The Impact of Placement Errors on the Tumor Coverage in MRI-Guided Focal Cryoablation of Prostate Cancer

Abstract

Rationale and Objectives:

There have been multiple investigations defining and reporting the effectiveness of focal cryoablation as a treatment option for organ-confined prostate cancer. However, the impact of cryo-needle/probe placement accuracy within the tumor and gland has not been extensively studied. We analyzed how variations in the placement of the cryo-needles, specifically errors leading to incomplete ablation, may affect prostate cancer’s resulting cryoablation.

Materials and Methods:

We performed a study based on isothermal models using Monte Carlo simulations to analyze the impact of needle placement errors on tumor coverage and the probability of positive ablation margin. We modeled the placement error as a Gaussian noise on the cryo-needle position. The analysis used retrospective MRI data of 15 patients with biopsy-proven, unifocal, and MRI visible prostate cancer to calculate the impact of placement error on the volume of the tumor encompassed by the −40°C and −20°C isotherms using one to four cryo-needles.

Results:

When the standard deviation of the placement error reached 3 mm, the tumor coverage was still above 97% with the −20°C isotherm, and above 81% with the −40°C isotherm using two cryo-needles or more. The probability of positive margin was significantly lower considering the −20°C isotherm (0.04 for three needles) than using the −40°C isotherm (0.66 for three needles).

Conclusion:

The results indicated that accurate cryo-needle placement is essential for the success of focal cryoablation of prostate cancer. The analysis shows that an admissible targeting error depends on the lethal temperature considered and the number of cryo-needles used.

INTRODUCTION

Focal cryoablation (FC) has been investigated as a minimally-invasive option for the management of low-risk organ-confined prostate cancer (PCa) and a salvage treatment option for postradiation recurrence (1,2). Unlike radical treatments, FC aims to freeze and destroy only the lesion and the surrounding area using thin cryo-needles. FC is expected to reduce the risk of complications associated with the radical treatment (3), such as incontinence and impotence, while keeping acceptable oncological outcomes (4). A study on FC of low-risk primary PCa with 48 patients showed that 86% of patients had negative follow-up prostate biopsies (5). The effectiveness of FC has also been tested in salvage treatment of postradiation recurrence (2,4,6), which may affect around 40% of patients who underwent radiation therapy (7).

One of the significant technical challenges for FC is to deploy multiple cryo-needles to form an ablation zone that sufficiently covers the target volume while sparing critical structure around it. In practice, physicians rely on their own experience to plan the placement of the cryo-needles and manually insert them in order to achieve this goal. This practice, however, may lead to a positive ablation margin due to (1) suboptimal placement planning and (2) failure to execute the plan due to error in placing the cryo-needles. While several groups attempted to optimize cryoablation planning employing geometric (8) or thermal simulation (9,10), few efforts have been made to address the issue of needle placement error. Placement errors may occur as a result of needle deviation and prostate movement. Such errors can result in unnecessary damage to the tissue and prolonged procedure time due to repeated needle insertions, and/or suboptimal oncologic outcome. Therefore, understanding the impact of placement accuracy is a crucial step for future developments in prostate FC.

In this study, we analyzed how the misplacement of the cryo-needle can affect the coverage of the target tumor and the probability of positive margin (i.e., insufficient coverage of the tumor volume) using simulations based on geometric models. The tumors were segmented on retrospective MRI images of patients with unifocal MRI visible PCa. A Monte Carlo simulation was performed to estimate the lethal ablation zone around the cryo-needles considering 15 levels of placement error. For simplicity, we considered the −20°C and −40°C isotherms as the boundary of the lethal ablation zone. We estimated the average tumor coverage, the probability of positive margin, and the amount of adjacent nontumor tissue encompassed by the isotherm (Fig 1).

Fig. 1.

Diagram of our simulation study: Target volumes were segmented based on available MRI images of 15 patients. A desired configuration was defined for each patient. The Monte Carlo simulation considers the placement error as the random variable and provides the average tumor coverage and the probability of positive margin.

