Last updated: 2025-08-31

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After preprocessing the video and run TrackMate on ImageJ to get the tracks and .csv files on the positions of branch points and positions of tracked points, we run analysis on these collected information to study the movement of things on the microtuble.

Run CPLASS algorithm to get the segmented paths.
Run CSA algorithm to learn on distribution of inferred speeds.

Note The output from TrackMate contains lot of tracks. We notice an issue that some tracks may be accidently splited in small tracks due to the difficulty in observing the movement of materials on the microtubles, i.e., some blobs disappear for a while then appear again. This issue also leads to missing data points.

There are two approaches that we want to note in this report.

First approach: Keep all the tracks output from TrackMate
Second approach: Use a merging rule to merge the tracks that are close to each other.

For both approaches, the analysis procedure is

Run segmentation algorithm CPLASS to get the segmented path, inferred speed and time.
Run CSA algorithm to get the speed analysis.

Here is the data after running TrackMate/ImageJ

data <- read_csv(here("data","processed_spots.csv"))
df = data %>% select(ID,TRACK_ID, POSITION_X, POSITION_Y, POSITION_T)
df <- df[-c(1:3), ]
df[] <- lapply(df, as.numeric)
head(df)

# A tibble: 6 × 5
     ID TRACK_ID POSITION_X POSITION_Y POSITION_T
  <dbl>    <dbl>      <dbl>      <dbl>      <dbl>
1 93569        0       612.       176.          2
2 93505        0       616.       175.          0
3 95109        0       582.       178.         25
4 97733        0       534.       218.         66
5 97412        0       534.       209.         61
6 93639        0       611.       176.          3

branch_points <- read_csv(here("data","branch_points.csv"), 
    col_types = cols(x = col_number(), y = col_number()))

1. First approach

first = list()
list_tracks = unique(df$TRACK_ID)
for (i in 1:length(unique(df$TRACK_ID)))
{

  subdf = df %>% filter(TRACK_ID == list_tracks[i])

# sort by POSITION_T
subdf = subdf %>% arrange(POSITION_T)

first[[i]] = list(
  t = subdf$POSITION_T,
  x = subdf$POSITION_X,
  y = subdf$POSITION_Y,
  track_id = subdf$TRACK_ID
)

}

af_first = list()
for(i in 1:length(first))
{
  path = first[[i]]
  t = path$t
  x = path$x
  y = path$y
  track_id = path$track_id
  af_first[[i]] = fill_missing_data(t,x,y, unique(track_id))
}
# saveRDS(af_first,here("data","first_approach_data.rds"))

1.1. Run CPLASS to get segmented paths

# cplass_paths = CPLASS_paths(af_first, time_rate = 1,iter_max = 4000, PARALLEL = FALSE, speed_pen = FALSE)
# saveRDS(cplass_paths,file="data/CPLASS_MTEB1_1st.rds")

1.2. Visualization

We will have some plots for the two tracks here. For the full gallary, please visit analysis/figures.

Note:

the black dashed-lines are for detected changepoint times.
The triangle blue dots are for the branch points.
The red dots are for the fill-in position.
The green areas show the motile segments while the pink areas show the stationary segments.

path_list = readRDS(here("data","CPLASS_MTEB1_1st.rds"))
#######################
motor = "MTEB1-1st" #change the name to the name of your data
dist_max = c()
t_max = c()
speed_max = c()

for (i in c(1,6)){
  path = path_list[[i]]$path_inferred
  segments = path_list[[i]]$segments_inferred
  speed_max = c(speed_max,max(path_list[[i]]$segments_inferred$speeds))
  
  dist_max = c(dist_max,max(c(max(path$x)-min(path$x)),
                            max((path$y)-min(path$y))))
  t_max = c(t_max,max(path$t) - min(path$t))
}
xy_width = 1.2*max(dist_max)
# t_lim = c(0,ceiling(max(t_max)))
t_lim = c(0,150)
max_speed = ceiling(max(speed_max))

for (i in c(1,6))
{
dashboard = plot_path_inferred_fill_in(path_list[[i]],xy_width,t_lim, motor, max_speed, branch_points = branch_points)
  print(dashboard)
}

