopsies. With over 1 million

prostate biopsies performed annually in the United States and Europe [10], the MRI time

required for fusion will simply be overwhelming. As such, the large majority of prostate

biopsies remain systematic, and will likely continue so in the foreseeable future. With current

systematic biopsy methods the sensitivity and specificity of the biopsy test are low [11].

Therefore, if anything could be done to improve systematic biopsies, then it probably should.

Margins of leeway exist in several aspects, for example in regard to the manual execution

errors. Biopsy targeting errors are significant even among experienced urologists, in average

9.0 mm, and with significant variation among urologists [12]. For this, new biopsy devices

are emerging to assist the physicians [13, 14]. Another source of error is the deflected path of

needle insertion that is typical with biopsy needles (commonly have a bevel point) [15].

In this study we focus on the actual biopsy plan, to see if the systematic biopsy schemata

could be improved for a higher cancer detection yield. Currently, the most formal definition

of the sextant biopsy plan is a grid of points on a 2D coronal view of the prostate [16]. As

shown in Figure 1ab, this definition is vague from a geometric standpoint. The sextant

divisions and the location of the points within the sextant regions is subjective. In 3D the

uncertainty widens, leaving much room for subjective interpretation as shown in Figure 1c.

Computer simulated biopsy studies to determine optimal biopsy plans have been performed

based 3D images or whole mount prostates [17-22]. One notable approach was to produce a

continuous cancer distribution probability function from histopathology series of

prostatectomy specimens. Based on this probability model, the detection rates of different

biopsy plans were measured by calculating the number of tumors detected by the simulated

biopsy cores and an optimal protocol was determined. The biopsy schemata were defined

precisely with coordinate locations and core directions. Among them, results were somewhat

different possibly due to different statistical maps of tumor occurrences [17, 18].

Another optimization approach used 2D analyses to determine the probability of significant

cancer detection for transperineal biopsy using equally spaced parallel needles [23, 24]. This

probability is calculated based on the area sampled by the cores per unit grid on the

transversal 2D cross section. The study also showed that false-negative probability could be

evaluated.

Our approach builds upon the 2D probability calculation model of [24] by expanding it to 3D

and transrectal TRUS-guided biopsy. Specifically, their circle area model was extruded to a

Figure 1: Definition of (a) 6-core and (b) 12-core sextant biopsy schemata. (c) One possible

interpretation of the 12-core in 3D

cylindrical volume with semi-spherical ends, which we defined as a capsule model. Biopsy

optimizations were implemented based on this model to maximize the probability of

significant cancer detection. Preliminary results of this work were reported at the Engineering

and Urology Society conference [25].

Material and Methods

To develop the tumor detection probability model, we first assumed that tumors are spherical

in shape. This model is the worst-case scenario since the sphere has the lowest surface to

volume ratio making it hardest to detect per unit volume [23]. That is, for an identical volume

the furthest distance between any two points is smallest on the sphere (Figure 2a), requiring

the highest density of biopsy cores to be detected. This also assures that the probability of

detection is independent of the biopsy needle orientation [23].

Next, we assumed that the probability of tumor occurrence is uniform throughout the prostate

volume. This also represents a worst-case scenario, since only sampling certain regions of the

prostate would require less biopsy cores.

Finally, we defined the clinically significant tumor size 0.5cm3 (radius 4.924mm) and

insignificant tumor size 0.2cm3 (radius 3.628mm) [26].

In the capsule model, a tumor was considered sampled if the biopsy core intersected the

tumor. The tumor intersects the core if the distance from its center to the axis of the needle is

smaller than its radius (d R), which makes its center fall within the capsule (Figure 2b).

From this, a single core’s sampling volume for a spherical tumor of radius R can be

quantified as the volume of the capsule with the radius of the sphere (R) and the length of the

core (L). We neglect the thickness of the biopsy core since they are very slim and have a

small influence to the sampling volume.