METHODS

Desired cryo-needle placement

In order to define the desired cryo-needle placement, a search algorithm was implementedin a medical image computing platform (11) based on the Nelder-Mead approach. We assumed that the cryo-needles were inserted transperineally using a template with a fixed needle orientation (12). The algorithm explores cryo-needle configurations that maximize the target tumor and minimize nontumor tissue encompassed by the ablation zone using the cost function:

$$J=-k_1{p}_c+k_2{h}_c+g$$ (1)

where p_c is percentage of target tumor covered, h_c is the volume of nontumor tissue within the ablation zone and k₁ and k₂ are the trade-off gains (in this study they were set to 10 and 1, respectively). A penalty function was included to guarantee a minimum distance between the cryo-needles, such as:

$$g=\{\begin{array}{c}0,d_i\ge 5\mathrm{mm}\\ \gamma /d_i,d_i<5\mathrm{mm}\end{array}$$ (2)

where d_i is the distance between the cryo-needles. The minimum distance between the cryo-needles was set to 5 mm based on the hole spacing on the needle-guiding template used in the clinical practice. We also assumed that the lethal ablation zone was defined by either the −40°C and −20°C isotherms based on previous studies suggesting that the temperature inducing tissue necrosis varies between those values (13). Therefore, by choosing two isotherms we provide upper and lower limits of possible lethal ablation zones. We used the geometry of the −40°C and −20°C isotherms provided by the cryo-system manufacturer (14). The IceSeed cryo-needle (Galil Medical Inc., Yokeneam, Israel) was assumed because the size of its ablation zone is suitable for focal ablation of the prostate. The use of geometric models has a few advantages for our study. First, the geometric approach applies a fixed-shape isotherm without patient-specific parameters. Second, such model allows a straightforward interpretation of the results, without the need for in-depth knowledge about confounding factors specific to the simulation technique.

Placement error

We modeled the placement error as a zero-mean Gaussian noise with a given standard deviation on the three directions in the Right-Anterior-Superior (RAS) patient coordinate system (Fig 2). The placement error is a combination of needle deviation during insertion and prostate movement after the acquisition of the planning image; since both error sources are incidental, the combined error was modeled as a Gaussian placement error with respect to the desired needle placement. The standard deviation (σ) varied from 0 to 9 mm along each axis, which provides an average absolute three-dimensional error ranging from 0 mm to 14.5 mm. The error range was defined based on previous studies on transperineal prostate biopsy with 18-gauge needles, which have shown a median targeting error around 6 mm (15). It is safe to assume that the 17-gauge cryo-needles are less prone to deviation due to their stiffness and symmetric tip. Therefore, we considered the typical biopsy error plus a 50% margin as the largest misplacement along each axis. The placement errors were modeled as Gaussian translational errors, because the template physically constrained the cryo-needle. While the needle deviation appears as a combination of translational and rotational displacement of the needle tip, in this study, the latter is ignorable given that the deviation was relatively small compared to the insertion length. For instance, assuming a needle tip deviation of 5 mm, and that the insertion depth is 100 mm, the isotherm angulation would be 0.05 rad. When a −20°C isotherm rotated by 0.05 rad with respect to the guiding-template is matched with an isotherm translated by 5 mm, the intersection between both represents 99% of the original isotherm volume. Therefore, given the ellipsoidal shape of the isotherm, it is safe to incorporate the small orientation errors into the Gaussian translation error without significant loss.

Fig. 2.

Noise and isotherm models: (a) Axial view of the desired placement of the cryo-needles is defined by the planning algorithm. The purple dots represent the desired needle position, the blue circles are the cross section of the isotherm model, and the red line is the contour of the tumor. (b) shows one axial slice of the simulated procedure, where placement errors are added along the three axes. The coordinate system was defined using the RAS (Right, Anterior, Superior) convention, where R is from left towards right, A is from posterior towards anterior, and S from inferior towards superior. The light blue area is the amount of tumor coverage, while the yellow area represents the amount of healthy tissue undesirably encompassed by the isotherm. (c) shows the geometric model of the isotherms using the IceSeed cryoneedles (Galil Medical Inc., Yokeneam, Israel).

