Assessment of temperature measurement error and its correction during Nd:YAG laser ablation in porcine pancreas

Abstract

Purpose: The aim of this study was to experimentally assess temperature measurement error, or artefact, in ex vivo healthy porcine pancreases undergoing laser ablation due to direct light absorption by thermocouples, investigate this artefact at different relative positions between thermocouples and laser applicator, and correct the artefact by a three-variables model.

Materials and methods: Temperature in ex vivo healthy porcine pancreases undergoing laser ablation, using a Nd:YAG laser at two low powers (i.e. 1.6 W and 2 W) and a single applicator, was monitored by thermocouples. Artefact caused by laser light absorption of thermocouple metallic wires was assessed at 12 relative positions by changing the relative distance (d) and the angle (θ) forming between applicator and thermocouples. Reference temperature was measured by fibre Bragg grating sensors. Trials were performed using a three-variables model (i.e. power, d and θ) based on Pennes’ equation to correct the artefact.

Results: The higher d and θ, the lower the artefact (e.g. at θ = 0° and power = 2 W, the artefact is 14.0 °C at d = 3 mm and 4.0 °C at d = 7 mm). Artefact increases with power. The three-variables model allows the minimising of the artefact: the maximum artefact decreases from 14 °C to 2.8 °C applying the proposed correction.

Conclusions: Artefact is strongly influenced by the relative position between applicator and thermocouples. The correction based on the model minimises the artefact at the two low powers employed during the experiments. Further trials are required to investigate the feasibility of the model at higher powers.

• Invasive thermometry
• laser ablation
• pancreas
• thermocouples

Introduction

Laser ablation (LA) is a minimally invasive clinical procedure, which induces tumour cellular necrosis due to a localised high temperature increase [1]. The laser light is guided through a fibre optic inside the tumoural volume; the absorption of laser energy within the tissue results in localised heating, able to induce cellular death. LA is employed in clinical practice to treat liver, prostate, brain and lung tumours, in place of surgical resection [2–4]. Because of the high mortality and the complexity of the surgical procedure (i.e. the Whipple procedure) used to treat pancreas neoplasia, in the last few years we have been working to employ LA on this gland; encouraging results have been obtained on porcine models [5,6].

The optimal LA outcome is irreversible neoplastic tissue damage due to the local temperature increase, avoiding thermal damage to the nearby healthy tissue. The knowledge of temperature mapping within the tissue may be particularly beneficial for adjusting laser settings applied during treatment (i.e. laser power, treatment time and total energy), because it defines the ablation zone.

Although a crucial role is played by temperature distribution in hyperthermia treatment planning (HTP) and in LA, the accuracy of temperature prediction is lacking. An accurate prediction is mainly limited by considerable uncertainties in the thermal and optical properties of tissue due to intra- and inter-patient variability and their non-linear dependence on temperature [7]. These concerns related to temperature prediction promoted research devoted to providing a temperature feedback during hyperthermia treatments. Therefore, recent decades saw several groups of research developing techniques for temperature monitoring during LA, in order to improve outcome and to spread this technique for other organs (e.g. pancreas). The approaches employed to monitor the temperature increase during LA can be divided in two categories [8]: non-invasive techniques (i.e. infrared thermography [9], magnetic resonance imaging-based thermometry [10], and computed tomography-based thermometry [11,12]); and invasive ones (i.e. thermocouples [13], fluoroptic sensors [14], and fibre Bragg grating (FBG) sensors [15–17]). Although growth interest is in the introduction of non-invasive techniques due to the non-invasiveness and to the chance of obtaining a temperature map all around the applicator with good spatial resolution, invasive techniques are still generally employed. The widespread use of invasive techniques is mainly motivated by their accuracy (better than 0.1 °C), short response time (shorter than 1 ms) and good spatial resolution. In particular, thermocouples present other advantages being easy to use and inexpensive. On the other hand, a substantial measurement error can occur due to the direct absorption of laser light. This direct absorption, caused by the metallic wires which constitute the thermocouple, can entail a significant artefact (i.e. almost 20 °C [13]) when thermocouples are employed during Nd:YAG laser treatments. Different techniques have been proposed to minimise the aforementioned artefact (or artifact in the USA) [18].

