Department of Mathematics, University of Dayton, 300 College Park Ave., Dayton, OH 45469, USA

Department of Biology, University of Dayton, 300 College Park Ave., Dayton, OH 45469, USA

Department of Mechanical and Aerospace Engineering, University of Dayton, 300 College Park Ave., Dayton, OH 45469, USA

Abstract

Background

Energy-based surgical scalpels are designed to efficiently transect and seal blood vessels using thermal energy to promote protein denaturation and coagulation. Assessment and design improvement of ultrasonic scalpel performance relies on both in vivo and ex vivo testing. The objective of this work was to design and implement a robust, experimental test matrix with randomization restrictions and predictive statistical power, which allowed for identification of those experimental variables that may affect the quality of the seal obtained ex vivo.

Methods

The design of the experiment included three factors: temperature (two levels); the type of solution used to perfuse the artery during transection (three types); and artery type (two types) resulting in a total of twelve possible treatment combinations. Burst pressures of porcine carotid and renal arteries sealed ex vivo were assigned as the response variable.

Results

The experimental test matrix was designed and carried out as a split-plot experiment in order to assess the contributions of several variables and their interactions while accounting for randomization restrictions present in the experimental setup. The statistical software package SAS was utilized and PROC MIXED was used to account for the randomization restrictions in the split-plot design. The combination of temperature, solution, and vessel type had a statistically significant impact on seal quality.

Conclusions

The design and implementation of a split-plot experimental test-matrix provided a mechanism for addressing the existing technical randomization restrictions of ex vivo ultrasonic scalpel performance testing, while preserving the ability to examine the potential effects of independent factors or variables. This method for generating the experimental design and the statistical analyses of the resulting data are adaptable to a wide variety of experimental problems involving large-scale tissue-based studies of medical or experimental device efficacy and performance.

Background

Blood vessel transection and sealing requires that tissue segments be held together with an immediate and temporary bond that prevents leakage and holds long enough to allow the adjacent tissue margins to re-grow, heal, and regenerate structural connections through the natural healing process. Energy-based vessel sealing methods use no exogenous materials to accomplish vessel closure, but rely on acute vessel compression, thermally induced tissue injury, and tissue healing to generate the seal. This process limits inflammation and eliminates concerns with biocompatibility and immunogenicity associated with using an exogenous material such as sutures, staples, or bonding adhesives. In addition, energy-based methods are easier and faster to use than materials-based methods, especially for endoscopic surgeries, resulting in a decrease in operative time and surgical invasiveness, and reduced infection rates. Ultrasonic scalpel technology has been used extensively in fine tissue dissection, hemostasis, vessel closure and transection

Methods

Porcine vessel sealing and burst pressure test

Porcine vessel sealing and burst pressure testing were performed as previously described ^{® }software was used to record the data.

Biostatistical experimental matrix design

The design included three factors: The temperature of the solution (Temp - two levels; ambient (23°C) or 37°C), the type of solution that was utilized (Sol - three types; 0.9% saline; 6% Hetastarch (HES); "Plasma protein" enriched buffer (95% Hanks balanced salt solution, 4.7% bovine serum albumin fraction V, 0.36% fibrinogen type IV)) and the type of vascular tissue used (Vessel - two types; carotid or renal artery).

Sample size calculation

A number of preliminary experiments (n = 4-12) were carried out as described above. The data were used to perform basic sample size computations to aid in determining the sample size for the main experiment. All computations were based on comparisons of two means. To determine the sample size necessary to detect a significant difference between the means of two factors at a desired significance level and with given power, the observed sample means and the pooled standard deviation corresponding to the two factors from the pilot were computed. The Analyst application in SAS was utilized to compute the sample sizes. The input consisted of the two observed sample means, the pooled standard deviation, the desired significance level and the desired power for the test.