The sampling volume of one core for a tumor of radius R within the prostate is,

Vs,1R = Vp ∩ Vc

R (Eq. 1)

For n cores, intersection of sampling volumes should be considered. Therefore,

Vs,nR = Vp ∩ ( Vc,1

R ∪ Vc,2R ⋯ ∪ Vc,n

R ) (Eq. 2)

The probability of detection for multiple cores is:

PnR =

Vs,nR

Vp=

Vp ∩( Vc,1R ∪Vc,2

R ⋯ ∪Vc,nR )

Vp (Eq. 3)

Figure 2: (a) Equal volume (0.5 cm3) tumor (blue) and a sphere model (yellow). (b) Capsule model defin

ition and detected (red) and undetected (yellow) tumors

The significant and insignificant probabilities of detection are:

P𝑠 = P4.924 and P𝑖 = P3.628 (Eq. 4)

The probability of a false-negative result is then (100 − P𝑠 ).

The P is a function of the position and orientation of the biopsy cores. Core orientation may

be parameterized by the biopsy needle entry point location and the core center position.

Therefore, a biopsy plan for n cores may be defined as a state matrix Π(n × 6) as:

Π = [

𝑒11

⋮𝑒𝑛1

𝑒12

⋮𝑒𝑛2

𝑒13

⋮𝑒𝑛3

𝑐11

⋮𝑐𝑛1

𝑐12

⋮𝑐𝑛2

𝑐13

⋮𝑐𝑛3

] (Eq. 5)

where, 𝐸𝑖𝑗(𝑒𝑖1, 𝑒𝑖2, 𝑒𝑖3) and 𝐶𝑖𝑗(𝑐𝑖1, 𝑐𝑖2, 𝑐𝑖3) are the needle entry point respectively the core

center positions of core 𝑖.

Then, the P (Π) for any given biopsy plan Π is defined as:

PnR =

N(Ω)

N(Γ) (Eq. 6)

where, N(Ω) and N(Γ) is the number of voxels within the prostate and voxels of the capsule

that overlap with the prostate respectively.

Core positions and entry points are subject to the following anatomical constraints:

1. Core positions should avoid the urethra (green in Figure 3) to prevent hematuria and

urinary retention. This is achieved by manually setting a bounding box of the urethra.

2. The entry point constraints of each biopsy path reduces the rank of the state matrix, (Eq.5)

enabling the parameterization of a simplified state matrix Ψ as follows.

Transrectal biopsy: The needle is passed alongside the TRUS probe, which is pivoted

about the anal sphincter. The entry points are constrained to the probe circumference

(Figure 3a, yellow circle) and are determined by the probe rotation 𝜃𝑖. Accordingly,

the state matrix Ψ(n × 4) becomes:

Ψ = [𝜃1

⋮𝜃𝑛

𝑐11

⋮𝑐𝑛1

𝑐12

⋮𝑐𝑛2

𝑐13

⋮𝑐𝑛3

] (Eq. 7)

Template transperineal biopsy: The needle directions are parallel to each other. The

entry points are constrained to the discrete grid hole locations 𝑋𝑖𝑗(𝑥𝑖1, 𝑥𝑖2) of the

template (Figure 3b). The core positions are restricted along the direction of the

needle at depth 𝑑𝑖. Accordingly, the state matrix Ψ(n × 3) becomes:

Ψ = [

𝑥11

⋮𝑥𝑛1

𝑥12

⋮𝑥𝑛2

𝑑1

⋮𝑑𝑛

] (Eq. 8)

Angled transperineal biopsy: The entry points are constrained to the perineum and

may be parameterized to points 𝑋𝑖𝑗(𝑥𝑖1, 𝑥𝑖2) in a constrained region on the perineum

plane (Figure 3c, yellow circle). Accordingly, the state matrix Ψ(n × 5) becomes:

Ψ = [

𝑥11

⋮𝑥𝑛1

𝑥12

⋮𝑥𝑛2

𝑐11

⋮𝑐𝑛1

𝑐12

⋮𝑐𝑛2

𝑐13

⋮𝑐𝑛3

] (Eq. 9)

The optimization problem is to find the biopsy plan Ψ that maximizes the probability of

detection of significant tumors.

Ψoptimal

= argmax( P𝑠 (Ψ)) (Eq. 10)

Intuitively, the algorithm searches for a solution Ψ that maximizes the sampling of the

prostate by capsules by minimizing overlapping between capsules and avoiding extending out

of the prostate. The maximization may be implemented with iterative methods such as a

gradient descent or pattern search optimization method [27]. Here we show the

implementation of the pattern search, which is a heuristic algorithm [27].