Patient data

Fifteen patients with biopsy-proven MRI visible unifocal PCa (average volume of 1.1cc, ranging from 0.4cc to 3.5cc) were included in this study. For each patient, multiparametric MRI exam consisting of T2-weighted MRI, diffusion-weighted, and dynamic contrast-enhanced MRI was obtained. The tumors were contoured on the axial slices of T2-weighted MRI by a board-certified radiologist who is an expert in prostate MRI (CMT). The imaging parameters for the T2-weighted MRI are TR/TE = 2700–5440 ms/85–107 ms, flip angle = 90°–150°, field-of-view = 160 mm², slice thickness = 3 mm, number of slices 30–40, matrix size = 255 × 255–385 × 224. This retrospective analysis of the MRI data was approved by the institutional review board.

Simulation analysis

We investigated the impact of inaccurately placing the cryo-needles through a simulation study using 65 different conditions, varying the number of cryo-needles, isotherm temperature, and σ. The simulations were performed with 15 different values of σ. For each condition, the placement error’s impact was tested using the Monte Carlo method, where the placement errors were considered the random variables. The same isotherm model used to define the desired cryo-needle placement was employed in the simulations. To guarantee a percentage estimation error below 10% using a confidence level of 95%, we defined the number of samples N = 10⁴. For each initial condition, the following information was recorded:

• Target volume;

• Maximum target radius in the R-A directions (2);

• Average (μ_c) tumor coverage (p_c):

  $${\mu }_c=\frac{1}{N}\sum _{i=1}^N{p}_c(i)$$ (3)
• Probability of positive margin (λ_pm), which was defined as the trials with less than 99% of the target volume covered by the isotherm, such as:

  $${\mathrm{\lambda }}_{pm}=\frac{1}{N}\sum _{i=1}^{N}f(i)$$ (4)

  $$f(i)=\{\begin{array}{c}0,if{p}_c>0.99\\ 1,if{p}_c\le 0.99\end{array}$$ (5)
• Average $({\mathrm{\upsilon }}_h)$ adjacent nontumor tissue involvement (θ). This metric quantifies the amount of nontumor tissue within the isotherm volume (θ_{nontumor ∩ iso}) with respect to the total target tumor volume (θ_tumor), such as:

  $${\mathrm{\upsilon }}_h=\frac{1}{N}\sum _{i=1}^N\mathrm{\vartheta }(i)$$ (6)

  $$\mathrm{\vartheta }(i)=\frac{{\mathrm{\vartheta }}_{\text{non}-\text{tumor}\cap \text{iso}}}{{\mathrm{\vartheta }}_{\text{tumor}}}$$ (7)

RESULTS

The relationship between the average tumor coverage and needle placement error is presented in Figure 3. As expected, the average tumor coverage (μ_c) was more robust to placement errors when considering the −20°C isotherm than considering the −40°C isotherm due to its larger dimensions. When σ = 3 mm (i.e. an average 3D error of 4.1 mm), the tumor coverage with the −20°C isotherm was 97%, 99%, and 100% using two, three and four cryo-needles, respectively. The tumor coverage with the −40°C isotherm was 81%, 89%, and 94% using two, three, and four cryo-needles, respectively. When using just one cryo-needle, the tumor coverages with the −20°C and the −40°C isotherms were 92% and 64%, respectively.

Fig. 3.

Simulation results: Evolution of the tumor covered (μ_c), the probability of positive margin (λ_pm) and nontumor tissue involvement (υ_h) considering the −20°C and −40°C isotherms.

The relationship between the probability of positive margin (λ_pm) and the placement error is also shown in Figure 3. The probability significantly increases when σ > 1.0 mm and σ > 3 mm using two and three cryo-needles, respectively. When σ = 3mm, the probability of positive margin (λ_pm) with the −20°C isotherm was 0.20, 0.04, and 0.02 using two, three, and four needles, respectively. The probability of positive margin (λ_pm) with the −40°C isotherm was 0.84, 0.66, and 0.48 using two, three, and four needles, respectively. The impact of placement errors on the amount of nontarget tissue encompassed by the isotherm is depicted in Figure 3c. When σ = 3mm, the nontumor tissue involvement (υ_h) with the −20°C isotherm was 13.9, 17.6, and 19.9 using two, three and four needles, respectively, whereas the with the −40°C isotherm was 3.6, 5.3, and 6.4 using two, three, and four needles, respectively.