Statistical analyses of the data

The statistical package SAS was used to carry out the data analysis. The factors temperature, solution and vessel type, as well as "Session" (with 48 levels) were declared as class variables for the analysis of variance. To incorporate the information about the randomization restrictions discussed above, PROC MIXED was used, and Session was declared as a random effect as suggested in

SAS code

PROC MIXED data = dataset;

CLASS Session Temp Sol Vessel;

MODEL response = Temp|Sol|Vessel;

RANDOM session;

RUN;

Interpretation of SAS output

SAS computed the ANOVA table displaying the p-values for the main effects (temperature, solution and vessel type) and their interactions. Using the significance level of 0.05, a p-value of less than 0.05 indicates a (statistically) significant main effect or interaction effect.

Results

The objective of this work was to design and implement a robust, experimental test matrix with randomization restrictions and predictive statistical power, which allowed for identification of those experimental variables that may affect the quality of the seal obtained ex vivo. A number of pilot studies using small sample sizes were initially performed to determine which variables likely contribute to seal quality and therefore should be included in the test design. The factors initially studied included temperature of the solution, type of infusion solution, vessel type, and infusion flow rate during blood vessel transection/sealing. The response variable in each case was the burst pressure (mmHg) at which the seal failed.

In addition, the pilot data was used to estimate the sample size needed to obtain significant results (at a significance level of 0.05) with a power of 0.9, or the probability that a test with the specified assumptions (sample size, observed difference of means, observed pooled standard deviation, and type of alternative hypothesis) would correctly reject the null hypothesis when the alternative hypothesis was true. Given the minimum desired detectable difference, as well as (an estimation for) the standard deviation and the desired significance level of the test, the sample size that was necessary for a two-sample test to have a given power was computed. The sample size computations were based on pairwise comparisons, in which each factor level was examined as to its potential effect on burst pressure. In some cases, it was clear that these comparisons were not trending towards showing significant differences, and the corresponding factors (or factor levels) were therefore not included in the experimental design. However, those comparisons that were not statistically significant in the pilot study due to small sample size but showed a trend toward predicted statistical significant differences with an increased sample size (based on the power calculation) were included in the experimental design. In addition, the interaction effects of the included factors (comparisons between combinations of two or three factors) were deemed important to assess.

Based on the pilot studies, the effects of solution temperature, solution type, and vessel type were chosen to be studied. Taking into account the sample size computations made from the pilot study and the practical limitations imposed by the experimental test setup, the size of the matrix and experimental design was determined. A balanced design for the test matrix was selected where each treatment combination was observed the same number of times. The experiment included three factors, with a total of 12 possible treatment combinations. While the vessel type could be varied at random from run to run, the temperature and solution were hard-to-change factors. This physical reality forced randomization restrictions on the design. The experiment consisted of 480 runs (40 per treatment combination), divided into 48 sessions of 10 runs each. For each session, one of the six combinations of levels for temperature and solution was chosen (each combination was used for eight different sessions) and held fixed. The assignment of the treatment combinations to the sessions was carried out at random. This assignment was done in Excel. Using a column for temperature and a column for solution, eight copies of the treatment combinations of temperature and solution were generated. A third column contained random numbers. The data in the three columns was then sorted in ascending order of the random numbers to create a random order of the treatment combinations. The treatment combinations were then assigned to the 48 sessions in that order. Each session contained ten runs (five runs per vessel type) chosen in random order using the same procedure in Excel. The procedure to generate a random order of the sessions is shown in Table

Two copies of the six Temperature/Solution combinations, plus a column of random numbers.

**Temperature**

**Solution**

**Random number**

Temp1

Sol1

0.617940611

Temp1

Sol2

0.739488341

Temp1

Sol3

0.088714721

Temp2

Sol1

0.556090887

Temp2

Sol2

0.55227804

Temp2

Sol3

0.691030612

Temp1

Sol1

0.286876071

Temp1

Sol2

0.535759581

Temp1

Sol3

0.882488882

Temp2

Sol1

0.981425728

Temp2

Sol2

0.228304389

Temp2

Sol3

0.606414609

Two copies of the six Temperature/Solution combinations, ordered by the size of the random numbers.