The optimization starts with an initial biopsy plan Ψ0 that follows the sextant plan (Figure 4).

At each step 𝑘, an exploratory move Δ𝑘 is applied to each element 𝜓𝑖𝑗𝑘−1 of the current state

Ψ𝑘−1, where

Δ𝑘 = [ δ1 δ2 … δ𝑚], where δ𝑗 > 0 for 𝑗 = 1 … 𝑚 (Eq. 11)

An exploratory move δ𝑗 is applied to each state matrix element while maintaining the other

elements:

Ψ𝑖𝑗± 𝑒𝑥𝑝𝑙 = {

𝜓𝑞𝑟𝑘−1 ± δ𝑗

𝜓𝑞𝑟𝑘−1

, 𝑞 = 𝑖 𝑎𝑛𝑑 𝑟 = 𝑗, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

, 𝑓𝑜𝑟 𝑖 = 1 … 𝑛 𝑎𝑛𝑑 𝑗 = 1 … 𝑚 (Eq. 12)

The probability of detection P𝑠 (Ψ𝑖𝑗± 𝑒𝑥𝑝𝑙) is calculated for all 2𝑛𝑚 exploratory moves. If any

of these provides a positive gain relative to the previous state, the move Ψ 𝑒𝑥𝑝𝑙 that provided

the maximum gain is retained to update the state matrix of the next iteration:

Figure 4: Initial biopsy plan for (a) transrectal, and transperineal (b) grid and (c) angled biopsies

Figure 3: Anatomical constraints for (a) transrectal, transperineal (b) grid and (c) angled biopsies

Ψ𝑘 = {Ψ

𝑒𝑥𝑝𝑙 | Max ( P𝑠 (Ψ𝑖𝑗±

𝑒𝑥𝑝𝑙)) 𝑖𝑓 P𝑠 (Ψ𝑖𝑗±

𝑒𝑥𝑝𝑙) − P𝑠 (Ψ𝑘−1) > 0

Ψ𝑘−1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(Eq. 13)

If there is no positive gain, the exploratory move Δ is reduced:

Δ𝑘 = λ Δ𝑘−1 with reduction parameter 0 < λ < 1 (Eq. 14)

When this reaches a small cutoff value, it is then reset to the initial value Δ0 and the above

steps are repeated to check convergence to a better optimal solution, until there is no

improvement.

In our case 𝛥0 = {5.0 𝑚𝑚, ( 𝑐𝑖𝑗, 𝑥𝑖𝑗 , 𝑑𝑖 )

10°, ( 𝜃𝑖 ) , 𝜆 = 0.5 and cutoff value of 0.1mm was chosen.

For biopsy simulation we reconstructed the male pelvic anatomy of the Visible Human

Project(VHP) [28]. Manual segmentations of the prostate, urethra, rectum, and pubic bone

with the perineal wall were done by an experienced urologist using the Amira Visualization

platform (FEI Company, Burlington, MA). In the actual case, only the prostate segmentation

is required, which is commonly done with semi-automatic segmentation algorithms [29].

The biopsy plan optimization was implemented with custom developed C++ modules for the

Amira using an Intel Core I7 CPU. The size of the prostate, 21.4 cm3, was also measured

using the Amira. To simulate the effect of prostate volumes on detection probability, the

VHP’s prostate was uniformly scaled about the center of its bounding box to 5 sizes: 20 cm3

to 100 cm3 in 20 cm3 increment.

First, to determine convergence of the optimization method, the 12-core transrectal biopsy

optimization using the typical 18 mm core length was performed for the 20 cm3 prostate. The

initial condition was based on the classic systematic biopsy (Figure 1), where the position and

orientation of the biopsy plane were manually selected to simulate the variation in biopsy

planning. A total of 100 optimization trials with different initial conditions were performed.

Then, we investigated the relationship between the number of cores and the size of the

prostate while maintaining the standard 18 mm core length. For this, the P𝑠 were evaluated

for 18 biopsy plans of 6 to 40 cores (increment of 2, added symmetrically on the left and right

lobes) for each of the 5 prostate sizes.