Tables 1 and 2 summarize the characteristics of all 15 tumors and their respective values of μ_c, λ_pm, and υ_h with three illustrative placement errors. Figure 4 illustrates how μ_c and λ_pm are influenced by the combination of placement error and tumor volume, and the combination of placement error and maximum radius of the target tumor. Figure 5 illustrates examples of two cases (Case 8 and 14) presenting tumors with similar volumes (0.7 cc) but different shapes. Case 8 presented an elongated lesion in the left peripheral zone with a maximum radius of 14.3 mm, while in Case 14, the lesion in the right peripheral zone is more symmetric and with a radius of 10.6 mm. This difference in the shape resulted in higher values of λ_pm in Case 8. For instance, when σ = 6 mm, the probability of positive margins was 0.38 and 0.23 for Cases 8 and 14, respectively, using two cryo-needles and −20°C isotherm.

TABLE 1.

Representative Results with −20°C Isotherm. (μ_c is the Average Tumor Coverage; λ_pm is the Probability of Positive Margin and ν_h is the Nontumor Tissue Involvement)

Case	Tumor Volume [cc]	Max. Radius [mm]	Std. Dev. Error = 3 mm
			One Needle			Two Needles			Three Needles			Four Needles
			μc [%]	λpm	νh	μc [%]	λpm	νh	μc [%]	λpm	νh	μc [%]	λpm	νh
1	2.3	22.3	87.5	0.88	2.1	96.3	0.44	5.1	99.2	0.12	5.1	99.8	0.03	5.5
2	3.5	20.5	82.0	0.97	1.2	93.6	0.69	3.0	97.0	0.44	3.0	98.6	0.22	3.7
3	1.4	16.9	93.7	0.61	4.1	94.2	0.42	8.7	100	<0.01	8.7	100	<0.01	10.0
4	1.1	16.8	94.1	0.60	5.1	97.7	0.23	10.7	99.6	0.04	10.7	100	<0.01	11.8
5	1.1	16.3	93.2	0.59	5.1	97.3	0.26	10.9	99.9	0.01	10.9	100	<0.01	12.2
6	0.5	16.1	93.3	0.50	10.1	95.9	0.35	18.8	100	<0.01	18.8	100	<0.01	22.0
7	1.0	15.9	95.2	0.46	7.0	99.3	0.09	13.9	99.9	<0.01	13.9	100	<0.01	15.8