Version	Author	Date
f71b1fa	Ldo3	2025-08-31

Version	Author	Date
f71b1fa	Ldo3	2025-08-31

# path_list = readRDS(here("data","CPLASS_MTEB1_1st.rds"))
# #######################
# # for REAL DATA use the lines below.
# file_list = c("MTEB1-1st")
# filestub = paste0("figures/Real",file_list[1])
# # infile = paste0(filestub,"_cplass.rds")
# outfile = paste0(filestub,"_gallery.pdf")
# # path_list = readRDS(infile)
# # 
# motor = "MTEB1-1st" #change the name to the name of your data
# 
# #######################
# # #for SIMULATED DATA use the lines below.
# # filestub = paste0("OFR Final/Sim",experiment_num,"_",theta$motor,"_",Hz,"Hz_cplass_",sp)
# # infile = paste0(filestub,".rds")
# # outfile = paste0(filestub,"_gallery_",sp,".pdf")
# # path_list = readRDS(infile)
# # 
# # if(theta$motor == "CKP"){
# #     motor = "Base"
# #   }else if(theta$motor == "kin1"){
# #     motor = "Contrast"
# #   }else if(theta$motor == "Mimic"){
# #     motor = "Mimic"
# # }
# 
# 
# pdf_output = TRUE
# 
# if (pdf_output == TRUE){
#   pdf(outfile,onefile = TRUE,width=7,height=5)
# }
# 
# dist_max = c()
# t_max = c()
# speed_max = c()
# 
# for (i in 1:length(path_list)){
#   if (i %% 20 == 0){
#     print(paste("Working on path",i))
#   }
#   path = path_list[[i]]$path_inferred
#   segments = path_list[[i]]$segments_inferred
#   speed_max = c(speed_max,max(path_list[[i]]$segments_inferred$speeds))
#   
#   dist_max = c(dist_max,max(c(max(path$x)-min(path$x)),
#                             max((path$y)-min(path$y))))
#   t_max = c(t_max,max(path$t) - min(path$t))
# }
# xy_width = 1.2*max(dist_max)
# # t_lim = c(0,ceiling(max(t_max)))
# t_lim = c(0,150)
# max_speed = ceiling(max(speed_max))
# 
# for (i in 1:length(path_list)){
#   if (i %% 20 == 0){
#     print(paste("Working on path",i))
#   }
#   
#   # #REAL DATA PLOTS (dashboard)
#   # dashboard = plot_path_real(path_list[[i]],xy_width,t_lim)
#   # print(dashboard)
# 
#   # SIMULATION PLOTS (dashboard)
#   dashboard = plot_path_inferred_fill_in(path_list[[i]],xy_width,t_lim, motor, max_speed, branch_points = branch_points)
#   print(dashboard)
# 
#   # SIMULATION PLOTS (only x-y plot)
#   # plot_xy = plot_path_inferred_xy(path_list[[i]],xy_width,t_lim, motor, max_speed)
#   # print(plot_xy)
#   
# }
# 
# if (pdf_output == TRUE){
#   dev.off()
# }

2. Second approach

A path \(j\) is considered as a potential candidate to merge to the \(i\)th-path if: \(t_{end}\) of \(i\)th-path \(< t_{start}\) of \(j\)th-path. For all potential candidates, calculate the Euclidean distance between the endpoint of path \(i\) and the start point of path \(j\), i.e., \[\sqrt{(x_{i_{end}}-x_{j_{start}})^2+(y_{i_{end}}-y_{j_{start}})^2}\] Among those candidates, select the one with the minimum distance value. Return the final candidate to merge. In the final round, we look at the video to confirm which case looks like a good merge.

With this strategy, we return 18 paths. The following shows the index of merged tracks corresponding to each path. For example, path 1 in this second approach is the output after merging TRACK 0 and TRACK 73.

oam = readRDS(here("data","original_tracks_after_merging.rds"))
chains = list()
for (i in 1:length(oam))
{
  chains[[i]] = unique(oam[[i]]$TRACK_ID)
}
# Build edges from consecutive nodes in each chain
edges <- do.call(rbind, lapply(chains, function(chain) {
  if (length(chain) > 1) {
    cbind(head(as.character(chain), -1),
          tail(as.character(chain), -1))
  } else NULL
}))

g <- graph_from_edgelist(edges, directed = TRUE)

plot(g,
     vertex.size = 17,
     vertex.label.cex = 1,
     vertex.color = "skyblue",
     edge.width = 2,            # make edges thicker
     edge.color = "darkred",    # change edge color
     edge.arrow.size = 1,     # make arrows bigger
     layout = layout_with_fr)

