Knee and Hip Kinematics on Sloped Surfaces
Introduction
This is a project that was done by myself and three others during my senior year at the University of Oregon. This was a biomechanics class and final project was to run an experiment related to biomechanics using some techniques and software we had learned about in class. Our group decided to use a motion tracking software to gather data on clinical knee and hip angles of subjects while walking on different variations of sloped surfaces. The slopes we chose were: flat, 4° incline, 8° incline, 4° decline, and 8° decline.
At the time of doing this project, I had not yet been exposed to any programming languages and I had not yet started my journey down the path of data science and analytics. I wanted to revisit this project with the tools and knowledge I have now, and essentially use this data to make better visualizations and a better report overall.
Background
What does clinical knee angle mean? What about clinical hip angle?
Clinical knee angle is the angle created by the shin and by extending a line out from the femur (see picture below for example). Clinical hip angle is very similar except its the angle created by the femur and by extending a line through a persons center of mass.
It has already been shown that lower limb kinematics and walking posture change when walking on a sloped surface. We already know that during the initial heel strike, clinical knee angle is greater while walking on an incline compared to flat ground and decline and during mid strike clinical knee angle decreases more for an incline than on flat ground. For hip kinematics, we know there is a Significant increase in hip extension and flexion when walking uphill compared to flat ground and there is No change in hip flexion or extension when walking downhill.
Purpose
These changes in gait are important to everyone as sloped surfaces are a part of everyday life. These changes in gait are especially important to those who are injured or are just coming off of an injury, using these slopes can be advantageous to physical therapist who want to target a specific movement or muscle group in their patient. It is also important to track any changes to the center of mass while walking on these slopes for the elderly population. A drastic change to the center mass would cause someone to fall, this data can be used as a precursor to show those who may be at risk of falling when walking on a sloped surface.
Analysis
To start, we are going to load in a few packages.
library(readxl)
library(ggplot2)
library(plotly)
library(dplyr)
library(tidyr)
library(BayesFactor)
The initial analysis was done in excel, so our data is located in an excel file. Lets load that in and take a look.
# read in the excel file
file_path <- "C:\\Users\\drewc\\OneDrive\\Documents\\RStudio\\Portfolio\\Datasets\\Knee Hip Data\\knee_hip_angles.xlsx"
knee_hip_angles <- read_xlsx(path = file_path, sheet = 1)
# the data is currently a tibble, I would prefer a dataframe
knee_hip_angles <- as.data.frame(knee_hip_angles)
knee_hip_angles$Subject <- as.factor(knee_hip_angles$Subject)
str(knee_hip_angles)
## 'data.frame': 110 obs. of 12 variables:
## $ Subject : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
## $ Time : num 0.0333 0.0666 0.0999 0.1332 0.1665 ...
## $ flat_K : num 5.1 11.3 13.9 11.6 18.4 ...
## $ four_incline_K : num 9.28 5.29 12.53 18.39 17.21 ...
## $ four_decline_K : num 7.26 10.61 13.82 18.78 17.58 ...
## $ eight_incline_K: num 7.37 10.93 13.94 14.48 15.85 ...
## $ eight_decline_K: num 10.05 7.66 10.9 16.53 16.56 ...
## $ flat_H : num 86.2 85.9 82.8 78.8 84.7 ...
## $ four_incline_H : num 78.5 68.7 60.8 64.5 64.4 ...
## $ four_decline_H : num 91.7 91.7 86.6 83.6 86 ...
## $ eight_incline_H: num 81.9 79.5 78.7 72.8 66.8 ...
## $ eight_decline_H: num 92 85.5 88.2 85 83.3 ...
Here we see that there are three subjects and a time variable tells us how far along in the gait cycle the subject is. The other columns are the measured angles of the knee and hip for each different angle that was tested.
The data frame looks and works fine, but we can do so much better. For starters, I don’t want to write out those column names every time I go to plot the data and making the plots will be difficult since each angle type is in its own column. To change that this we are going to reshape our data from the wide format to the long format. This will put all of the angles into one column which makes plotting them much much easier.
