# In silico evaluation of geometry variations with respect to the thermal spread during coagulation of egg white using bipolar vessel sealing instruments

- Jay Wagenpfeil
^{1}Email authorView ORCID ID profile, - Christina Schöllig
^{1, 2}, - Volker Mayer
^{3}, - Ronny Feuer
^{1}, - Bernhard Nold
^{3}, - Alexander Neugebauer
^{3}, - Michael Ederer
^{3}, - Ralf Rothmund
^{4}, - Bernhard Krämer
^{4}, - Sara Brucker
^{4}, - Markus Enderle
^{3}, - Oliver Sawodny
^{1}and - Julia Rex
^{1}

**15**:117

https://doi.org/10.1186/s12938-016-0238-2

© The Author(s) 2016

**Received: **16 August 2016

**Accepted: **24 October 2016

**Published: **2 November 2016

## Abstract

### Background

Bipolar vessel sealing is an efficient electrosurgical procedure for the occlusion of blood vessels particularly during minimally invasive surgery. Reliable knowledge of the thermal spread is crucial for a safe application of bipolar vessel sealing instruments when operating close to thermo-sensitive structures, such as nerves. The evolution of the thermal spread over time and space depends on a variety of parameters, such as the biological tissue, the energy applied to the tissue, and the geometry of the vessel sealing instrument. Mathematical modeling has proven useful for the prediction of the thermal spread. It is, thus, a promising tool for the systematic analysis of the influence of geometrical changes on the thermal spread.

### Results

We present an experimentally validated in silico study to evaluate the impact of geometry variations on the progression of chicken egg white coagulation and the final shape of coagulated egg white as an approximation of the temporal and spatial evolution of the thermal spread during bipolar vessel sealing. Egg white has similar thermal and electrical properties to human tissue, with the advantage being that the spatial and temporal evolution of the thermal spread can be visually gauged. The simulations were performed using a mathematical model based on the finite element analysis of chicken egg white. The progression of egg white coagulation was predicted for two different peak voltages and various electrode geometries. Starting with two planar electrodes, one electrode was gradually changed to adopt a wedge shape. These changes to the geometry showed a distinct influence on the progression of egg white coagulation in the simulations. The predictions were successfully validated using an experimental setup with two different electrodes representing the extreme geometries.

### Discussion

The predicted spatial temperature distributions were experimentally validated for two geometries. Our simulation study shows that the geometry has a pronounced influence on the thermal spread and, thus, is a suitable parameter to reduce thermal damage. The in silico optimization of instrument designs is a suitable tool to accelerate the development of new vessel sealing instruments, with only a few promising designs having to be tested as prototypes.

### Keywords

Bipolar vessel sealing Thermal spread Mathematical modeling Finite element analysis Egg white model## Background

An improved understanding of the parameters influencing the extent of the thermal spread into the lateral tissue is essential for a substantiated assessment and advancement of thermofusion instruments, an understanding that allows for safe usage, also in more delicate surgical procedures. Several studies compared different electrothermal vessel sealing methods and instruments, using both ex vivo [10, 11] and in vivo models [12–15], and investigated the thermal spread. The thermal damage to the tissue is generally investigated using histomorphological analysis at the end of the thermofusion process. A major disadvantage of this technique is that only the resulting overall damage to the tissue can be captured without consideration of the dynamic distribution of the thermal spread during the process. Information about the temperature distribution over time and space can be partially provided by the use of infrared cameras. Thermal imaging is, however, limited to measuring the surface temperature of the tissue. Sensors were therefore inserted into the tissue in a few studies to measure temperatures below the surface. Due to restricted space, the number of sensors and thus the information provided remains limited.

A mathematical model of the vessel sealing process allows for a more systematic investigation and provides deeper insight into the evolution of the process variables, such as the tissue temperature at any given point in time and space. Most of the reported models use finite elements (FE) for a coupled simulation of the electric field and the tissue’s temperature. A major challenge is the high complexity and the validation of such models, which has thus far significantly limited the application of mathematical models in electrosurgery. Dodde et al. [16] developed a thermo-electric model to study the temperature distribution during bipolar electrosurgery. This model was then extended to account for changes in the specific heat capacity, electrical resistance and water contents of the tissue during the thermofusion process [17]. Gonzalez-Suarez et al. [18] developed another FE model to investigate the thermal spread when using a bipolar instrument with internally cooled electrodes. In a previous work [19] we established an egg-white model for the experimental investigation of the thermal spread caused by bipolar vessel sealing devices. This experimental model was accompanied by a validated mathematical model of the coupled heat transfer and electrostatic partial differential equations (PDEs). The mathematical model allows for the detailed study of the thermal spread’s progression and local inhomogeneities of the spatial temperature distribution. Since egg-white has thermal and electrical properties very similar to those of human or animal tissue with high water contents [20, 21], it is a suitable replacement for tissue in many cases, with the benefit being that egg white is much more available than animal tissue. The main benefit of using egg white is the fact that the denaturation process—which occurs between 57 and 63 °C—can be visually observed. This allows for the verification and validation of the mathematical model’s transient behavior, particularly with respect to the formation of hotspots and the evolution of the thermal spread.

