Assessing the Extent of Skin Damage after Exposure to Hot Fluids

By: Preston Hoang (ID: 58904993) Alex Almanza (ID: 32214258)

Abstract How dangerous is it to spill a cup of coffee in your lap? In order to give a precise answer

to this question, we want to have precise, quantitative answers and to address specific variables such as the amount of skin burnt..

With the use of MATLAB, it is easy to meet the two aforementioned criteria. We answer

this question by using a finite­difference model for convection conduction. Essentially, we divided the different layers of skin into individual nodal sections, then used a set of partial differential equations to estimate the temperature at each node (these skin nodes will later be referred to as the “temperature vector”). The precise computational method we have implemented in our study follows closely to one outlined by Diller for use in excel [1]. Nevertheless, since we used MATLAB there are some differences. For instance, the architecture of our code uses two for­loops: one to update the elements of the temperature vector, and one to increase the time­step by a deltaT. We set the convection process for the first node, then the diffusion process for the rest of the skin.

After running the simulation, we have reached the following conclusions. Modifying the

ambient (environment) temperature has minimal effect on the extent of a burn when viewed over short time periods, but becomes an important factor as the observed time period is increased. Similarly, changing the heat transfer constants has only minor effects on the burn. And, when comparing time vs. accumulated skin damage, the accumulated skin damage begins to increase logarithmically as time progresses.

Introduction: In 1994, Liebeck won approximately $3 million dollars in damages as a result of

third­degree burns from a McDonald's coffee cup [2]. Although this case has been touted as frivolous by media and commentators, it also underscores the importance of scalding and burns.

According the American Burn Association, there have been 50,000 reported cases of

scald burns in the United States [3]. Out of the selected group, the ones that are most affected are the elderly and young children. The elderly are a high­risk group since they have thinner skins with lower, which leaves them vulnerable to deeper burns compared to other categories of individuals [4]. In addition, children are also likely to be burned due to their lack of ability to comprehend danger, and to escape a situation involving burns [4]. It is also important to address the severity of scald burns since most of these injuries have occurred at home. As a result, most of these injuries are preventable by changing one’s habits and environment. Although some burns can be superficial, there are other cases (i.e. third­degree burns) that may require immediate medical treatment such as skin grafting [5]. Due to these growing number of scalding cases, my partner and I are compelled to study this phenomena in more detail.

Our study objective is to quantitatively assess the extent of the burn damage in skin after exposure to a hot liquid. In order to achieve that objective, we will use MatLab to simulate the effects of a burn using a finite difference model. As mentioned earlier, my partner and I have written a program that uses partial differential equations to model the temperature at different points of the skin. We hope this information can provide better understanding and awareness of how burns can operate. This would enable medical doctors and other practitioner’s to make better judgements on how to treat the patient’s ailments. Guided Questions:

Given a constant coffee temperature, how will changing the environmental temperature (i.e. T_inf), affect the severity of a skin burn?

After the coffee has been spilled, how does time play a role in determining the extent of

the skin damage? (i.e. 90 seconds vs. 10 seconds)

From the McDonald’s case, it is not evidently clear that the woman’s car had her air­conditioner on. How would a running air­conditioner (i.e. forced convection) affect the extent of the skin damage?

GUIDING QUESTION: Given a constant coffee temperature, how will changing the environmental temperature (i.e. T_inf), affect the severity of a skin burn? Introduction. When a hot liquid is spilt on skin, the liquid­skin interface will likely be in an open air environment. As a result, there will be both conductive as well as convective forms of heat transfer. This means some appreciable amount of cooling is logically going to occur, especially in sub­zero temperatures. In order for us to accurately model skin burns, it is therefore important for us to understand how ambient temperature relates to the severity of a skin burn. Approach. In order to test the extent of convective cooling, our 1d model was run for two sets of seven iterations. During each set of seven iterations, the ambient temperature was the only variable that was altered. Moreover, between each set the observed time span was altered . With this particular approach, we were able to observe how different ambient temperature relate to the relative severity of a burn for time spans both short and long. Moreover, this approach allowed us to compare how great a factor the ambient temperature plays within the overall working of our 1d model. Data.

Figure A

Key results From our results, we learned that the ambient temperature only has an appreciable effect on the severity of a burn when the burn is acquired over a prolonged period of time. For burns that happen quickly, the ambient temperature plays little role in the extent of tissue damage. This is revealed in the above graph. Looking at the set that was conducted over a longer period of time, a distinct curve for each of the seven temperatures is clearly visible. In that particular set, the iterations involving cooler ambient temperatures had lower overall nodal temperatures and therefore lesser tissue damage. Conversely, there is little variance for each curve belonging to the iterations of the set with a shorter time period.Thus, the ambient temperature played little part in the extent of the acquired tissue damage. With these two facts in mind, we now understand that scald burns acquired in warmer climates will likely be the most damaging.