Next, we investigated the relationship between the core lengths and the size of the prostate

for the 12-core biopsy. For this, the P𝑠 were evaluated for 14 core lengths between 14mm

and 40mm (2 mm increment) for each of the 5 prostate sizes.

In all cases, the optimal biopsy plan Ψ was determined by maximizing the significant tumor

probability of detection 𝑀𝑎𝑥 ( P𝑠 (Ψ)) for all three biopsy paths. The probability of

inadvertently detecting insignificant tumors with the optimal plan P𝑖 (Ψ) was then evaluated,

as well as the ratios of the P𝑠 to P𝑖 .

Results

The convergence of this nontrivial optimization problem was verified with multiple

experiments. Figure 5Figure 5a shows an example of randomly selected 10 optimization trial

results on a 20 cm3 prostate. The dotted lines denote the Ps of 10 different trials, and the red

solid line denotes the average of all trials. The optimized plan has a higher Ps than the

systematic biopsy plan. The average Ps of the initial systematic and the optimized biopsy

plan are 61.1% and 81.8% respectively, with standard deviation of 3.6% and 0.7%

respectively. Although the coordinates of the optimized cores were different, the Ps

converged with small variance. The average computation time of each iteration and total

computation was 0.29s(s) and 34.7(s).

An example of a transrectal biopsy plan optimization that starts from the systematic biopsy

plan is presented in Figure 5Figure 5b (12-cores, 18 mm core length, 40 cm3 prostate). The

P𝑠 increased from 42.5%. to 54.4% after optimization.

The results correlating the dependency of the Ps , P𝑖 , and their ratio on the number of the

biopsy cores for a constant 18mm biopsy core length are represented in Figure 6abc.

Figure 5. (a) Iterative improvement in the probability of detection during the optimization process (20 c

m3 prostate size) and (b) a typical example of systematic (left) and optimized (right) biopsy plans shown

with capsules (top) and cores (bottom)

The P𝑠 increased with more cores and thus, larger prostates required more cores to achieve a

certain Ps level (Figure 6a). The Ps and P𝑖 are similar for different biopsy paths, with

slightly higher P𝑠 values in the order of transrectal, angled transperineal, and template

transperineal biopsy. Concurrently, when more cores were used the P𝑖 also increased (Figure

6b). The P𝑠 to P𝑖 ratio decreased with the number of cores for all 3 biopsy paths (Figure

6c). For a 12-core transrectal biopsy (18 mm) on a 40 cm3 prostate, the P𝑠 and P𝑖 were

54.1% and 28.0% respectively, and the P𝑠 to P𝑖 ratio was 1.9.

For prostate sizes larger than 60 cm3, 99% P𝑠 couldn’t be reached even with 40 cores. Before

the P𝑠 curves plateaued, these were approximately linear, so that the number of cores

required to achieve the same P𝑠 level is proportional to the prostate volume.

Figure 6def depicts the dependency of the probability of cancer detection on the length of the

biopsy cores for the common 12-core extended biopsy. The P𝑠 increases with the length of

the core (Figure 6d). This saturates at a length that is close to the depth of the prostate in the

direction of biopsy (90% @ 25mm for a 20 cm3 prostate). The increase in the core length is

also followed by increased P𝑖 (Figure 6e). Before saturation, P𝑠 and P𝑖 were approximately

linear to the core length. The ratio of P𝑠 to P𝑖 decreased with the core length for all 3 biopsy

paths (Figure 6f).

Figure 6. (a) P𝑠 , (b) P𝑖 , (c) P𝑠 / P𝑖 , versus the number of cores for different prostate sizes and

(d) P𝑠 , (e) P𝑖 , (f) P𝑠 / P𝑖 , versus the core length for different prostate sizes

Discussion

A novel capsule model is defined to evaluate the probability of prostate cancer detection that

a biopsy schema may yield. This also enables to optimize the schema to maximize the

detection of PCa.

Currently, biopsy plans are not typically individualized for patients. It was suggested that

biopsy core numbers should be adjusted [30, 31] based on the prostate volume, yet it remains

unclear if and how it should be done [30, 32]. Our results confirm that more and longer cores

are needed for larger prostates up to a certain saturation limit, being in agreement with

previous studies [18, 30].