These studies demonstrate that mathematical modeling is a valid tool for analyzing the influence of process parameters on the temperature distribution before experimental testing. An important parameter is the design and geometry of the bipolar instrument’s forceps. Improved forceps designs have the potential of significantly reducing thermal damage [22]. Zhao et al. [23] compared a concave–convex electrode geometry with a conventional smooth electrode during colonic anastomoses. They found that the concave–convex geometry positively influenced the thermal diffusion and could possibly reduce the risk of thermal necrosis. Rothmund et al. [15] found that the use of instruments with large electrodes and correspondingly large heat capacity may have an adverse influence on the thermal damage under certain circumstances. Several other studies, e.g., [11, 16, 24], have shown that thermal damage can differ significantly between vessel sealing instruments. A systematic optimization of the instrument geometry remains, however, difficult. So far, the largest challenge is there is no way to assess the effect of geometry changes a priori. Instead, it has to be evaluated in experimental testing with a sufficiently high sample size. This is a time-consuming and cost-intensive process and, due to the high variability of biological tissue [25], it is often difficult to deduct a clear relationship. Here, a validated mathematical model can unfold its full potential.

The aim of this study is to investigate variations of the electrode geometry with respect to the spatial and temporal evolution of the thermal spread during the coagulation of egg white. We use our previously developed mathematical model [19] to evaluate the influence of geometry variations in silico. The thermal spread predicted by the mathematical model is experimentally validated for two geometries. The proposed combination of in silico analysis of parameter variations and few experimental validations of distinct parameter combinations has the potential to drastically reduce the number of prototypes required and thus accelerate the development process.

In the following, we will illustrate how a mathematical process model can be used to predict the coagulation of egg white for different instrument geometries. The results will be evaluated with particular focus on the formation of hotspots and the spatial temperature distribution, i.e. the shape of the coagulated egg white in the predictions. The paper is organized as follows. In "Methods" section, the mathematical modeling approach is briefly reviewed and the simulation study as well as the corresponding experimental setup is described. The results of the simulation study and the validation experiments are presented in "Results" section and discussed in "Discussion" section. A properly verified model is the basic requirement for obtaining meaningful predictions. The simulations in [19] were obtained using slightly differing values of the electrical conductivity of egg white, which resulted in small errors with respect to the temporal dynamics. These errors did not affect the general statement of [19], but with regard to the goal of the study at hand, proper verification results are given in Appendix 2.

## Methods

### Mathematical model

*t*and the spatial coordinates \(\xi\). The density \(\rho\), the heat capacity

*c*, and the thermal conductivity

*k*are assumed to be constant in the relevant temperature range. Please refer to Table 1 for the parameter values used in the simulations. Refer to Appendix 1 for a detailed description of crucial parameter values and their derivation, particularly the temperature dependent conductivity of egg white \(\sigma (T)\) which has a distinct influence on the coagulation process.

Material properties used in the simulations

Property | Egg white | Electrode | Isolator |
---|---|---|---|

Density \(\rho \; ({\rm kg}/{{\rm m}^3})\) | 1030 | 8000 | 1030 |

Specific heat capacity \(c \; ({\rm kJ}/{{\rm kg}\,{\rm K}})\) | 3.550 | 500 | 2200 |

Thermal conductivity \(k \; ({\rm W}/{{\rm m}\,{\rm K}})\) | 0.55 | 15 | 0.25 |

Electrical conductivity \(\sigma \; ({\rm S}{\rm m})\) | 0.74–1.9 | 1.33 × 10 | 1.0 × 10 |

### Simulation study and experimental setup

For the simulation results presented in this paper, the PDE system was discretized via the Finite Element Method (FEM) using the software ANSYS 15.0. Starting from a typical instrument geometry with two planar electrodes, one of the two electrodes increasingly assumed a wedge shape. The planar electrode had a conductive area of 5.7 by 20 mm and a thickness of 4.7 mm. The electrodes were covered with a 0.15 mm thick isolating material on the non-conducting surfaces. Five different heights of the wedge were investigated, namely 0, 0.1, 0.5, 1.0 and 2.85 mm, corresponding to wedge angles of 180°, 176°, 160°, 141° and 90° respectively. The wedge was added to one of the two electrodes. Zero wedge height, respectively a wedge angle of 180°, is equivalent to a planar electrode. The distance between the tip of the wedge and the opposing planar electrode was kept at 1 mm independent of the wedge height. In our previous work we saw that the shape of the coagulated egg white distinctly differed depending on the applied voltage. Therefore, two generator settings with peak voltages of 35 and 165 V_{p}, respectively, were selected for the simulation study.

