Visibility-based layout of a hospital unit – An optimization approach

Abstract

A patient fall is one of the adverse events in an inpatient unit of a hospital that can lead to disability and/or mortality. The medical literature suggests that increased visibility of patients by unit nurses is essential to improve patient monitoring and, in turn, reduce falls. However, such research has been descriptive in nature and does not provide an understanding of the characteristics of an optimal inpatient unit layout from a visibility-standpoint. To fill this gap, we adopt an interdisciplinary approach that combines the human field of view with facility layout design approaches. Specifically, we propose a bi-objective optimization model that jointly determines the optimal (i) location of a nurse in a nursing station and (ii) orientation of a patient's bed in a room for a given layout. The two objectives are maximizing the total visibility of all patients across patient rooms and minimizing inequity in visibility among those patients. We consider three different layout types, L-shaped, I-shaped, and Radial; these shapes exhibit the section of an inpatient unit that a nurse oversees. To estimate visibility, we employ the ray casting algorithm to quantify the visible target in a room when viewed by the nurse from the nursing station. The algorithm considers nurses' horizontal visual field and their depth of vision. Owing to the difficulty in solving the bi-objective model, we also propose a Multi-Objective Particle Swarm Optimization (MOPSO) heuristic to find (near) optimal solutions. Our findings suggest that the Radial layout appears to outperform the other two layouts in terms of the visibility-based objectives. We found that with a Radial layout, there can be an improvement of up to 50% in equity measure compared to an I-shaped layout. Similar improvements were observed when compared to the L-shaped layout as well. Further, the position of the patient's bed plays a role in maximizing the visibility of the patient's room. Insights from our work will enable understanding and quantifying the relationship between a physical layout and the corresponding provider-to-patient visibility to reduce adverse events.

Appendices

Appendix 1 Bilinear interpolation technique

Bilinear interpolation is a resampling method that estimates the value of a desired point with a distance weighted average of four nearest points to this desired point. The weights used are inversely proportional to the length of the source and destination point [58].

In our implementation, the nursing station is first converted into uniform rectangular grids with a step size of x units. Then, we run a ray casting algorithm on each grid point in advance and record each grid point's visibility value, which are later used to estimate the visibility from any location in the grid.

Fig. 15

Example of bilinear interpolation method in a nursing station

For instance, in the Fig. 15, assume that we need to calculate the visibility values at point (x, y), with the four nearest points in the grid system being (x₁,y₁), (x₁,y₂), (x₂,y₁), (x₂,y₂) and their respective visibility values, say (Q₁₁, Q₁₂, Q₂₁, Q₂₂). Firstly, we calculate the interpolation in the x-direction as follows:

$$\begin{array}{cc}{{\text{R}}}_{1}= \frac{{{\text{x}}}_{2}- x}{{{\text{x}}}_{2}- {{\text{x}}}_{1}}{{\text{Q}}}_{11}- \frac{x- {{\text{x}}}_{1}}{{{\text{x}}}_{2}- {{\text{x}}}_{1}}{{\text{Q}}}_{21}& {\text{and}}\end{array}$$

(9)

$${{\text{R}}}_{2}= \frac{{{\text{x}}}_{2}- x}{{{\text{x}}}_{2}- {{\text{x}}}_{1}}{{\text{Q}}}_{12}- \frac{x- {{\text{x}}}_{1}}{{{\text{x}}}_{2}- {{\text{x}}}_{1}}{{\text{Q}}}_{22}.$$

(10)

Then, we proceed by interpolating in the y-direction and calculating the interpolated value as follows:

$$P= \frac{{{\text{y}}}_{2}- y}{{{\text{y}}}_{2}- {{\text{y}}}_{1}}{{\text{R}}}_{1}- \frac{y- {{\text{y}}}_{1}}{{{\text{y}}}_{2}- {{\text{y}}}_{1}}{{\text{R}}}_{2},$$

(11)

where P is the interpolated visibility value at point (x, y). The interpolated value of a target (bed or head) are used in the objective function of the optimization model. Table 9 shows the performance of the bilinear interpolation technique on a Pareto solution from an L-shaped layout with a low obstruction level.

Table 9 Accuracy of the bilinear interpolation technique

Appendix 2 Result from all experiments

Table 10

Table 10 Summary of results for patient's bed and head as target

Appendix 3 Pareto solutions from two different nurse positions (close and away) as discussed in Insight 3

Figure 16 illustrates the nurse positions (close and away) in a L-shaped layout, while Fig. 17 shows the corresponding Pareto solutions.

Fig. 16

Pareto solutions for the nurse position in the nursing station (shaded) with bed as target (L-shaped layout)

Fig. 17

Pareto frontier based on solutions from Fig. 16