The capsule model also enables to estimate the probability of a false-negative result [24]

together with the risk of over diagnosis, that is the risk of detecting insignificant cancer (<0.2

cm3). We believe that this study is first to quantitatively report the probability of detecting

insignificant cancer.

Results shows that the risk of detecting insignificant cancer ( P𝑖 ) is a tradeoff of sampling

more biopsy cores for higher P𝑠 . Moreover, P𝑖 increases faster than P𝑠 with the number of

cores, especially for smaller prostates. Thus, careful consideration for over detection should

be given when increasing the number of cores. This agrees with clinical findings in this

respect [33]. The ultimate goal would be to determine the biopsy plan that would detect all

significant tumors utilizing the lowest number of biopsy cores, and minimize P𝑖 [34].

Besides its theoretical role, the method could be used practically within limitations. The

method demands the use of 3D imaging for the 3D reconstruction of the prostate, and

defining anatomical constraints for needle access. For this, the method applies directly to

modern biopsy devices such as mechanically [13] and magnetically tracked [35] TRUS

probes, image fusion systems [6], TRUS robots [14, 36], and MR Safe robots [37]. These

devices will also substantially improve the biopsy execution accuracy. The method does not

apply to standard 2D TRUS-guided biopsy.

The proposed method is a purely geometrical analysis with several assumptions. First, tumors

are considered to be spherical shape rather than irregular, curvilinear, or fusiform [23].

Second, our model assumes that tumors are evenly distributed within the gland while the

majority of tumors occur in the peripheral zone [38]. Finally, scaling the prostate model is a

limitation as the prostate shape would change as it enlarges. Some of these limitations are

worst case scenarios with respect to cancer detection rates. As such, the method establishes

the lowest expectation level on potential improvements that could be made to the “blind”

systematic biopsy.

For example, current clinical values on the probability of significant cancer detection with

conventional 12-core freehand TRUS biopsy averages 43% [12] in a small prostate. Could

this be improved without the fusion? Our study demonstrates that if a urologist (device)

would perfectly execute the 12-core sextant schema the rate would be no less than 61% (20

cm3 prostate); with the optimized schema this could be at least 82%.

As such, we demonstrate mathematically that substantial leeway exists to improve sextant

biopsy methods, and define the expectation levels of PCa detection for several parameters.

There is no question that targeted biopsy methods such as the fusion are superior, having the

potential to achieve 100% detection with 1-core. However, systematic methods are here to

stay for primary biopsies, and these could be markedly improved.

Acknowledgements

This research was supported by the Patrick C. Walsh Prostate Cancer Research Foundation at

the Johns Hopkins University.

REFERENCES

1. Siegel RL, Miller KD, Jemal A: Cancer statistics, 2016. CA Cancer J Clin. Jan 2016; Vol.66(1)

pp.7-30. PMCID:26742998

2. Schröder F, Hugosson J, Roobol M, Tammela T, Ciatto S, Nelen V, Kwiatkowski M, Lujan M,

Lilja H, Zappa M, Denis L, Recker F, Berenguer A, Määttänen L, Bangma C, Aus G, Villers A,

Rebillard X, Kwast T, Blijenberg B, Moss S, Koning H, Auvinen A: Screening and Prostate-

Cancer Mortality in a Randomized European Study. N Engl J Med. March, 26 2009; Vol.360

pp.1320-1328.

3. Kelloff GJ, Choyke P, Coffey DS: Challenges in clinical prostate cancer: role of imaging. AJR Am

J Roentgenol. Jun 2009; Vol.192(6) pp.1455-1470. PMCID:19457806

4. Stoianovici D: Technology Advances for Prostate Biopsy and Needle Therapies. Editorial.

Journal of Urology. Oct 2012; Vol.188(4) pp.1074-1075. PMCID:22901579

5. Ball MW, Ross AE, Ghabili K, Kim C, Jun C, Petrisor D, Epstein JI, Macura K, Stoianovici D,

Allaf ME: Safety and Feasibility of Robot-Assisted Direct MRI-Guided Transperineal Prostate