The setups of the simulation study and the validation experiment were developed in parallel to ensure that the simulation results be easily comparable with experimental data. In a first attempt, the complete experimental setup was modeled—the instrument’s two jaws and the whole surrounding egg white (see Fig. 2b, upper segment). Simulation results showed that the coagulation process between the electrodes is nearly homogeneous along the *z*-axis (parallel to the instrument jaws). Only a small cutout of the instrument’s central part was modeled for the simulation study (see the lower section of Fig. 2b), thus reducing the necessary number of finite elements to less than 21,000 while still achieving a high resolution with respect to the *x*-*y*-plane.

## Results

### Simulation study

We conducted an in silico study to investigate how the geometry of the electrodes influence the progression of egg white coagulation and the shape of the coagulated egg white, and the thermal spread using our previously published model [19]. Starting from a typical setting with two planar electrodes, namely a wedge angle of 180°, one of the electrodes was changed to a wedge shape with 176°, 160°, 141° and 90°, respectively. Simulations were performed for all five geometries at peak voltages of 35 and \(165\,{V_p}\), respectively.

#### Low voltage (\(35\,{V_p}\))

As the upper electrode obtains an increasingly narrow wedge shape, the coagulation process becomes slower, whereas the initial time point of egg white coagulation is only slightly postponed. Furthermore, the clot shape is significantly affected by the electrode’s geometry. Even the introduction of a slight wedge shape, for instance, altering the wedge angle about just 4°, considerably changes the shape of the coagulated egg white (second column of Fig. 3). Still, the coagulation zone manifests itself between the electrodes, but more in the center as an oval around the symmetry line. The coagulation spreads in an elliptical shape in the early stages. Then it approaches a more rectangular form similar to the planar electrodes with more rounded corners, until almost all of the egg white between the electrodes is coagulated. This occurs at 0.38 s after the formation of the initial clot and at 0.8 s after the start of the simulation.

With decreasing wedge angles, the initially formed clot becomes increasingly punctiform. It shifts towards the tip of the upper electrode. For the electrode with a wedge angle of 160° (third column of Fig. 3), the clot shape remains elliptical during the coagulation process. Even the final shape of the coagulated egg white maintains strongly rounded corners and does not fill all the space between the two electrodes. If the wedge angle is further decreased to 141°, the clot’s intermediate shape changes again and takes on a kidney-like appearance (forth column of Fig. 3), which is even more pronounced for a wedge angle of 90° (fifth column of Fig. 3). The coagulation process in these cases is significantly prolonged and lasts 1.5 and 3 s, respectively. In the case of the steepest wedge shape, this also leads to the heating of the electrode’s tip. The final shape of the coagulated egg white exhibits heavily rounded corners on the side facing the upper electrode, and in both cases does not reach the upper electrode’s surface.

#### High voltage (\(165\,{V_p}\))

### Experimental validation

#### Instrument A

#### Instrument B

## Discussion

### Effect of geometry variations

The simulation study shows a pronounced influence of the electrode’s geometry on the progression of coagulation. An increasingly pronounced wedge-shape results in an increasingly inhomogeneous spatial temperature distribution. Consequently, the initial coagulation zone becomes smaller. It only expands in an increasingly slow manner.

The simulation study illustrates that the geometry of the electrodes is a suitable parameter to selectively influence the temperature distribution. It becomes clear, however, that more complex geometries are required. The implementation and optimization of such geometries can be mostly done in silico and has to be validated by experiments with actual prototypes but only at certain milestones. This work-flow has the potential to significantly accelerate the development process of optimized instrument geometries in a cost-efficient way.

### Validation

The mathematical model captures well the spatial dynamics of the coagulation process. Hotspots, those areas where the coagulation process begins, and the shape of the coagulated egg white are well predicted by the model. The experimental results confirm the distinct influence of both the electrode’s geometry as well as the applied voltage seen in the simulation study. A thin layer of liquid egg white between the coagulated egg white and the planar electrode(s) is seen both in the simulations and the experiments for most of the duration of the coagulation process. The electrodes cool the surrounding egg white and prevent its coagulation. An exception are the edges of the electrodes, where, at high voltages, the high current density causes the egg white to coagulate in those parts.