**Temperature**

**Solution**

**Random number**

Temp1

Sol3

0.088714721

Temp2

Sol2

0.228304389

Temp1

Sol1

0.286876071

Temp1

Sol2

0.535759581

Temp2

Sol2

0.55227804

Temp2

Sol1

0.556090887

Temp2

Sol3

0.606414609

Temp1

Sol1

0.617940611

Temp2

Sol3

0.691030612

Temp1

Sol2

0.739488341

Temp1

Sol3

0.882488882

Temp2

Sol1

0.981425728

The twelve sessions in random order.

**Session**

**Temperature**

**Solution**

1

Temp1

Sol3

2

Temp2

Sol2

3

Temp1

Sol1

4

Temp1

Sol2

5

Temp2

Sol2

6

Temp2

Sol1

7

Temp2

Sol3

8

Temp1

Sol1

9

Temp2

Sol3

10

Temp1

Sol2

11

Temp1

Sol3

12

Temp2

Sol1

An analysis of variance was conducted to determine the effects of the factors and their interactions. The resulting ANOVA table is shown in Table

ANOVA Table.

**Effect**

**Num DF**

**Den DF**

**F Value**

**Pr > F**

Sol

2

426

0.21

0.812

Temp

1

426

1.14

0.2857

Sol*Temp

2

426

0.05

0.949

Vessel

1

426

2.65

0.1045

Sol*Vessel

2

426

0.83

0.4354

Temp*Vessel

1

426

1.36

0.2449

Sol*Temp*Vessel

2

426

3.64

0.027

Num DF = numerator degrees of freedom, Den DF = denominator degrees of freedom for the corresponding sum of squares. F Value = value of the corresponding F distribution. Pr > F = p-value.

Discussion

Assessing the efficacy of surgical device performance ex vivo is dependent upon the quality of the experimental design, and the ability of the test to control or measure those variables that contribute to device performance. Careful design of the experimental test matrix is an important first step in this process. Failure to appropriately consider practical limitations on randomization can substantially compromise the utility and significance of the data generated. The biostatistical methods described in this report provide a procedural model for the development of the design of factorial experiments that have randomization restrictions. Since the impact of more than two factors on a response variable were assessed in this experiment, it was appropriate to carry out an analysis of variance. However, an underlying assumption for the validity of the usual analysis of variance for a complete factorial design is that the runs are observed in a completely randomized order

Acute collateral damage, although expected, was not examined in this study. Histopathology is commonly used to estimate the extent and degree of thermally-induced coagulative necrosis and protein denaturation incurred in relation to the distance from the point of energy application

Conclusions

From this investigation, it was determined that the design and implementation of a split-plot experimental test-matrix provided a mechanism for addressing the existing technical randomization restrictions in a statistically meaningful way, while preserving the ability to examine the potential combinatorial effects of independent factors or variables that can be assessed in ex vivo testing. This type of approach would likely be useful to a broad spectrum of medical device researchers who must attempt to recapitulate in vivo conditions, ex vivo.

Competing interests

This research was funded by an industrial research contract from Ethicon Endo-Surgeries, Blue Ash, OH, to the University of Dayton. Publication costs are being defrayed by the University of Dayton through an unrestricted research account (CMK). The authors do not hold any stocks or patents related to this work.

Authors' contributions

WSD carried out the design of the experiment, generated the split plot design with randomization restriction, and performed the statistical analyses.

CMK jointly conceived of the study (with MFP), participated in the design and implementation of the experimental test set up, trained student research assistants, conducted vessel burst pressure testing, contributed to the interpretation of the data analysis, and jointly oversaw project coordination.

MFP jointly conceived of the study (with CMK), participated in the design and implementation of the experimental test set up, trained student research assistants, conducted vessel burst pressure testing, performed the data analysis, and jointly oversaw project coordination. All co-authors contributed to the preparation of the manuscript, and have read and approve the final manuscript.

Acknowledgements

The authors would like to thank University of Dayton undergraduate students Courtney Gardner, Emily Kitchin, Anne Klapheke, Mercedes Thompson, Kevin Timms, and Eric Whitney for their technical assistance, and Dr. Peter Hovey, Department of Mathematics, University of Dayton, for critical review of this manuscript. This research was funded by an industrial research contract from Ethicon Endo-Surgery, Blue Ash, OH, to the University of Dayton.

Pre-publication history

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