8	0.7	14.3	90.1	0.65	11.1	99.3	0.08	21.7	99.8	0.03	21.7	100	<0.01	23.8
9	0.5	13.5	97.6	0.32	11.0	100	0.01	21.5	100	<0.01	21.5	100	<0.01	24.2
10	0.8	12.9	96.2	0.40	8.0	99.8	0.02	16.2	99.9	<0.01	16.2	100	<0.01	17.3
11	0.6	12.3	90.5	0.53	11.4	99.8	0.02	22.0	100	<0.01	22.0	100	<0.01	26.3
12	0.5	11.9	93.5	0.46	13.5	98.7	0.14	26.2	99.9	<0.01	26.2	100	<0.01	29.0
13	0.4	11.6	97.1	0.30	17.0	99.1	0.08	31.6	100	<0.01	31.6	100	<0.01	36.2
14	0.7	10.6	88.4	0.52	12.1	98.3	0.14	23.2	100	<0.01	23.2	100	<0.01	25.7
15	0.4	9.7	89.5	0.56	16.1	99.8	0.02	30.3	100	<0.01	30.3	100	<0.01	36.4
Case	Tumor Volume [cc]	Max. Radius [mm]	Std. dev. Error = 6 mm
			One Needle			Two Needles			Three Needles			Four Needles
			μc [%]	λpm	νh	μc [%]	λpm	νh	μc [%]	λpm	νh	μc [%]	λpm	νh
1	2.3	22.3	52.6	0.97	2.4	72.9	0.85	4.6	85.2	0.66	6.5	91.6	0.44	7.8
2	3.5	20.5	57.9	0.99	1.5	79.2	0.95	2.9	89.5	0.85	4.1	95.3	0.70	5.3
3	1.4	16.9	59.7	0.86	4.4	83.2	0.71	8.4	95.1	0.40	11.3	98.5	0.23	13.8
4	1.1	16.8	62.3	0.84	5.3	81.7	0.59	9.8	92.9	0.35	13.3	97.2	0.16	15.7
5	1.1	16.3	60.6	0.84	5.4	85.0	0.64	10.0	94.6	0.39	13.8	98.2	0.22	16.6
6	0.5	16.1	59.3	0.80	10.4	85.7	0.62	18.5	92.9	0.28	24.5	97.3	0.15	29.7
7	1.0	15.9	65.4	0.77	7.3	87.4	0.49	13.0	94.0	0.25	17.4	98.1	0.12	20.7
8	0.7	14.3	67.3	0.85	11.4	85.4	0.57	20.1	95.7	0.38	27.4	98.5	0.21	32.6
9	0.5	13.5	61.9	0.71	11.3	76.0	0.41	20.1	92.9	0.22	27.1	97.1	0.11	32.5
10	0.8	12.9	59.6	0.76	8.3	86.8	0.48	14.6	94.6	0.31	19.9	97.5	0.15	23.7
11	0.6	12.3	70.5	0.78	11.7	90.5	0.46	20.9	96.3	0.27	28.1	98.6	0.17	34.5
12	0.5	11.9	57.9	0.76	13.8	86.1	0.50	24.4	94.3	0.27	32.9	97.4	0.12	39.4
13	0.4	11.6	63.6	0.68	17.3	81.2	0.45	30.4	95.9	0.21	40.6	98.2	0.10	49.0
14	0.7	10.6	69.8	0.74	12.4	88.8	0.49	21.5	96.1	0.23	29.0	98.6	0.10	34.8
15	0.4	9.7	67.6	0.77	16.4	86.2	0.45	29.0	94.7	0.26	38.8	98.3	0.15	47.6