Version	Author	Date
f71b1fa	Ldo3	2025-08-31

There are missing time steps, we need to fill in those missing

af = list() #after fill-in
for (i in 1:length(oam))
{
  t = oam[[i]]$POSITION_T
  x = oam[[i]]$POSITION_X
  y = oam[[i]]$POSITION_Y
  track_id = unique(oam[[i]]$TRACK_ID)
  af[[i]] = fill_missing_data(t,x,y,track_id = track_id)
}
# saveRDS(af,here("data","second_approach_data.rds"))

2.1. Run CPLASS

# cplass_paths = CPLASS_paths(af, time_rate = 1,iter_max = 4000, PARALLEL = FALSE, speed_pen = FALSE)
# saveRDS(cplass_paths,file="data/CPLASS_MTEB1_2nd.rds")

2.2. Visualization

We will have some plots for some tracks here. For the full gallary, please visit analysis/figures.

Note:

the black dashed-lines are for detected changepoint times.
The triangle blue dots are for the branch points.
The red dots are for the fill-in position.
The green areas show the motile segments while the pink areas show the stationary segments.

path_list = readRDS(here("data","CPLASS_MTEB1_2nd.rds"))
#######################
# for REAL DATA use the lines below.
file_list = c("MTEB1-2nd")
filestub = paste0("figures/Real",file_list[1])
# infile = paste0(filestub,"_cplass.rds")
outfile = paste0(filestub,"_gallery.pdf")
# path_list = readRDS(infile)
# 
motor = "MTEB1-2nd" #change the name to the name of your data
dist_max = c()
t_max = c()
speed_max = c()

for (i in c(1,3,5,10)){
  path = path_list[[i]]$path_inferred
  segments = path_list[[i]]$segments_inferred
  speed_max = c(speed_max,max(path_list[[i]]$segments_inferred$speeds))
  
  dist_max = c(dist_max,max(c(max(path$x)-min(path$x)),
                            max((path$y)-min(path$y))))
  t_max = c(t_max,max(path$t) - min(path$t))
}
xy_width = 1.2*max(dist_max)
# t_lim = c(0,ceiling(max(t_max)))
t_lim = c(0,150)
max_speed = ceiling(max(speed_max))

for (i in c(1,3,5,10))
{
dashboard = plot_path_inferred_fill_in(path_list[[i]],xy_width,t_lim, motor, max_speed, branch_points = branch_points)
  print(dashboard)
}

Version	Author	Date
f71b1fa	Ldo3	2025-08-31

Version	Author	Date
f71b1fa	Ldo3	2025-08-31

Version	Author	Date
f71b1fa	Ldo3	2025-08-31

Version	Author	Date
f71b1fa	Ldo3	2025-08-31

# path_list = readRDS(here("data","CPLASS_MTEB1_2nd.rds"))
# #######################
# # for REAL DATA use the lines below.
# file_list = c("MTEB1-2nd")
# filestub = paste0("figures/Real",file_list[1])
# # infile = paste0(filestub,"_cplass.rds")
# outfile = paste0(filestub,"_gallery.pdf")
# # path_list = readRDS(infile)
# # 
# motor = "MTEB1-2nd" #change the name to the name of your data
# 
# #######################
# # #for SIMULATED DATA use the lines below.
# # filestub = paste0("OFR Final/Sim",experiment_num,"_",theta$motor,"_",Hz,"Hz_cplass_",sp)
# # infile = paste0(filestub,".rds")
# # outfile = paste0(filestub,"_gallery_",sp,".pdf")
# # path_list = readRDS(infile)
# # 
# # if(theta$motor == "CKP"){
# #     motor = "Base"
# #   }else if(theta$motor == "kin1"){
# #     motor = "Contrast"
# #   }else if(theta$motor == "Mimic"){
# #     motor = "Mimic"
# # }
# 
# 
# pdf_output = TRUE
# 
# if (pdf_output == TRUE){
#   pdf(outfile,onefile = TRUE,width=7,height=5)
# }
# 
# dist_max = c()
# t_max = c()
# speed_max = c()
# 
# for (i in 1:length(path_list)){
#   if (i %% 20 == 0){
#     print(paste("Working on path",i))
#   }
#   path = path_list[[i]]$path_inferred
#   segments = path_list[[i]]$segments_inferred
#   speed_max = c(speed_max,max(path_list[[i]]$segments_inferred$speeds))
#   
#   dist_max = c(dist_max,max(c(max(path$x)-min(path$x)),
#                             max((path$y)-min(path$y))))
#   t_max = c(t_max,max(path$t) - min(path$t))
# }
# xy_width = 1.2*max(dist_max)
# # t_lim = c(0,ceiling(max(t_max)))
# t_lim = c(0,150)
# max_speed = ceiling(max(speed_max))
# 
# for (i in 1:length(path_list)){
#   if (i %% 20 == 0){
#     print(paste("Working on path",i))
#   }
#   
#   # #REAL DATA PLOTS (dashboard)
#   # dashboard = plot_path_real(path_list[[i]],xy_width,t_lim)
#   # print(dashboard)
# 
#   # SIMULATION PLOTS (dashboard)
#   dashboard = plot_path_inferred_fill_in(path_list[[i]],xy_width,t_lim, motor, max_speed, branch_points = branch_points)
#   print(dashboard)
# 
#   # SIMULATION PLOTS (only x-y plot)
#   # plot_xy = plot_path_inferred_xy(path_list[[i]],xy_width,t_lim, motor, max_speed)
#   # print(plot_xy)
#   
# }
# 
# if (pdf_output == TRUE){
#   dev.off()
# }