Biopsy. Urology. 2016. PMCID: under review

6. Marks L, Young S, Natarajan S: MRI-ultrasound fusion for guidance of targeted prostate biopsy.

Curr Opin Urol. Jan 2013; Vol.23(1) pp.43-50. PMCID:23138468

7. Okoro C, George AK, Siddiqui MM, Rais-Bahrami S, Walton-Diaz A, Shakir NA, Rothwax JT,

Raskolnikov D, Stamatakis L, Su D, Turkbey B, Choyke PL, Merino MJ, Parnes HL, Wood BJ,

Pinto PA: Magnetic Resonance Imaging/Transrectal Ultrasonography Fusion Prostate Biopsy

Significantly Outperforms Systematic 12-Core Biopsy for Prediction of Total Magnetic

Resonance Imaging Tumor Volume in Active Surveillance Patients. J Endourol. Oct 2015;

Vol.29(10) pp.1115-1121. PMCID:25897467

8. Thoma C: Prostate cancer: MRI/TRUS fusion outperforms standard and combined biopsy

approaches. Nat Rev Urol. Mar 2015; Vol.12(3) pp.119. PMCID:25687268

9. Frye TP, Pinto PA, George AK: Optimizing Patient Population for MP-MRI and Fusion Biopsy

for Prostate Cancer Detection. Curr Urol Rep. Jul 2015; Vol.16(7) pp.50. PMCID:26063625

10. Loeb S, Vellekoop A, Ahmed HU, Catto J, Emberton M, Nam R, Rosario DJ, Scattoni V, Lotan

Y: Systematic review of complications of prostate biopsy. Eur Urol. Dec 2013; Vol.64(6) pp.876-

892. PMCID:23787356

11. Shariat SF, Roehrborn CG: Using biopsy to detect prostate cancer. Rev Urol. Fall 2008; Vol.10(4)

pp.262-280. PMCID:19145270

12. Han M, Chang D, Kim C, Lee BJ, Zuo Y, Kim HJ, Petrisor D, Trock B, Partin AW, Rodriguez R,

Carter HB, Allaf M, Kim J, Stoianovici D: Geometric Evaluation of Systematic Transrectal

Ultrasound Guided Prostate Biopsy. Journal of Urology. Dec 2012; Vol.188(6) pp.2404-2409.

PMCID:23088974

13. Eigen: Artemis: 3D Imaging and Navigation for Prostate Biopsy. Available at:

http://www.eigen.com/products/artemis.shtml.

14. Stoianovici D, Kim C, Schafer F, Huang CM, Zuo YH, Petrisor D, Han M: Endocavity

Ultrasound Probe Manipulators. IEEE/ASME TRANSACTIONS ON MECHATRONICS. Jun 2013;

Vol.18(3) pp.914-921. PMCID:24795525 ISI:000321010000010

15. Jun C, Kim C, Chang D, Decker R, Petrisor D, Stoianovici D: Beveled Needle Trajectory

Correction. American Urological Association, Engineering and Urology Society, 28th Annual

Meeting. 2013; pp.37. http://engineering-urology.org/am/28EUS_2013.pdf.

16. Wein A, Kavoussi LR, Novick AC, Partin AW, Peters CA: Campbell-Walsh Urology. 10 ed;

2012.

17. Hu Y, Ahmed H, Carter T, Arumainayagam N, Lecornet E, Barzell W, Freeman A, Nevoux P,

Hawkes D, Villers A, Emberton M, Barratt D: A biopsy simulation study to assess the accuracy of

several transrectal ultrasonography (TRUS)-biopsy strategies compared with template prostate

mapping biopsies in patients who have undergone radical prostatectomy. BJU Int. Mar 6 2012;

Vol.110(6) pp.812-820. PMCID:22394583

18. Kanao K, Eastham J, Scardino P, Reuter V, Fine S: Can transrectal needle biopsy be optimised to

detect nearly all prostate cancer with a volume of ≥0.5 mL? A three-dimensional analysis. BJU

Int. Nov 2013 Vol.112(7) pp.898-904.

19. Chen M, Troncoso P, Johnston D, Tang K, Babaian R: Optimization of prostate biopsy strategy

using computer based analysis. J Urol. Dec 1997 Vol.158(6) pp.2168-2175.