TABLE 2.

Representative Results Using −40°C Isotherm. (μ_c is the Average Tumor Coverage; λ_pm is the Probability of Positive Margin and ν_h is the Nontumor Tissue Involvement)

Case	Tumor Volume [cc]	Max. Radius [mm]	Std. Dev. Error = 3 mm
			One Needle			Two Needles			Three Needles			Four Needles
			μc [%]	λpm	νh	μc [%]	λpm	νh	μc [%]	λpm	νh	μc [%]	λpm	νh
1	2.3	22.3	46.3	1.00	0.54	69.3	1.00	0.31	79.0	1.00	1.13	86.2	1.00	1.59
2	3.5	20.5	40.7	1.00	0.59	61.2	1.00	0.39	73.7	1.00	0.27	80.5	0.98	0.89
3	1.4	16.9	60.9	0.90	0.39	78.6	0.63	1.35	86.9	0.38	2.37	94.8	0.19	2.68
4	1.1	16.8	63.0	1.00	0.37	82.6	0.91	1.83	90.8	0.75	2.78	94.4	0.58	3.53
5	1.1	16.3	63.5	0.89	0.36	83.1	0.62	1.86	90.3	0.42	2.76	95.0	0.30	3.47
6	0.5	16.1	68.2	1.00	2.32	86.0	0.87	4.08	93.2	0.67	5.60	96.1	0.57	7.10
7	1.0	15.9	65.4	1.00	1.35	84.8	0.85	2.65	92.8	0.63	3.81	93.6	0.37	5.65
8	0.7	14.3	65.0	0.83	2.35	82.4	0.66	4.71	90.5	0.39	6.75	94.6	0.18	7.89
9	0.5	13.5	72.2	1.00	2.28	89.9	0.98	4.40	96.1	0.87	6.05	97.8	0.61	7.90
10	0.8	12.9	68.9	0.93	1.31	84.8	0.86	3.14	91.9	0.72	4.73	97.1	0.30	5.42
11	0.6	12.3	69.4	0.99	2.31	76.8	0.75	5.13	84.8	0.47	7.77	97.1	0.29	8.13
12	0.5	11.9	71.2	0.90	3.14	89.1	0.73	5.66	94.9	0.45	7.95	97.2	0.29	9.72
13	0.4	11.6	73.8	1.00	4.04	86.5	0.88	7.47	94.8	0.65	10.37	98.3	0.45	12.29
14	0.7	10.6	68.4	1.00	2.32	89.5	0.94	4.85	95.4	0.71	6.92	98.3	0.62	8.40
15	0.4	9.7	72.2	1.00	3.56	85.3	0.95	6.89	93.7	0.80	9.65	96.8	0.63	11.69
Case	Tumor Volume [cc]	Max. Radius [mm]	Std. Dev. Error = 6 mm
			One Needle			Two Needles			Three Needles			Four Needles
			μc [%]	λpm	νh	μc [%]	λpm	νh	μc [%]	λpm	νh	μc [%]	λpm	νh
1	2.3	22.3	24.6	1.00	0.75	39.5	1.00	0.61	49.2	1.00	1.47	58.7	1.00	2.20
2	3.5	20.5	21.4	1.00	0.79	35.1	1.00	0.65	45.2	1.00	0.60	52.7	1.00	1.38
3	1.4	16.9	27.7	1.00	0.72	44.5	1.00	2.08	54.7	0.99	3.13	68.2	0.97	4.02
4	1.1	16.8	33.3	1.00	0.67	52.3	1.00	2.32	65.7	0.98	3.66	75.1	0.94	4.77
5	1.1	16.3	27.9	1.00	0.72	45.5	0.99	2.43	58.1	0.98	3.84	68.7	0.95	4.99
6	0.5	16.1	31.2	1.00	2.69	51.2	0.99	5.07	64.4	0.95	7.35	73.2	0.91	9.53
7	1.0	15.9	33.3	1.00	1.65	52.3	1.00	3.24	65.7	0.97	4.97	75.1	0.93	6.80
8	0.7	14.3	28.2	1.00	2.72	46.0	0.99	5.54	57.6	0.97	8.30	69.5	0.92	10.53
9	0.5	13.5	33.2	1.00	2.67	54.3	0.97	5.53	67.7	0.90	8.04	75.9	0.83	10.45
10	0.8	12.9	30.0	1.00	1.70	47.3	0.99	3.97	59.6	0.95	5.80	72.1	0.89	7.43
11	0.6	12.3	29.9	0.99	2.70	42.1	0.97	5.99	54.4	0.94	8.75	71.6	0.85	10.91
12	0.5	11.9	30.7	0.98	3.55	49.5	0.94	6.90	63.8	0.88	9.98	73.1	0.82	12.80
13	0.4	11.6	31.7	0.97	4.46	48.5	0.93	8.75	63.1	0.86	12.67	74.2	0.77	16.05
14	0.7	10.6	29.1	0.98	2.71	51.5	0.93	5.97	62.7	0.87	8.72	73.7	0.79	11.21
15	0.4	9.7	29.4	0.99	4.00	47.0	0.95	8.14	60.5	0.89	11.95	70.7	0.81	15.30

Fig. 4.

Multiparametric analysis: The combined impact of placement error, target size and shape considering −20°C and two and three cryo-needles. The markers represent the raw data used to generate the smoothed 3D surface. The plots on the left represent the results using two cryo-needles, while the plots on the right represent the results using three cryo-needles. One can observe that the tumor volume and maximum radius variation resulted in a more significant impact of the probability of positive margin than on the amount of tumor covered by the isotherm.

Fig. 5.

Impact of tumor shape: Two representative cases with similar volume (0.7cc) but different maximum radius. The elongated shape of Case 8 resulted in a higher probability of positive margin than Case 14, especially when using two cryo-needles.