Guiding Question: After coffee has been spilled, how does time play a role in determining the extent of the skin damage? (i.e. 90 seconds vs. 10 seconds) Introduction: Time is an important factor (independent variable) in assessing the extent of the skin damage. Intuitively, the longer a person is exposed to a hot surface, the more skin damage they accumulate. In order to refine our understanding, we want to establish a quantitative relationship between both variables. Approach: In order to address this question, we use the finite­difference model for heat transfer. To explain, what we did was divide the three skin layers into nodes, each with their own Δx. After running the convection model for 45 seconds (with a time­step of ≈ 0.006 seconds), we assess the skin damage at each interval. When the skin is exposed to temperatures ≥ 44C, it starts to break down due to proteins losing their 3D structure [2]. With this fact in mind, we created a function that basically checks the temperature of each node sequentially. When we reach a node that is under that temperature threshold (44C), we add up the Δx values to get the total skin damage. Data

Figure B

Key results: Skin damage accumulates logarithmically as a function of time. Since the body goes through homeostasis, it slows down (but does not stop) the extent of the skin damage.

Guiding Question: From the McDonald’s case, it is not evidently clear that the woman’s car had her air­conditioner on. How would a running air­conditioner (i.e. forced vs. unforced convection) affect the extent of skin damage? Introduction: An accurate model needs to account for significant factors such as convection. If the hot liquid is spilled, it may be possible to prevent significant burns by cooling it via air conditioning. Approach: In order to address this question, we run the finite­difference convection model multiple times using different H­values. To explain, the H­values represent the heat transfer coefficients for convection. At higher values, there is more heat transferred between the surface and the fluid (i.e. air, water). The convective heat transfer coefficient for forced air convection (i.e. air conditioners) is 100 ­ 200 W/m^2K [8]. For free air convection, the coefficient value lowers to 5 W/m^2K [8]. With these values in mind, we ran a for­loop that checks all the H­values from 0 to 200. Data:

Figure C

Key results: Based on the left graph, the skin damage accumulated for both the free air convection (i.e. 5 W/m^2K) and forced air convection is roughly the same (i.e. 200 W/m^2K). In other words, turning on the air conditioner does not appear to play a significant role in reducing the amount of damage done. However, there is a noticeable (but slight) declining effect as one increases the H­values.

Conclusion: The key results for the aforementioned simulations runned in MatLab are as follows:

The environmental temperature plays a minimal role in influencing skin damage, when viewed over short periods of time. However, over longer periods of time, the ambient temperature becomes an increasingly important factor for determining the extent of the skin damage.

Skin damage accumulates logarithmically as a function of time. Counterintuitively, turning on the air conditioner does not reduce the damage of coffee

burns on skin. Based on these conclusions, mitigating the risk of injury posed by hot coffee is best achieved by lowering the temperature of the coffee itself, rather than changing the external conditions that surround the coffee.

According to the American Burn Association (ABA), third­degree burns occur in as little as one second for coffee temperatures above 155F (1 second) [4]. Given that McDonald's coffee is over 190F, Liebeck was justified in suing for damages, particularly since 6% of her skin endured 3rd degree burn. Moreover, she went skin grafting for eight days during her hospitalization [13]. From the data collected on our MatLab, we support the ABA’s claims that the coffee temperature should be lowered to 135 to 140F for safe consumption.

What could we do if we had 10 weeks to do this project?

There would be many significant revisions to this project if we are given 10 more weeks to do this. For instance, early on in the project, my partner and I had hoped of implementing a 2D (or 3D model) of this project. However, in order to accomplish the aforementioned task, it would require us to have a better understanding of partial differential equations, and more time to implement, test, and debug the overall code.

In addition, we also had hoped to include cotton pants as another layer on top of coffee within our calculations. Similar to the first aspiration, this part was discarded in the later stages of our project, since we lacked the necessary time to research which kinds of fabrics have higher heat conductivities than others.

Assuming MatLab supports GUI features, we would also create a user­friendly application that incorporates all the variables that we modified / tested for the guiding questions. Ideally, its functionality would be similar to LabView, with buttons, colors, and images, rather than an old­fashioned command­line window.

