Of Finite-Element Analysis and A Winning Smile
Evolution and Analysis of the Toothbrush
By Kyle W. Sembera

The following article on the evolution and analysis of the toothbrush was written by Kyle Sembera, a mechanical engineering senior at Lamar University, Beaumont, Tex., as a final assignment for an elective design class. Sembera’s toothy research project was inspired by course professor P.R. Corder who, during a recent visit to the dentist, found himself musing on the merits of modern toothbrush design.

Have you ever tried brushing your teeth with a smashed stick? While today there are many sophisticated options for the orally conscious, during the dawn of civilization, the smashed stick—the earliest predecessor of the modern toothbrush—had a corner on the market. By chewing the end of a soft twig flat, people created a rudimentary brush, which aided in the removal of food particles. Before this method was developed, people may have used a stick similar to a toothpick to perform the task.

Demonstrating the benefits of modern toothbrush technology ME senior Kyle Sembera flashes his pearly whites.

Because of the ubiquitous place toothbrushes hold in modern society, the need no longer exists to brush with a smashed stick, yet some native tribes still use simple sticks to clean their teeth.

This article looks at the origin and evolution of modern toothbrushing and, for those who have ever worried about catastrophic toothbrush failure, assuages fears with a finite-element analysis, comparing a traditionally styled toothbrush to a modern one.

Origin of the Toothbrush

The Toothstick
Physical evidence from well-preserved Egyptian tombs dating back over 5,000 years suggests that the Egyptians used toothsticks for dental hygiene. Even before this civilization, the Mesopotamians wrote of the siwak, another version of the basic toothstick. These original toothpicks were most often made from porcupine quills, bird feathers, or wooden thorns.

During eighteenth-and nineteenth-century Europe, ornate metal toothpicks were developed. Serving as both art and status symbol, these were often copper, silver, or even gold.

Currently, some 10 million people in the Middle East and other parts of the world use toothpicks daily as their primary tooth-cleaning mechanism. In fact, toothpicks were used as the primary method for cleaning teeth as late as the early 1950s in some isolated sections of the United States.

The First Toothbrush
In the seventeenth century, Europeans often used rags or sponges dipped in sulfur oil or a salt solution to rub their teeth clean. Sometimes these rags were attached to a stick to help reach the back teeth, but the teeth were essentially being mopped, rather than brushed. From this practice evolved the first toothbrush, invented in 1780 by William Addis of Clerkenwall, England.

Addis attached hairs from the tail of a cow to the end of a whittled thighbone from the same animal, which was reportedly the only bone strong enough to survive the bristle-attachment procedure and still maintain its strength when wet. Eventually, boar hairs replaced the hairs from the cow’s tail. To this day, descendants of William Addis still manufacture toothbrushes at a factory in England.

Celluloid Handle
During World War I, the bones that were being used for toothbrushes were usurped by the soup industry due to the nutritional demands of war. The resultant shortage called for the development of a new toothbrush-handle material. Celluloid handles, constructed by injecting plastic into molds and cooling them in a given shape, met this demand. Then, in the 1920s, a new method of attaching bristles to the handle was developed: drilling holes into the brush head, forcing in bunches of bristles, and securing them with a staple. This method is still used by some manufacturers today.

Nylon Bristles
Prior to World War II, Chinese boar hairs were the favored material for bristles, but during the war a roadblock out of Chung-King impeded the export of these popular hairs. Nylon filament, having been developed in 1938, was an ideal replacement.

The nylon filament came with several advantages, including a dramatic reduction in production costs and the ability to control bristle texture. Manufacturers could also shape the filament tip and vary its diameter for improved performance. Boar hair, on the other hand, often fell out, did not dry well, and was prone to bacterial growth. Although nylon continues to dominate the market today, boar-hair bristles still account for about 10 percent of toothbrushes sold worldwide.

Today’s Toothbrush
A study of worldwide patent applications between the years 1963-1998 reveals about 3,000 toothbrush patents. The brands, styles and colors of toothbrushes are virtually endless.