20. Karakiewicz P, Hanley J, Bazinet M: Three-dimensional computer-assisted analysis of sector

biopsy of the prostate. Urology. Aug 1998 Vol.52(2) pp.208-212.

21. Mohan P, Ho H, Yuen J, Ng W, Cheng W: A 3D computer simulation to study the efficacy of

transperineal versus transrectal biopsy of the prostate. Int. J. Computer Assisted Radiology and

Surgery. 2007; Vol.1(6) pp.351-360.

22. Sofer A, Zeng I, Mun S: Optimal Biopsy Protocols for Prostate Cancer. Annals of Operations

Research. 2003; Vol. 119 pp.63–74.

23. Ahmed H, Emberton M, Kepner G, Kepner J: A biomedical engineering approach to mitigate the

errors of prostate biopsy. Nat Rev Urol. Feb 7 2012; Vol.9(4) pp.227-231.

24. Kepner G, Kepner J: Transperineal prostate biopsy: analysis of a uniform core sampling pattern

that yields data on tumor volume limits in negative biopsies. Theor Biol Med Model. Jun 2010;

Vol.17 pp.7-23.

25. Chang D, Xue C, Kim C, Jun C, Petrisor D, Han M, Stoianovici D: The Number of Systematic

Biopsy Cores Raises Predominantly the Detection of Insignificant Cancer. American Urological

Association, Engineering and Urology Society, 29th Annual Meeting. 2014; pp.15.

http://engineering-urology.org/am/29EUS_2014.pdf.

26. Epstein J, Walsh P, Carmichael M, Brendler C: Pathologic and clinical findings to predict tumor

extent of nonpalpable (stage T1c) prostate cancer. JAMA. Feb 2 1994; Vol.271(5) pp.368-374.

27. Hooke R, Jeeves T: "Direct Search'" Solution of Numerical and Statistical Problems. Journal of

the ACM. April 1961; Vol.8(2) pp.212-229.

28. Spitzer V, Ackerman M, Scherzinger A, Whitlock D: The visible human male: a technical report.

J Am Med Inform Assoc. Mar-Apr 1996; Vol.3(2) pp.118-130.

29. Mahdavi S, Chng N, Spadinger I, Morris W, Salcudean S: Semi-automatic segmentation for

prostate interventions. Medical Image Analysis. April 2011; Vol.15(2) pp.226-237.

30. Eskicorapci S, Guliyev F, Akdogan B, Dogan H, Ergen A, Ozen H: Individualization of the

biopsy protocol according to the prostate gland volume for prostate cancer detection. J Urol. May

2005; Vol.173(5) pp.1536-1540.

31. Karakiewicz P, Bazinet M, Aprikian A, Trudel C, Aronson S, Nachabé M, Péloquint F,

Dessureault J, Goyal M, Bégin L, Elhilali M: Outcome of sextant biopsy according to gland

volume. Urology. January 1997; Vol.49(1) pp.55-59.

32. Kommu S: Re: Individualization of the biopsy protocol according to the prostate gland volume for

prostate cancer detection. J Urol. Nov 2005 Vol.174(5) pp.2068.

33. Andriole GL: Pathology: the lottery of conventional prostate biopsy. Nat Rev Urol. Apr 2009;

Vol.6(4) pp.188-189. PMCID:19352393

34. Scattoni V, Raber M, Abdollah F, Roscigno M, Dehò F, Angiolilli D, Maccagnano C, Gallina A,

Capitanio U, Freschi M, Doglioni C, Rigatti P, Montorsi F: Biopsy schemes with the fewest cores

for detecting 95% of the prostate cancers detected by a 24-core biopsy. European Urology.

January 2010; Vol.57(1) pp.1-8.