DISCUSSION

Our simulation results indicate that cryo-needle placement errors may increase the risk of positive ablation margin. To the best of our knowledge, this is the first study analyzing the impact of misplacing the cryo-needles in the context of FC. Without knowing the effect of placement error, even an optimized cryo-needle placement plan might not be translated to improved effectiveness.

While the impact of placement error has not been investigated in the context of cryoablation, it has been studied for targeted prostate biopsies (16). Unlike prostate biopsy, where the needle is often inserted using the transrectal approach, cryoablation is commonly performed using the transperineal method making it more prone to placement error and prostate movement due to longer insertion depth. Therefore, it is crucial to understand the impact of placement error in this context.

The simulation results presented in Figure 3 indicates that, considering the −20°C isotherm, it was possible to reach an average tumor coverage above 90% using two, three, and four needles with a standard deviation of the needle placement error up to 5 mm. On the other hand, the analysis revealed that the positive margin and the tumor coverage are more prone to needle placement error when the −40°C isotherm was considered as the boundary for the lethal ablation zone due to its smaller footprint. Several studies indicated that the lethal temperature during cryoablation might range from −20°C to −40°C depending on the type of tissue (13,17). However, it should be noted that the single lowest temperature achieved during cryoablation is not the sole condition to induce the tissue necrosis; there are other factors including the number of freeze-thaw cycles and the rate of thawing (18).

The study also revealed that the use of three or four cryo-needles was more robust to placement errors than two needles. In theory, these results would suggest more needles would be preferable in terms of the robustness to placement errors, but clinical decision on the number of needles depends on other factors not included in this study, such as proximity to critical structures and heat sources. Besides, the analysis of the nontumor tissue involvement (Fig 3c) shows that increasing the number of cryo-needles will increase the volume of adjacent nontumor tissue, which can lead to undesirable damage to healthy tissue.

Figure 4 and Tables 1 and 2 also suggest that the chances of having a positive margin may be affected not only by the tumor size but also by the shape of the target tumor. Tumors with similar volumes but different shapes may result in different values of λ_pm. Although the maximum radius and the tumor volume are fairly proportional in our dataset, it was possible to observe the influence of the target shape in a couple of cases (Fig 5). The results suggest that the oblateness of the tumor may be one of the factors that influence λ_pm, although we did not have enough subjects to statistically evaluate this hypothesis. This impact could be reduced with an ability to tilt the cryo-needle trajectory and change the angulation of the isotherm, but it would require the development and validation of new guiding devices.

The use of the geometric model has imperfections as it does not take into account the thermal effects from other cryo-needles and various heat sources. It has been known that multi-needle arrangements present a synergistic effect, which may increase the ablation zone. A recent study demonstrated the importance of the synergistic effect in predicting the ablation zone (19), and the results suggest that our future investigation should also analyze the synergistic effect in the context of the placement inaccuracies. In addition, the geometric model of the isotherm used in this study was determined by the manufacturer in gel experiments, which has different thermal properties than in-vivo tissues (20). Nevertheless, gel phantoms have been used to characterize the isotherms (21,22), and Shah et al. (21) highlighted that, even though obtained in gel phantoms, their isotherms closely resembled the histologic ablation zone dimensions in a small in-vivo study (23).

There are other limitations to this study. A more comprehensive database would allow us to perform an in-depth analysis of the influence of the tumor shape. Second, our study considers the insertions to be independent of each other, but in the clinical practice, the physician may use the information acquired introducing the first cryo-needle to adjust the subsequent insertion. Nevertheless, the presented results indicate that the admissible targeting error depends on the lethal temperature considered and the number of cryo-needles used.

CONCLUSION

We performed a simulation study to evaluate how cryo-needle misplacement may affect MRI-guided prostate FC. The results indicated that reducing the placement error significantly increases the chances of proper coverage of the target tumor by the −20°C and −40°C isotherms. These results would help determining the accuracy requirements for guidance tools for focal cryoablation of prostate cancer in future studies.