My partner and I could also research in the literature other models that are used to assess the damage of the burn. We could then write a technical report discussing the strengths and weaknesses of each study. For instance, we found a study that was conducted with the purpose of finding the ideal temperature to serve coffee [6]. In this study, the author’s compared data regarding the temperature people liked to drink their coffee with relative risk that each temperature posed for injury. They then took tried to calculate a temperature to serve coffee that would satisfy the most individuals while posing the least amount of risk. The problem with their study, however, is that they implemented the less accurate error function dependent version of the heat transfer model when calculating burns.

Sources:

1. Diller, K.R. Development and solution of finite­difference equations for burn injury with spreadsheet software J Burn Care Rehabil. 1999 Jan­Feb; 20(1 Pt 1): 25–32.

2. Stout, Hilary. "Not Just a Hot Cup Anymore." The New York Times. The New York

Times, 20 Oct. 2013. Web. 24 Feb. 2014.

3. Bessey, Palmber Q. 2012 National Burn Repository. Rep. Chicago: American Burn Association, 2012. Print.

4. Scalds: A Burning Issue. N.p.: American Burn Association, 2000. PDF.

5. Scald Injury Education: Educator’s Guide. N.p.: American Burn Association, n.d. PDF. 6. Fredericka Brown, Kenneth R. Diller, Calculating the optimum temperature for serving

hot beverages, Burns, Volume 34, Issue 5, August 2008, Pages 648­654, ISSN 0305­4179, http://dx.doi.org/10.1016/j.burns.2007.09.012. (http://www.sciencedirect.com/science/article/pii/S0305417907002550)

7. Marx, John A. Rosen's Emergency Medicine: Concepts and Clinical Practice.

Philadelphia: Mosby/Elsevier, 2006. Print.

8. Whitelaw, Jim H. Convective Heat Transfer. Rep. Thermopedia, 2 Feb. 2011. Web.

9. "List of Weather Records." Wikipedia. Wikimedia Foundation, n.d. Web. 24 Feb. 2014. <http://en.wikipedia.org/wiki/Highest_temperature_ever_recorded_on_Earth#Heat>.

10. "Lowest Temperature Recorded on Earth." Wikipedia. Wikimedia Foundation, 16 Feb. 2014. Web. 24 Feb. 2014. <http://en.wikipedia.org/wiki/Lowest_temperature_recorded_on_Earth>.

11. "Thermal Diffusivity." Wikipedia. Wikimedia Foundation, 16 Feb. 2014. Web. 23 Feb. 2014. <http://en.wikipedia.org/wiki/Thermal_diffusivity>.

12. "Water Properties." Water Properties. N.p., n.d. Web. 24 Feb. 2014. <http://people.ucsc.edu/~bkdaniel/WaterProperties.html>.

13. "The McDonald’s Hot Coffee Case." Customer Attorneys of California. N.p., n.d. Web. 23 Feb. 2014.

Appendix Preston Hoang:

There are several things I got out of this project. One critical thing I learn is the importance of using specific timetables in order to meet project deadlines. To be more specific, although we got our programming done on Saturday, we failed to anticipate the time and effort it takes to organize the entire report. If things were done differently, we would get our program done earlier, and do the guided questions in a more well­paced manner. Another thing I learned (or rather re­learned) is the importance of organization in coding. Throughout BME 60B and previous programming courses, there was little incentive to organize and comment my code, since I could mentally tackle the little assignments / homework with ease. However, what I’ve realized from bigger projects is that it is impossible to keep track of everything mentally. In other words, one should have a written specific plan / outline before tackling said project.

Regarding my contributions, I have answered guiding questions #2 and #3 for the report. In addition, I have provided an initial working model that we could use for the project, then incorporated the three­skin layer model. I also contributed to the research in finding the relevant constants (e.g. the k­values, the alpha constants) in various journals. I had also contributed heavily to the formation of these guiding questions. Alex Almanza:

Like Preston, this project has shown me how essential it is to stay organized throughout the process of creating a program. For instance, on several different occasions we went through many different versions of very similar codes. Since we did not use clearly defined naming conventions, I had great difficulty sifting through these alternative versions when it came time to compile our code. This was in part due to poor use of file directories. I simply had way too many of them, and it made it difficult to track down the files that I need when it came time to compile everything.

A second thing learned is how important it is to do research.For instance, the Friday before this project was due I decided to do supplemental research for an already working version of our code. During this time, I found the article we cited by Diller. In that paper, he essentially outlined the specifics of our second working code. Nevertheless, he outlined modeling burns for spreadsheet software, so converting the code into MATLAB was not a painless process. If we would done more research at the start, we would have likely found this article earlier and spared ourselves a time crunch at the end.

For this project, I contributed by implementing convection within our final program, answered the first guiding question, and managed the compiling of our code throughout the program creation process, save for at the end when Preston added final touches.