35. Xu HX, Lu MD, Liu LN, Guo LH: Magnetic navigation in ultrasound-guided interventional

radiology procedures. Clin Radiol. May 2012; Vol.67(5) pp.447-454. PMCID:22153232

36. Ho H, Mohan P, Lim E, Li D, Yuen J, Ng W, Lau W, Cheng C: Robotic ultrasound-guided

prostate intervention device: system description and results from phantom studies. Int J Med

Robot. Mar 2009; Vol.5(1) pp.51-58. PMCID:19145573

37. Stoianovici D, Kim C, Srimathveeravalli G, Sebrecht P, Petrisor D, Coleman J, Solomon SB,

Hricak H: MRI-Safe Robot for Endorectal Prostate Biopsy. IEEE-ASME Transactions on

Mechatronics. Aug 2014; Vol.19(4) pp.1289-1299. PMCID:4219418 ISI:000335915800019

38. McNeal J, Redwine E, Freiha F, Stamey T: Zonal distribution of prostatic adenocarcinoma.

Correlation with histologic pattern and direction of spread. Am J Surg Pathol. Dec 1988;

Vol.12(12) pp.897-906.

Doyoung Chang received the B.S. degree in 2006 and the Ph.D. degree in 2012 from the Department of

Mechanical and Aerospace Engineering both from Seoul National University, Seoul, Korea. Between 2012-2015,

he was a Postdoctoral Research Fellow at the Urology Robotics Lab, Johns Hopkins University, Baltimore, MD, USA. He is currently a Research Assistant Professor at the Miller School of Medicine, University of Miami,

Miami, FL, USA. His research interests include image-guided medical robotics and biologically-inspired robot

design.

Xue Chong received his medical degree from Shanghai Second Military Medical University, and his Ph.D. degree

from Peking Union Medical College, China. He completed his residency at the Institute of Hematology &

Hospital of Blood Disease, Chinese Academy of Medical Sciences. He is currently an Attending Surgeon of Urology at the Second Affiliated Hospital, Zhejiang University. His main clinical focus is in urological oncology

with a special emphasis in prostate cancer.

Chunwoo Kim received the B.S. degree from the Department of Mechanical Aerospace Engineering, Seoul

National University, Seoul, Korea, in 2008, and the Ph.D. degree from Johns Hopkins University, Baltimore, MD,

in 2014. He is currently a Postdoctoral Research Fellow at the Pediatric Cardiac Bioengineering Lab, Boston Children’s Hospital, Boston, MA, USA. His research interests include image-guided robots and medical imaging.

Dr. Kim is a recipient of the Fulbright scholarship and the Prostate Cancer Research Training Award of the United

States Department of Defense.

Changhan Jun received the B.S. degree from the Department of Mechanical, Materials and Aerospace

Engineering, Illinois Institute of Technology, Chicago, IL, in 2010. He received the M.S. degree at the

Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA in 2013. Since 2013, he has been working toward the Ph.D. degree at the Urology Robotics Lab, Johns Hopkins University, Baltimore,

MD, USA. His research interests include image-guided robots and medical instruments.

Doru Petrisor received a M.S. degree in Mechanical Engineering from the University of Craiova, Romania in

1988, the PhD from the University of Petrosani, Romania in 2002, followed by a research fellowship in Urology

at the Johns Hopkins University. Between 1991-1994 he was Assistant Professor at the University of Craiova and Lecturer since 1994. In 2002 he joined the Urology Robotics research group at Johns Hopkins and currently is

Research Associate Professor. Dr. Petrisor's specialty is design of interventional and surgical robots, medical

instrumentation, and CNC manufacturing. His bibliography includes numerous articles, presentations, and 4 patents of invention.

Misop Han MD, MS received his undergraduate, medical school, and urology training at the Johns Hopkins

University, Baltimore, MD. He is Associate Professor of Urology and Oncology at the James Buchanan Brady

Urological Institute, Johns Hopkins Medicine. His main clinical focus is in urological oncology with a special emphasis in prostate cancer and kidney cancer. His research interests include the outcome of radical

prostatectomy and image-guided surgery using surgical robots. He has published extensively in these subjects.

Dan Stoianovici received the Ph.D. degree from Southern Methodist University, Dallas, TX, in 1996. He is

Professor of Urology, Mechanical Engineering, Neurosurgery, and Oncology at the Johns Hopkins University and

Director of the Robotics Program in Urology. His specialty is medical robotics in particular robotic hardware and image-guided interventions. His editorial boards activities include the IEEE/ASME TRANSACTIONS on

Mechatronics, Journal of Endourology, International Journal of Medical Robotics and Computer Aided Surgery,

Journal of Medical Robotics Research, and is the Executive Director of the Engineering & Urology Society.