The aim of this study is threefold. 1) To experimentally assess the artefact induced by the direct absorption at different distances (d) and angle (θ) between the thermocouple and the laser applicator, and at two laser powers (P). The analysis is performed on ex vivo healthy porcine pancreases undergoing laser ablation. 2) To introduce a three-variables (i.e. P, d and θ) model which allows predicting the magnitude of the artefact. 3) To correct the artefact.

Materials and methods

Experimental set-up and procedure

Ex vivo healthy porcine pancreases were treated by employing a Nd:YAG laser (1064 nm, Smart 1064, DEKA, Florence, Italy) at two powers (i.e. 1.6 W and 2 W) in continuous mode. The laser light was conveyed into a quartz bare fibre applicator (core of 300 µm diameter). Freshly excised tissues were obtained from porcine pancreases and maintained at environmental temperature (about 25 °C) until tested. Tissue temperature was monitored by four K-type thermocouples, connected to a 4-channel data acquisition system (FX100, Yokogawa) developed at Università Campus Bio-Medico di Roma.

The thermocouples were introduced into the tissue and held in position with an ad hoc designed, poly(methyl methacrylate) mask (Figure 1A). This mask allows the insertion of the thermocouples on a perpendicular plane to the laser applicator (Figure 1C), and allows the adjustment of the relative distances (d) and angles (θ) among them (Figure 1B). In all ex vivo pancreases, temperature was monitored in four different positions by inserting the four thermocouples within the gland.

Figure 1. (A) 3D cad of the PMMA mask; (B) schematic representation of the top view of the PMMA mask. The holes designed to insert the thermocouples during the experiments and their distances to the hole used to insert the applicator are shown; (C) picture of the pancreas after the insertion of the thermocouples and the laser applicator thanks to the PMMA mask.

The values of d and θ relative to the 18 holes numbered in Figure 1(B) are reported in Table 1.

Table 1. Values of d and θ for the 18 holes (12 different positions).

	d (mm)	θ (°)
Holes 1 and 5	5.0	53.1
Holes 2 and 4	3.6	33.7
Hole 3	3.0	0
Holes 6 and 10	6.4	38.7
Holes 7 and 9	5.4	21.8
Hole 8	5.0	0
Holes 11 and 15	8.1	29.7
Holes 12 and 14	7.3	15.9
Hole 13	7.0	0
Hole 16	10.0	0
Hole 17	12.0	0
Hole 18	15.0	0

Table 1 shows 12 different couples of d and θ set during trials. Both the parameters were changed to assess their influence on the artefact on a wide range of values (i.e. d from 3 mm to 15 mm, and θ from 0° mm to 53.1°), in order to estimate the artefact very close to the applicator (e.g. the closest position is at d = 3 mm), where a high magnitude is expected, and far from the applicator (e.g. the biggest d value is 15 mm), where the magnitude should be negligible. A second set of measurements were performed by substituting the thermocouples with FBG sensors. The outputs of these sensors were monitored by an optical spectrum analyser (OSA) (Optical Sensing Interrogator, sm125, Micron Optics, Atlanta, GA). A computer was employed to collect data obtained by the OSA.

All trials were performed as follows: the laser was turned on for 10 s and then turned off for a time interval ranging from 30–60 s. In order to keep the tissue temperature lower than 50 °C, each trial consisted of 20 repetitions of turning the laser on and off. This solution, also employed in other studies (e.g. in Reid et al. [14]), improves the repeatability of the measurements avoiding tissue coagulation during the experiments. It must be also considered that the artefact happens during the first seconds after the laser is turned on, when tissue coagulation is absent. Lastly, the mean value and the uncertainty of the 20 artefacts were calculated for each trial. The uncertainty was estimated by considering a Student reference distribution with 19 degrees of freedom and a level of confidence of 95%.