One manufacturer markets both a toothbrush with two heads which surround the teeth, claiming it will clean teeth more effectively, and a toothbrush with a built-in tongue scraper, designed to remove bacteria, which builds up on the tongue.

Another manufacturer stresses the importance of maintaining a cleaner toothbrush. Their design incorporates a unique hole in the center of the bristle head, ensuring that all food and other debris is easily rinsed off the brush. Still other manufacturers stress that bristle orientation is key to maintaining clean teeth. They sell toothbrushes with angled bristles, which tackle the teeth at different angles to maximize cleaning effectiveness.

One thing most manufacturers can agree on is the importance of having a handle that assists the user in reaching the back teeth, the most neglected and difficult to reach. One popular remedy has been to angle the toothbrush handle.

Figure 1-Classic-Style Toothbrush

Design Comparison Between an Old-Style and a Modern Toothbrush
In this study, a classic-style toothbrush with relatively simple geometry was modeled in ProEngineer and analyzed in ProMechanica. The results are compared with those from a modern-style brush with advanced structure and enhanced strength. The classic brush is flat with nearly uniform thickness along its length (Figure 1).

Figure 2-Modern Style Toothbrush

In contrast, the modern toothbrush has a larger cross-section as well as a reinforced handle where the higher stresses are expected (Figure 2). The gently angled section at the head of the brush absorbs the majority of the brushing load and prevents a large stress concentration. The increased cross-sectional thickness allows the brush to withstand a greater load with less deflection. In order to compare stress within the brush and the overall deflection of the toothbrush’s tip, each toothbrush bristle area was loaded with 35 N (approximately 8 lbs.) distributed uniformly on the head of the brush. Each material was assumed to be common plastic (PVC), with yield strength of 17 MPa. This load is rather large (about twice what one might expect), but it does give a reasonable comparison between the two brushes.

Each brush was constrained at the point where the hand would grip, which is also where the cross-sectional geometries of the brushes change significantly.

Figure 3- Classic-Style Toothbrush dimensions, load application, and high stress point.

The classic brush experiences most of its stress at two significant area changes: where the handle narrows to meet the neck, and again where the neck meets the brush head. The larger stress occurs at the latter point, where the neck is only 8mm wide (Figure 3). The Von Mises stress in this brush peaks at about 7.8 N/mm squared (1,131 psi) in this section, while the brush tip deflects 8.6 mm over this length of the tip (about 66 mm or 13 percent deflection).

Figure 4 illustrates the modern brush with the same 35 N load applied. It has only one major stress concentration: where the neck of the brush meets the head. The Von Mises stress at this point reaches only 3.6 N/mm squared, or 522 psi (roughly half that of the classic brush).

Figure 4-This view shows the major stress concentration where the neck meets the head, caused by the change in geometry.

The larger cross-section and less abrupt changes in geometry (sloped versus the flat neck) help reduce the amount of stress in this brush. However, the largest difference between these two brushes is portrayed in their maximum displacement difference. The modern toothbrush deflects 1.6 mm over its length of 73 mm, just over 2 percent deflection, compared to the classic brush’s 13 percent.

The 35 N loads were rather large, yet the deflections and stresses exhibited by these brushes should not affect the brush’s performance over its relatively short lifetime. Neither brush would be expected to fail due to these loads, because the stresses are found to be significantly lower than the yield strength of the material (7.8 and 3.6 MPa vs. a yield strength of 17 MPa).

Over the centuries, the toothbrush has seen many changes in configuration, material and geometry. Today’s toothbrushes come in a large variety of shapes, styles, sizes, and colors, yet despite this incredible selection, toothbrush geometry is not nearly as important to dental health as brushing frequency and technique. All of today’s brushes should be able to withstand any reasonable brushing load; therefore, the brush that suits you best is the one you enjoy using.

Acknowledgement: I’d like to acknowledge Dr. P.R. Corder, of Lamar University, for his guidance throughought this project and his assistance in the creation of this article.