Run CSA for both approaches

pdf_output = TRUE

real_data_not_merged_file = c(here("data","CPLASS_MTEB1_1st.rds"))
real_data_merged_file = c(here("data","CPLASS_MTEB1_2nd.rds"))

real_path_not_merged_list = readRDS(real_data_not_merged_file)
real_path_merged_list = readRDS(real_data_merged_file)


cohort_list = c("MTEB1: 1st approach", 
                "MTEB1: 2nd approach")
color_list = c("MTEB1: 1st approach" = "grey", 
               "MTEB1: 2nd approach" = "lightblue") 

pdf_output = TRUE


##### Create Segment Summary ####
segment_summary = summarize_segments_inferred(real_path_not_merged_list,cohort_list[1])
segment_summary = bind_rows(segment_summary,
                            summarize_segments(real_path_merged_list,cohort_list[2]))

max_speed = min(15,max(segment_summary$speeds))

# Assumes theta is the same for all frame rates involved
speed_mesh = seq(0,max_speed,length = 200)
ds = speed_mesh[2] - speed_mesh[1]
subsample_size = 200
num_subsamples = 30

csa = tibble()
#### Bootstrap CSA for Real Data 1st approach ####
for (m in 1:num_subsamples){
    subsample = sample(1:length(real_path_not_merged_list),subsample_size,replace = TRUE)
    path_subsample = list()
    for (i in 1:length(subsample)){
      path_subsample[[i]] = real_path_not_merged_list[[subsample[i]]]
    }
    this_segments_summary = summarize_segments_inferred(path_subsample,"Sample")
    this_csa = compute_csa(this_segments_summary, speed_mesh)$csa
    csa = bind_rows(csa,
                tibble(
                  s = speed_mesh,
                  csa = this_csa,
                  dcsa = c(diff(this_csa)/ds,0),
                  error = NA,
                  error_pct = NA,
                  label = cohort_list[1],
                  Hz = NA,
                  subsample = m
                ))
}


#### Bootstrap CSA for Real Data 2nd approach ####
for (m in 1:num_subsamples){
    subsample = sample(1:length(real_path_merged_list),subsample_size,replace = TRUE)
    path_subsample = list()
    for (i in 1:length(subsample)){
      path_subsample[[i]] = real_path_merged_list[[subsample[i]]]
    }
    this_segments_summary = summarize_segments_inferred(path_subsample,"Sample")
    this_csa = compute_csa(this_segments_summary, speed_mesh)$csa
    csa = bind_rows(csa,
                tibble(
                  s = speed_mesh,
                  csa = this_csa,
                  dcsa = c(diff(this_csa)/ds,0),
                  error = NA,
                  error_pct = NA,
                  label = cohort_list[2],
                  Hz = NA,
                  subsample = m
                ))
}


csa = csa %>% mutate(cohort = paste(label,subsample))


p_csa = ggplot(csa %>% filter(label == cohort_list[1] | 
                                      label == cohort_list[2]))+
  geom_line(aes(x = s, y = csa, col = label, group = cohort))+
  ggtitle("MTEB1")+
  ylab("Cumulative Speed Allocation")+xlab(expression(paste("Speed (",mu,"m/sec)")))+
  scale_color_manual(values = color_list)+
  theme_minimal()
# +
  # theme(legend.position = "none")

print(p_csa)