Theoretical background

The thermal response of tissue is related to the P deposition in tissue and can be theoretically predicted by Pennes’ Equation [1], as shown in Equation 1. where ρ is the tissue density (kgċm⁻³), c_s is the tissue specific heat (Jċkg⁻¹ċK⁻¹), k is the tissue heat conductivity (Wċm⁻¹ċK⁻¹), Q_e takes into account the power absorption due to water evaporation, and T(x,y,z,t) is the tissue temperature, expressed as function of spatial coordinates x, y, z and of time, t (s). In Equation 1 the metabolic heat generation and the heat contribution due to blood perfusion are considered null, because the model is applied to ex vivo tissues.

As described in previous publications [5,15], laser beam irradiance, I(x,y) (Wċm⁻²), is modelled using a 2D Gaussian distribution with standard deviation, σ, equal to three times the applicator radius: where is the collimated irradiance (Wċm⁻²). The relationship between the transmitted light and the distance the light travels through a specific material, z, is usually expressed by Lambert-Beer's law. It provides an expression between laser heat source term Q_laser (Wċm⁻³) and z, taking into account the tissue optical properties (the effective attenuation coefficient, μ_eff):

Equation 3 shows that the heat-source term, thus the number of photons emitted by the laser, exponentially decreases with the distance from the applicator. This phenomenon is strongly related to the artefact. In fact, during laser irradiation the two metallic wires, which constitute the thermocouple, strongly absorb laser light causing a local increase of temperature, and, as consequence, an artefact in tissue temperature measurements. The temperature rise measured by thermocouples during laser treatment is caused by two phenomena: the light directly absorbed by the thermocouple, which causes the artefact, and the temperature increase actually caused by the tissue temperature increase. The temperature trend recorded by the thermocouples can be described by the following equation which takes into account the two phenomena mentioned [18]: where A₁ is a constant, B₁ċe^−C₁ċt is the gradual temperature variation due to the actual tissue temperature increase, and D₁ċe^−E₁ċt is the rapid component of temperature variation due to light absorbed by the thermocouple. This rapid component is evident when the laser is turned off (rapid temperature decrease) or turned on (rapid temperature increase).

The amplitude of the artefact, T_a, was calculated as the temperature increase (or decrease) experienced by the tissue during the 4 s after the laser was turned on or turned off. The threshold of 4 s has been experimentally assessed by comparing temperature trends measured by the thermocouples with the ones measured by sensors which are not affected by the artefact. During these trials we employed FBG sensors, which do not present artefacts because of their immunity from electromagnetic interferences and their low light absorption [19]. The temperature increase experienced by FBG after the 4 s was negligible during all trials; therefore we hypothesised that the increase measured by thermocouple during the time interval mentioned was caused by the direct absorption. The value of the time interval threshold (i.e. 4 s) agrees with data reported in the literature [14], where the dynamic of the artefact is considered in the order of magnitude of few seconds [20], and the temperature increase for conduction phenomenon is considered negligible in the first seconds (e.g. a time constant of hundredths of a second at 4 mm of distance from the applicator has been calculated in Saccomandi et al. [15] during pancreatic LA).

Results

Estimation of the artefact

Figure 2 shows the temperature trend, T_t, measured in two positions (bigger artefact, thermocouple inserted in hole 8; smaller artifact, thermocouple placed in the hole 5) within pancreas undergoing laser treatment at 2 W.

Figure 2. Temperature within panceras measured by thermocouple during 20 cycles of laser turned on and off at P = 2 W. Thermocouple inserted in the hole 8 (d = 5 mm, and θ = 0°) shows high artefact, thermocouple inserted in the hole 5 (d = 5 mm, θ = 53.1°) show low artefact.