I also would like an easy way to filter out just the knee angles or just the hip angles, so we can create a new column telling us which part of the body we are talking about and will help us with filtering. Another change I want to make is a simple one but one that I do think makes a difference when trying to understand the graph. I want to change the time variable to a percentage. Since each observation is one complete gait cycle, I think it makes more sense to look at it in terms of a percentage rather than as a unit of time. Once all of that is done we can create our ggplot object and pass that to ggplotly to make it animated. This will be done with both the knee and the hip, notice how easy this is because we were able to create our new “component” column. I’m going to exclude the code used to create the chart for the hip data, but it is exactly the same with the filter function changed to hip instead of knee.
# this functions allows our data to be saved during the animation
accumulate_by <- function(dat, var) {
var <- lazyeval::f_eval(var, dat)
lvls <- plotly:::getLevels(var)
dats <- lapply(seq_along(lvls), function(x) {
cbind(dat[var %in% lvls[seq(1, x)], ], frame = lvls[[x]])
})
dplyr::bind_rows(dats)
}
# create the ggplot object
p <- knee_hip_angles %>%
# change from a wide df to a long df
pivot_longer(cols = 3:12,
names_to = "angle_type",
values_to = "degrees") %>%
# create the new column using regex to find columns that have _K
mutate(component = if_else(grepl("_K", unlist(angle_type)), "Knee", "Hip"),
Time = round(Time/max(Time) * 100, 0)) %>%
# filter by just the knee thanks to our new column
filter(component == "Knee") %>%
accumulate_by(~Time) %>%
ggplot() +
geom_line(aes(x = Time,
y = degrees,
color = Subject,
frame = frame),
show.legend = FALSE) +
labs(y = "Clinical Knee Angle",
x = "") +
facet_grid(.~angle_type, labeller = as_labeller(c("eight_decline_K" = "8° Decline",
"eight_incline_K" = "8° Incline",
"flat_K" = "Flat",
"four_decline_K" = "4° Decline",
"four_incline_K" = "4° Incline"))) +
theme(axis.text.x = element_text(angle = 45))
knee_ani <- ggplotly(p, tooltip = c("color", "y")) %>%
layout(showlegend = FALSE) %>%
config(displayModeBar = FALSE) %>%
animation_opts(
frame = 100,
transition = 0,
redraw = FALSE) %>%
animation_slider(
currentvalue = list(prefix = "% of Gait Cycle: ")
)
The same code as above, just with the hip data instead.
Now that we know what the data looks like and can mess around with the sliders, its time for some statistics. My first thought here to run an anova between each of the angles for both the knee and the hip. In order to do this, there are some assumptions that need to be met:
- Our samples need to be normally distributed or near normally distribruted
- Equal variance between each our groups
- Independence between groups and within groups
We already know that the independence assumption is met, so lets check for normality first, starting with the knee for now.
First I want to assign this updated data frame to a variable. (same code as above)
# statistical analysis
knee_data <- knee_hip_angles %>%
pivot_longer(cols = 3:12,
names_to = "angle_type",
values_to = "degrees") %>%
mutate(component = if_else(grepl("_K", unlist(angle_type)), "Knee", "Hip")) %>%
filter(component == "Knee")
# checking the distributions
ggplot(data = knee_data) +
geom_density(aes(x = degrees, fill = angle_type, color = angle_type), alpha = 0.2) +
labs(title = "Destributions of Degrees for each Angle",
x = "Degrees",
y = "") +
scale_fill_discrete(name = "Angle Type",
labels = c("8° Decline", "8° Incline", "Flat", "4° Decline", "4° Incline")) +
guides(color = "none") +
theme(legend.position = c(0.8, 0.7))
# checking the variance
ggplot(data = knee_data) +
geom_boxplot(aes(x = angle_type, y = degrees, fill = angle_type, color = angle_type), alpha = 0.2, show.legend = FALSE) +
labs(title = "Variance For Each Angle",
x = "",
y = "") +
scale_x_discrete(labels = c("8° Decline", "8° Incline", "Flat", "4° Decline", "4° Incline"))
Our data is not normally distributed. This is okay though as a one way anova is typically pretty robust when it comes to data not being normally distributed, but this is something to keep in mind and we will try something different in a little bit that disregards the normality clause, so we will press on.
Our variance is looking pretty good from the boxplots, these seem to be equal and I don’t see the need to run a formal test to double check.
