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Inquiry: Prevention of Pressure Ulcers

This paper is written to deliberate on a condition known as pressure ulcers, also called pressure sores or bedsores. They are injuries to the skin and underlying tissue, caused by prolonged pressure on the skin area. They can occur to anyone, but usually affect patients who lie in bed or sit in a chair for extended periods of time. They remain a major health condition which a significant population of adults can face. Hospitalization cases resulting from the condition have been on the steady rise in recent times among the ageing population. A report by Ahn et al. (2016) indicates that over 2.5 million people in the United States suffer from bedsores across all healthcare facilities. This population consists of 0.4% to 38% in acute care hospitals, 0% to 17% in home-bases care, and 2% to 24% in long term care facilities (Ahn et al., 2016). Therefore, a concerted effort should be made in preventing their occurrence to avert the treatment costs and postoperative difficulties experienced by some patients.

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The objective of this essay is to present a clear historical and mathematical perspective on the topic under study. The level one historical question to be answered in the paper is what the history of pressure ulcers is. On the other hand, the level two historical question to be answered is what the existing protocols for averting the development of the lesions are. The level one mathematical question to be answered in the essay is what the statistical pieces of evidence of the occurrence of bedsores are. Similarly, the level two mathematical question to be responded to is whether there are protocols which can be used in preventing pressure ulcers.

Historical Perspective

Pressure ulcers have been viewed as a disease since a long time ago. An article by Mccoulough (2019) reports that the condition was observed in ancient Egyptian women about five thousand years ago. The Egyptians would use remedies such as honey, mouldy bread, meat, animal and plant extracts, copper, and zinc (Mccoulough, 2019). Another French surgeon, Ambrose Pare (1510-1590), perceived that man can only treat a wound but the healing process is done by God (Mccoulough, 2019). Ambrose later joined the army and used his medical knowledge in curing wounded soldiers of pressure ulcers by recommending good nutrition, pain relief, and debridement. Therefore, there is a rich background of useful knowledge in mathematics and other technical disciplines such as medicine.

Referring to the Brown-Sequard syndrome theory by Mauritian physiologist known as Charles Brown-Sequard (1817-1894), pressure inhibits blood circulation which results in bedsores. Brown-Sequard proved that avoidance of pressure in guinea pigs with injured spinal cords and the lesion does not develop, and that present ulcer heals when pressure is withdrawn (Mccoulough, 2019). The founder of present-day nursing, Florence Nightingale adhered to stringent repositioning of bend-bound patients while nursing them. Mccoulough (2019) reports that Florence Nightingale indicated in 1859, that it is a nurse’s fault for a bedridden patient to develop bedsore. Thus, the earlier scientists played critical roles in the current knowledge and disciplines.

In the nineteenth century, a French doctor known as Jean-Martin Charcot who studied diseases noticed that patients developed lesions on various body parts and died after a certain period. According to Zaidi and Sharma (2020), the doctor opted to name the condition “decubitus ominous” by which he meant death was inevitable for someone who developed lesion. In Charcot’s perspective, there were other causative factors of bedsore alongside pressure. He described a model known as neurotrophic theory which maintained that central nervous system damage directly caused bedsore (Zaidi & Sharma, 2020). This framework formed the basis of modern-day prevention or diagnosis of pressure ulcers due to its emphasis on risk factor assessment and proactive response to bedsore cases. Furthermore, the theory underscored the fact that not all pressure ulcers cases result in death since the condition can be mitigated.

Mathematical Perspective

Although medical practitioners recommend frequent repositioning of bed-bound patients in order to prevent them from developing bedsores, other scholars argue that the practice can be unreliable. For instance, Katzengold and Gefen (2019) state that the method has limitations based on “the required body posture during operation, mechanical ventilation, and connection to other life-support equipment” (pp. 1398-1399). Furthermore, nurses sometimes use inappropriate techniques and materials to reposition certain parts of patients such as the head and neck. They often use blankets and towels. This essay will, therefore, propose a technique used by the research done by Katzengold and Gefen to highlight the mathematical perspective of preventing bedsores.

Katzengold and Gefen propose the use of donut-shaped gel head supports to support patient heads while lying in hospital. Acceding to Katzengold and Gefen (2019), “by so-called “off-loading” the occiput, that is, shifting the head-weight forces from the central occipital region to other more peripheral head regions.” (p. 1399). The modelled geometry of the medical devices in research done by Katzengold and Gefen (2019) are shown in Figures 1 and 2.

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Side and Front view of the head model (Katzengold & Gefen, 2019).
Figure 1: Side and Front view of the head model (Katzengold & Gefen, 2019).
Mid-sagital Cross-section of the Head Model (Katzengold & Gefen, 2019)
Figure 2: Mid-sagital Cross-section of the Head Model (Katzengold & Gefen, 2019)

The research adopted the mechanical behavior of the skin and fatty tissues of the scalp and skull bone. Each tissue type was represented by the Mooney-Rivlin constitutive model:

Where W represent the strain energy density, I1 is the first invariant of the right Cauchy-Gree deformation tensor, J is the determinant of the deformation gradient tensor, G is the shear modulus and λ is Lame’s first parameter that can be converted to other frequently used elastic properties shown in Figure 3: elastic modulus E, the bulk modulus K, and Poisson’s ratio ν.

Mechanical properties and element data of the finite element (FE) model variants (Katzengold and Gefen, 2019).
Figure 3: Mechanical properties and element data of the finite element (FE) model variants (Katzengold and Gefen, 2019).

The elastic modulus is given as:

While the bulk modulus is calculated as follows:

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Whereas the Poisson’s ratio is calculated by the following formula:

The mechanical behaviors of the gel substance in the donut-shaped head support were measured for eight subjects in a laboratory in Massachusetts. The pressure distributions of the back of the head are represented in the Figure below:

Pressure Regions on the back head (Katzengold and Gefen, 2019).
Figure 4: Pressure Regions on the back head (Katzengold and Gefen, 2019).

Figure 5 comprises of different graphs of stress level of the skin and fat tissue when positioned with different head supports.

Stress Levels on Skin and Fatty Tissue with Different Head Support (Katzengold & Gefen, 2019).
Figure 5: Stress Levels on Skin and Fatty Tissue with Different Head Support (Katzengold & Gefen, 2019).

In conclusion, from the experiment it was established that the skin tissue was at the pressure scale of 4 kPa while the fatty tissues were at the 0-0.5 kPa range. This meant that skin tissue are normally subjected to greater stress values that the fatty one. The test proved that the donut-shaped gel head support does not work better than simple medical foam. Therefore, this finding reveals that the fluidized positioner was not placed at the same scale of stress-exposure-associated risk to scalp tissue health.


Ahn, H., Cowan, L., Garvan, C., Lyon, D., & Stechmiller, J. (2016). Risk factors for pressure ulcers including suspected deep tissue injury in nursing home facility residents: Analysis of national minimum data set 3.0. Advances in Skin & Wound Care, 29(4), 178-190. Web.

Katzengold, R., & Gefen, A. (2019). Modelling an adult human head on a donut‐shaped gel head support for pressure ulcer prevention. International Wound Journal, 16(6), 1398-1407. Web.

Mccoulough, S. (2019). The history of pressure ulcers. Osca. Web.

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Zaidi, S. R. H., & Sharma, S. (2020). Decubitus Ulcer. StatPearls Publishing

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