Assuming the assumptions reported above are valid, the artefacts were calculated as the temperature increase or decrease experienced by the thermocouples during the first 4 s after the laser was turned on or off, respectively. The uncertainties of the artefacts for all the positions and at the two p values are reported in Table 2.

Table 2. Values of artefact magnitude at the two laser powers and at the 12 positions.

	p = 1.6 W	p = 2.0 W
Holes 1 and 5 (d = 5.0 mm; θ = 53.1°)	1.0 ± 0.1	1.9 ± 0.2
Holes 2 and 4 (d = 3.6 mm; θ = 33.7°)	4.0 ± 0.3	4.4 ± 0.3
Hole 3 (d = 3.0 mm; θ = 0°)	9.1 ± 0.4	14.0 ± 1
Holes 6 and 10 (d = 6.4 mm; θ = 38.7°)	1.0 ± 0.1	2.5 ± 0.2
Holes 7 and 9 (d = 5.4 mm; θ = 21.8°)	2.0 ± 0.1	3.0 ± 0.2
Hole 8 (d = 5.0 mm; θ = 0°)	5.5 ± 0.3	8.7 ± 0.6
Holes 11 and 15 (d = 8.1 mm; θ = 29.7°)	0	0.9 ± 0.1
Holes 12 and 14 (d = 7.3 mm; θ = 15.9°)	0.5 ± 0.1	1.9 ± 0.1
Hole 13 (d = 7.0 mm; θ = 0°)	3.0 ± 0.2	4.0 ± 0.2
Hole 16 (d = 10.0 mm; θ = 0°)	0	1.5 ± 0.1
Hole 17 (d = 12.0 mm; θ = 0°)	0	0
Hole 18 (d = 15.0 mm; θ = 0°)	0	0

As was easily predictable from the basic theory of the direct absorption, the artefact amplitude increased with p (e.g. in position 3 it is 9.1 ± 0.4 °C and 14.0 ± 0.4 °C at 1.6 W and 2.0 W, respectively) and decreases with d and θ, as shown in Table 2. In particular, the artefacts experienced by the thermocouple as a function of d and at θ = 0° show a typical exponential trend, as shown in Figure 3.

Figure 3. Artifacts amplitude vs. d at θ = 0°. Experimental data (dots) and best exponential fitting (dashed line) at P = 1.6 W; Experimental data (asterisks) and best exponential fitting (continuous line) at P = 2.0 W.

The exponential decrease of the artefact as a function of d, T_a = αċe^−βċd, can be explained by considering Equation 3, being the artefact related to the photons directly absorbed by the thermocouple, which exponentially decreases with d. Therefore the data were fitted by the following curve: α and β being two constants obtained by the fitting. The best fitting curves were obtained for α = 24.5 °C and β = 0.32 mm⁻¹ at p = 1.6 W (dashed line in Figure 3) and α = 36.0 °C and β = 0.31 mm⁻¹ at p = 2.0 W (continuous line in Figure 3). These trends seem to be reasonable: the higher p the higher α; β remains almost constant considering the two p values. This datum can be explained by considering that β is related to the light absorption within the tissue, which is constant because we performed both the trials at the two laser powers on the same tissue (i.e. pancreas).

Correction of the artefact

In order to correct the artefact recorded within the pancreases undergoing LA, a three-variables model has been employed to approximate the magnitude of the artefact at the different relative positions between the thermocouple and the laser applicator: a, b, and c being constants obtained by fitting the data obtained at p = 1.6 W with the least mean square method. The experimental data and the best fitting surface are shown in Figure 4(A).

Figure 4. Artifacts amplitude vs. d and θ. The good agreement between the three-variables model and the experimental data allows to minimize the error of measured temperature during laser irradiation.