Version	Author	Date
f71b1fa	Ldo3	2025-08-31

speed_df1 = segment_summary%>% filter(label=="MTEB1: 1st approach")
speed_df2 = segment_summary%>% filter(label=="MTEB1: 2nd approach")

print("The highest speed value in the first approach is")

[1] "The highest speed value in the first approach is"

speed_df1%>% filter(speeds ==max(speeds))

# A tibble: 1 × 5
  durations states speeds label               path_id
      <dbl>  <dbl>  <dbl> <chr>                 <int>
1         1      1   28.4 MTEB1: 1st approach      34

print("The highest speed value in the second approach is")

[1] "The highest speed value in the second approach is"

speed_df2%>% filter(speeds ==max(speeds))

# A tibble: 1 × 5
  durations states speeds label               path_id
      <dbl>  <dbl>  <dbl> <chr>                 <int>
1         1      1   30.8 MTEB1: 2nd approach       9

ggplot(segment_summary, aes(x = speeds, fill = label)) +
  geom_density(alpha = 0.4) +
  labs(title = "KDE of inferred speed in different approaches", x = "Speed (mu/s)", y = "Density") +
  theme_minimal()

Version	Author	Date
f71b1fa	Ldo3	2025-08-31

From the CSA plot, the second approach provide more segments will speed between 0 -5 \(\mu m/s\) than in the first approach.

Merged tracks in the second approach provide us clearer picture where a blob pass branch points, e.g., paths we plotted above.

We also want to point out that CPLASS does not work well with too short path such as 10-20 time steps (see the plot gallery for the first approach), i.e., for too short path, the algorithm will detect a lot of changepoints. In the CPLASS, we discussed the consistency theory of CPLASS when we have the sample size is large enough.

sessionInfo()

R version 4.5.1 (2025-06-13)
Platform: aarch64-apple-darwin20
Running under: macOS Ventura 13.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/Chicago
tzcode source: internal

attached base packages:
[1] parallel  stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] igraph_2.1.4      doParallel_1.0.17 iterators_1.0.14  foreach_1.5.2    
 [5] patchwork_1.3.2   lubridate_1.9.4   forcats_1.0.0     stringr_1.5.1    
 [9] dplyr_1.1.4       purrr_1.1.0       readr_2.1.5       tidyr_1.3.1      
[13] tibble_3.3.0      ggplot2_3.5.2     tidyverse_2.0.0   limSolve_2.0.1   
[17] pracma_2.4.4      matrixcalc_1.0-6  Rlab_4.0          here_1.0.1       

loaded via a namespace (and not attached):
 [1] gtable_0.3.6       xfun_0.53          bslib_0.9.0        tzdb_0.5.0        
 [5] quadprog_1.5-8     vctrs_0.6.5        tools_4.5.1        generics_0.1.4    
 [9] pkgconfig_2.0.3    RColorBrewer_1.1-3 lifecycle_1.0.4    compiler_4.5.1    
[13] farver_2.1.2       git2r_0.36.2       codetools_0.2-20   httpuv_1.6.16     
[17] htmltools_0.5.8.1  sass_0.4.10        yaml_2.3.10        crayon_1.5.3      
[21] later_1.4.3        pillar_1.11.0      jquerylib_0.1.4    whisker_0.4.1     
[25] MASS_7.3-65        cachem_1.1.0       tidyselect_1.2.1   digest_0.6.37     
[29] stringi_1.8.7      labeling_0.4.3     rprojroot_2.1.1    fastmap_1.2.0     
[33] grid_4.5.1         cli_3.6.5          magrittr_2.0.3     utf8_1.2.6        
[37] withr_3.0.2        scales_1.4.0       promises_1.3.3     bit64_4.6.0-1     
[41] timechange_0.3.0   rmarkdown_2.29     bit_4.6.0          workflowr_1.7.2   
[45] hms_1.1.3          evaluate_1.0.4     lpSolve_5.6.23     knitr_1.50        
[49] rlang_1.1.6        Rcpp_1.1.0         glue_1.8.0         rstudioapi_0.17.1 
[53] vroom_1.6.5        jsonlite_2.0.0     R6_2.6.1           fs_1.6.6