I’m going to skip over showing the code for the hip data because it is essentially copy and paste but replace “knee” with “hip”. For the hip data, we do see a normal distribution of the data which is great. However, the variance is not as easy to determine, so Bartlett’s Test will be conducted to given a more definite answer on whether the variation is equal. (More about Bartlett’s Test here.)
bartlett.test(degrees ~ angle_type, data = hip_data)
##
## Bartlett test of homogeneity of variances
##
## data: degrees by angle_type
## Bartlett's K-squared = 37.555, df = 4, p-value = 1.384e-07
As we can see from the Bartlett’s Test, the p-value is very low which tells me that these samples do not have equal variances. Similarly to the normality of the knee data, one-way anovas are robust in dealing with data with unequal variances as long as each sample has the same sample size, which we do in our case.
The ANOVA
Now that we have done all of our checks, lets move on to the actual ANOVA.
First, I want to take a look our observed means and see what those look like when compared between the groups. To do this, I’m going to use the same boxplots from above, except I’m going to flip the axis and add a point for the mean for each group.
means_knee <- aggregate(knee_data, degrees ~ angle_type, FUN = mean)
means_hip <- aggregate(hip_data, degrees ~ angle_type, FUN = mean)
# knee
ggplot() +
geom_boxplot(data = knee_data,
aes(x = angle_type, y = degrees, fill = angle_type, color = angle_type),
alpha = 0.2, show.legend = FALSE) +
geom_point(data = means_knee,
aes(x = angle_type, y = degrees, color = angle_type),
cex = 6, inherit.aes = FALSE, show.legend = FALSE) +
labs(title = "Knee",
x = "",
y = "") +
scale_x_discrete(labels = c("8° Decline", "8° Incline", "Flat", "4° Decline", "4° Incline")) +
coord_flip()
# hip
ggplot() +
geom_boxplot(data = hip_data,
aes(x = angle_type, y = degrees, fill = angle_type, color = angle_type),
alpha = 0.2, show.legend = FALSE) +
geom_point(data = means_hip,
aes(x = angle_type, y = degrees, color = angle_type),
cex = 6, inherit.aes = FALSE, show.legend = FALSE) +
labs(title = "Hip",
x = "",
y = "") +
scale_x_discrete(labels = c("8° Decline", "8° Incline", "Flat", "4° Decline", "4° Incline")) +
coord_flip()
The points represent the means for each angle. For the knee, we can see that Flat has a noticeably higher mean than the rest of the angles, but the rest of the angles appear to be nearly the same. For the hip, we see that the 4° Decline appears to have a lower mean than the rest, but the rest all have a similar mean.
Lets see if these differences are significant or not.
aov_knee <- aov(degrees ~ angle_type, data = knee_data)
summary(aov_knee)
## Df Sum Sq Mean Sq F value Pr(>F)
## angle_type 4 2061 515.2 1.417 0.227
## Residuals 545 198172 363.6
aov_hip <- aov(degrees ~ angle_type, data = hip_data)
summary(aov_hip)
## Df Sum Sq Mean Sq F value Pr(>F)
## angle_type 4 1804 451.0 1.686 0.152
## Residuals 545 145766 267.5
Both tests returned a low F-value and a p-value greater than 0.05 which means that we fail to reject the null hypothesis and can conclude that there is no difference in the means of these different angle for both the knee and the hip.
Limitations
There are many limitations to this experiment that may have changed the outcome of the results. The first one being that this study was only done on 3 people who were all healthy college students. It would be beneficial to run this experiment on people of all different ages and view the differences there. Gather more data is always better as well because it becomes better to make an inference about the population when you have more samples.
Another limitation is the surface that was used for walking. Since we were limited to a classroom, we had to improvise on the walking surface that was used. We used two narrow, pliable boards that got propped up when necessary. These boards were not completely stable, which meant that participants may have altered their normal gait patterns to stable themselves out. This could have lead to greater flexion recorded than what was expected.
Conclusion
Although we found no significant difference in this study, there are a bunch of real life applications for using these kinematics. This data could be used to to develop targeted rehabilitation programs to minimize the aggravations of conditions irritated by walking on an inclined surface. Along with this, sloped surfaces could be used in preventative care to help people with injuries avoid further damage. A final use case would be in the development of lower limb prostheses to allow for effective sloped motion.
Whether it was found to be significant or note, it is important to note these changes when treating someone with knee or hamstring pain, or if you are caring for the elderly. Sloped surfaces are a part of everyday life and learning how to effectively use them could lead to increased biomechanical results.
Special thanks to: Megan Quan, Marie Soto, and Jonathan Nahass for running this experiment with me!