Table 3 shows the values of these three constants (i.e. a, b, and c) obtained by fitting the data obtained at p = 1.6 W with Equation 6. It also reports the correlation coefficient (R²) and the maximum difference, ε_T, between the T_a measured by thermocouples and T_a predicted by the theoretical model (Equation 6). In order to assess the capability of the model to reduce the artefact, Equation 6 and the values of a, b and c (see Table 3) are employed on the data obtained at p = 2 W. These experimental data and the surface obtained by Equation 6 are reported in Figure 4(B).

Table 3. Values of constants obtained by fitting experimental data with Equation 6. Also R², the maximum artifacts amplitude, and the maximum difference (ε_T) between the experimental values of T_a and theoretical ones are reported.

	a (°CċW^−1)	b (mm^−1)	c (°^−1)	R^2	Ta (°C)	εT (°C)
p = 1.6 W	17.6	0.36	0.02	0.95	9.1	1.0
p = 2.0 W	17.6	0.36	0.02	0.93	14	2.8

The high R² value at the two laser powers and the low value of maximum difference (ε_T) confirms the good agreement between the experimental data and the theoretical surface (Equation 6).

The two surfaces obtained by Equation 6 were employed to minimise the magnitude of T_a. This task is performed by subtracting the predicted value of T_a to the measured one. Since the artefact is the main source of error in the measurement of tissue temperature by thermocouples during LA, this solution allows improvement of the T measurement in this scenario.

Figure 5 shows the values of T_a at the 12 positions by applying the correction (left and smaller bars) and without it (right and bigger bars) at the two p values.

Figure 5. Artefacts with and without correction at 1.6 W and 2.0 W. Each couple of bars shows the artifacts without correction (right and higher bar) and with correction (left and smaller bar). In all the twelve positions the artefact is bigger without correction, see Table 2.

Figure 5 highlights the improvement obtained by applying the correction based on Equation 6. At 1.6 W, the maximum T_a value is 1.0 ± 0.2 °C with correction vs. 9.1 ± 0.4 °C without correction; at 2.0 W, the maximum value of T_a is 2.8 ± 0.3 °C with correction vs. 14.0 ± 1 °C without correction. The mean value of T_a considering all the 12 positions has been calculated. It also shows the marked improvement obtained by employing the correction: at 1.6 W, the mean artefact is 0.5 °C with correction vs. 2.2 °C without correction; at 2.0 W, the mean artefact is 0.7 °C with correction vs. 3.5 °C without correction.

Discussion and conclusion

Laser ablation is becoming an alternative to surgery in the treatment of some tumours. In this scenario hyperthermia treatment planning (HTP) is considered important in the current clinical setting. This paradigm is confirmed by the recent decision of the European Society for Hyperthermic Oncology to include HTP in their quality assurance guidelines for deep hyperthermia [21], and by the recent development of several commercial treatment planning packages [7]. Among the most important tasks covered by a correct HTP is the prediction of the resulting temperature distribution in the tissue by numerical simulations. For pancreatic tumour especially it is fundamental to accurately predict the temperature reached within the tissue, as it could cause pancreatitis. Although it has been laboratory-proven that no pancreatitis was found after an in vivo treatment in a pig model [22] at low laser power (i.e. 2 W and 3 W), for the future an improvement of the accuracy in temperature distribution prediction by HTP packages is expected [7]. This limitation motivates the research devoted to the introduction of invasive and non-invasive techniques for temperature monitoring during hyperthermia. In fact, experimental temperature data can be useful to correct model errors and in general to provide useful information to the clinicians during the treatment. Obviously, during in vivo trials non-invasive approaches are emerging, but invasive ones are also employed because of some advantages (e.g. accuracy, short response time). Moreover, invasive approaches are largely employed in ex vivo trials, which are useful to assess the performance of model prediction or in the design of new heating equipment.