The temporal dynamics, namely the speed of the coagulation progression, differ significantly from the predicted course, which is also consistent with our previous findings. Actual coagulation commencement at low voltages is approximately ten times slower in the experiments and three to four times slower than predicted by the simulations at high voltages. As already discussed in [19], this large discrepancy cannot be attributed to the modeling approach with the cutout-model since the same behavior was observed when using a model of the full setup. A possible explanation has been to date non-modeled resistances which may prove important when the electrical resistance of the egg white is small due to the close distance of the electrodes. Such resistances might be the contact resistance between the egg white and the electrodes, inductive resistances due to cables, or capacitive resistances caused by the bubbles in the egg white. These resistances are, however, expected to be small. The resulting influence should be far less pronounced.

In our analysis of the experimental results, we found that the AC generator supplied significantly less power than expected. For the validation experiments we used a commercial electrosurgical generator in a voltage controlled mode of operation. It appears, however, that from the point of view of the generator the coagulation of egg white substantially differs from the vessel sealing applications for which it has been designed and optimized. We noticed that the power factor of the generator falls as low as 40% in some experiments with \(35\,{V_p}\). This means that at the same voltage level, the actual power output is up to 60% lower compared to the simulations, where an ideal power factor of 100% is assumed. Even at high power settings, the power factor never exceeded 70%. In future validation experiments it is important to choose a power supply that is capable of applying the same energy as in the simulations, e.g. by using a power controlled signal generator. Extending the model to represent the complete electrical setup, including the AC generator, could be another way of significantly improving the quality of predictions with respect to the temporal dynamics.

We also found in video captures of the experiments that there are signs of convective movement. It appears that liquid egg white allows for a significant convective flow of heat. This is another possible reason for the large discrepancy of the temporal dynamics between the simulations and the experiments, particularly at low voltages where the overall progress is slow and heat losses, due to convective heat flows, have all the more influence. The impact of convective heat flow could be investigated in a future work using computational fluid dynamics (CFD) analysis. Additionally, the forceps of the actual instruments are not exactly parallel but open slightly towards the end of the instrument. This means, that there is effectively more egg white between the electrodes in the experiments, resulting in an increased resistance and heat capacity and thus slower heating of the egg white. While the opening angle is small, preliminary studies show that the coagulation speed is indeed reduced if the instrument is modeled more accurately in the simulation.

## Conclusions

In this work, we used our previously developed mathematical model of the egg white coagulation process to evaluate the influence of changes of the electrode geometry on the evolution of the thermal spread. The presented simulation study shows a distinct influence of the geometry on the shape of coagulated egg white. The validation of the simulations revealed that the spatial temperature distribution is properly predicted by the model despite rather large differences regarding the temporal dynamics. The results demonstrate that the proposed in silico evaluation of parameter variations—such as geometry changes—combined with supporting validation experiments is a promising tool for the systematic development and accelerated optimization of vessel sealing devices.

The deviations of the temporal dynamics may be partly explained by non-modeled effects of the coagulation process. There are three aspects of the experimental setup that we think attribute primarily to the observed deviations. First, we used an AC generator that is optimized for vessel sealing applications but supplied reduced power when coagulating egg white. Second, convective heat flows were not considered in the simulation model, but could have had a significant influence on the temperature of the egg white between the electrodes. Third, the jaws of the instrument were not parallel but slightly opened in the simulations, leading to more egg white between the electrodes. Considering these aspects in future works should significantly reduce the deviations of the temporal dynamics between the simulation and experimental results and make the proposed work flow even more advantageous.

## Declarations

### Authors' contributions

Design of the simulation study: JW and OS. Design of the experiments: CS, VM, BN, AN, MiE. Carrying out the experiments: CS, VM, BN. Evaluation of results: JW, CS, VM, BN, AN, MiE. Drafting of the manuscript: JW, JR, and OS. Critical revision and evaluation of manuscript from a technical point of view: BN, AN, RF. Critical revision and evaluation of manuscript from a medical point of view: RR, BK, SB. Project supervision: MaE, SB, OS. All authors read and approved the final manuscript.

### Acknowledgements

Not applicable.

### Competing interests

BN, AN, MiE, and MaE work for Erbe Elektromedizin GmbH. The authors declare that they have no competing interests.

### Funding

This work was supported by the German federal state Baden-Württemberg, the Erbe Elektromedizin GmbH, and the universities of Tübingen and Stuttgart within the Industry on Campus projects of the Inter-University Center for Medical Technology Stuttgart-Tübingen (IZST).

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## Authors’ Affiliations

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