Among a range other things, thermocouples are being widely investigated during LA. The main drawback is related to the direct absorption of laser light, which causes an artefact in temperature measurements. This artefact has already been observed for many years in different tissues (e.g. canine prostate 18], bovine muscle [19], porcine fat [23], water and porcine muscle [13]) and its dependence on relative position between laser applicator and thermocouples is investigated. This relationship depends on the absorption characteristics of the medium, therefore the artefact magnitude depends on the tissue. The present work reports an experimental assessment of the artefact magnitude in healthy pancreatic porcine tissue. The findings reported here further support the strong influence of the relative position between applicator and thermocouple. Moreover, the three-variables model allows the prediction of the magnitude of the artefact, hence it can serve as a correction to the artefact. In fact, correction based on the fitting allows the minimising of the measurement error caused by the artefact: considering the twelve different relative positions tested at the two laser powers, the maximum artefact decreases from 14 ± 1 °C to 2.8 ± 0.3 °C; the mean artefact decreases from 2.2 °C to 0.5 °C at 1.6 W, and from 3.5 °C to 0.7 °C at 2 W. The slight increase in the mean artefact at 2 W with respect to the mean obtained at 1.6 W (i.e. 0.7 °C vs. 0.5 °C) can be related to the higher artefact measured at higher power without correction (3.5 °C vs. 2.2 °C).

Summing up, the major findings of the present study are: (1) the assessment of artefact in porcine pancreatic tissue. This analysis has been performed at two laser powers and at twelve different relative positions between thermocouples and laser applicator. (2) A three-variables model has been proposed to predict the magnitude of artefacts at different relative positions. The proposed fitting shows good agreement with experimental data and can serve to correct the artefacts; and (3) the correction based on the three-variables model allows the minimising of artefacts (always lower than 2.8 ± 0.3 °C).

The potential clinical impact of this work is related to the recent effort devoted to the introduction of laser ablation on pancreatic cancer treatment [23]. The correction proposed may be particularly beneficial for the minimisation of artefacts due to direct light absorption. The invasive and accurate placement of 12 sensors is not safe and is time consuming during in vivo procedures; on the other hand only one or few sensors can provide useful information during the procedure. Therefore, the proposed correction could be useful to correct temperature measurement by thermocouples within other organs undergoing laser ablation or to provide feedback to correct model errors in HTP packages. In order to perform these tasks on other organs, experiments on the target organ could be carried out to calculate the numerical values for the constants (i.e. a, b, c) in Equation 6.

In our study 12 different positions have been analysed in order to report and correct the artefact, obtaining encouraging results. Obviously, during in vivo trials the application of 12 different sensors is not feasible; it is preferable to use non-invasive techniques, even if it is a matter of discussion, in so far as there are some drawbacks in the usage of these methods (e.g. CT-scan uses X-rays). To the best of our knowledge, the minimum number of thermocouples that could be used during hyperthermia treatment is not reported in published literature. During an in vivo trial on a rabbit model, one FBG sensor was used to measure the temperature increase of liver and kidney tumour, as reported by Webb et al. [24]. Lastly we would like to remark that the measurements performed in 12 positions will have been useful to provide a model to correct artefact that can be used during future trials employing a general number of thermocouples.

One of the major limitations of the study is that the trials were performed on healthy ex vivo porcine pancreases. Since there are substantial differences between the optical properties of the healthy pancreas and the tumour tissue, the artefact will be different in the clinical scenario. It is not possible to perform a numerical prediction of the difference because the optical property values of pancreatic tumours are lacking in the published literature. Also, the changes of the optical properties with temperature and during tissue coagulation may influence the artefact, although the artefact happens during the first seconds after the laser is turned on, when tissue coagulation is absent. Moreover, the coagulation influences the thermal properties of the tissue and consequently the heat transfer phenomenon. We minimised this effect by replacing the pancreas after each treatment. A further limitation is that the optical properties are also influenced by the wavelength of the laser power, and in this work all the trials are performed at only one wavelength (i.e. 1064 nm). Lastly, the trials were performed at only two laser powers and, although we chose low power in order to avoid pancreatitis, the model prediction should be assessed considering a wider range of laser power.

Declaration of interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.