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Introduction

Biopsy has been one of the leading diagnostics approaches to characterize oncology disease for many years. This well known procedure has saved many lives, however it has multiple crucial drawbacks including the high cost, discomfort it brings to the patient, difficulty of obtaining the samples in more complicated diagnosis and lastly it does not show the whole image of the tumour based on the tumour’s hete-rogeneous nature(1). The answer to these problems may in future be the liquid biopsy method. This method relies on the analysis of blood samples from patients, specifically the occurrence of circulating tumour DNA (ctDNA) in the sample(2) as can be seen in Figure 1. The goal of liquid biopsy is to monitor the development and progress of malignant disease and it’s reaction to therapy by analyzing blood samples of the patient. Furthermore, liquid biopsy proved to be a useful tool in the process of targeted therapy – changing of medicine and therapy based on changes in blood test results(1,2).
Cell apoptosis and/or cell necrosis leads to release of short nucleic fragments(<166bp) into plasma(3). These fragments are referred to as cfDNA – circulating cell-free
DNA. The tumour derived subset of cfDNA, caused by high turnover rate of tumour cells is called ctDNA – circulating tumour DNA(3). Circulating Tumour Cells (CTC) are rare cells released into patient’s bloodstream. These cells then extravasate to different organs, which in small fraction leads to formation of metastasis(1). Detection of these cells after the first cycles of therapy, combined with their short lifespan indicates a futility of the treatment(2).
There are several big challenges, that must be overcomed before liquid biopsy could be widely used in clinical practice.
Firstly, the concentration of ctDNAs in blood is very low, which leads to the need of extremely sensitive and specific analytic methods for the characterisation and even detection of these fragments. The concentration of ctDNA is even lower in samples of patients in early stages of cancer(2).
Secondly, even though the analysis of plasma samples, used in the ctDNA method is easier, the samples may be contaminated by cfDNA released during innate processes of cell life-cycle. The ctDNA method also severely lacks required standardisation of techniques.
Thirdly, the differences between healthy cfDNA and oncologic ctDNA are not significant which leads to problems in distinguishing them from each other.
Lastly, the liquid biopsy is not usable in testing of every cancer type or every patient, diagnosed with a given type of cancer. The main problem being the insufficient concentration of CTCs and ctDNA fragments into the bloodstream of the patient(4).
Multiple studies were conducted with the goal of confirming that there is a difference between the length of the ctDNA fragments and regular cfDNA fragments. Oncologic patients were proven to have increased quantity of cfDNA, which can be result of tumour shedding ctDNA fragments into the bloodstream(5).
The more valuable information is however, that the average size of ctDNAfragments is smaller than the size of a non-carcinome cfDNA(5,6). Some specific examples include:
Human Melanoma (Healthy-165bp, Oncologic-145bp(5), Human Lung Cancer (Healthy-283.7±4.1 bp, Oncologic-277.0±4.7bp)(5), Animal models of GBM (Most common length of Healthy fragments – 167bp, most common length of Oncologic fragments – 134 and 144bp)(5). It has also been proven, that the modal size of ctDNA fragments for most of the cancer types is bellow 167bp(6). The typical size of cfDNA fragments is between 150 and 200bp(7) which provides only small intersection of sizes. The shorter length of fragments originating from tumours compared to healthy fragments has been also confirmed by a study of dried blood samples, in which it was determined that the modal length of ctDNA fragments was 150bp compared to 170bp of healthy cfD-NA fragments(8) Furthermore a study from 2015, targeted at patients suffering from HCC observed a positive correlation between the proportion of DNA fragments less than 150bp and the tumour DNA fraction in plasma as well as negative correlation between the proportion of DNA fragments larger than 180bp and tumour DNA fraction.(9) The same study also determined based on the difference between cumulative frequencies between 8p deletions and 8q amplifications in plasma DNA of samples that since the difference attains maximum at 166bp the key difference between tumorous and nontumorous plasma DNA is the relavite abundance of DNA <166bp and 166bp(9).
It has been also proven, that not only the ctDNA fragments have shorter average length, but also, that the length of the fragment is clearly tied to the frequency of mutations on allele. In Melanoma Patients samples, the mutations occured in highest frequency on fragments of length between 110bp and 140bp(5). Lung cancer samples also showed higher frequency of mutations in shorter fragments(5).

Fragmentation of mutated ctDNA is much more prevalent than the fragmentation of healthy cfDNA(6) which could explain the overal shorter length of the ctDNA fragments.
It has also been suggested, that the maximum enrichment of the ctDNA occurs in fragments of length between 90 and 150bp, with a secondary group in ranges of 250 to 320bp(6).
The contradicting evidence or facts, that could prove problematic are less numerous, yet they are present. It has been concluded that fraction of ctDNA in early stages of cancer is very low(14) which could lead to fragments of ctDNA that are longer than expected.
In the process of testing the lung cancer samples, it was discovered that, there is a considerable overlap in peak values of healthy and oncologic fragments(5).
The studies that were analysed for this study overwhelmingly support the use of fragment length of the DNA fragments in plasma as a partial or independent predictor for differentiating healthy samples from carcinoma samples. This conclusion was achieved based on several independent studies, which provided result determining clear difference of length of ctDNA and cfDNA fragments(5-9).
The goal of our study was to learn whether the fragment length profiles of samples could be used as a partial predictor for machine learning based liquid biopsy. Fragment length profiles represent the amount of DNA fragments of every given length in bp (base pairs) found in sequenced samples. We aimed to analyse differences in length profiles between samples and suggest whether these profiles could be used in the process of diagnosis and monitoring of oncologic diseases.
Material and Methods
Data acquisition
We downloaded the dataset of 116 oncologic samples from 44 patients (multiple samples were obtained from several patients as the disease progressed) and 22 control healthy samples(10) (EGA Study ID EGAS00001003530). All four grades of tumour severity(11) were present among the sam-ples retrieved from patients.
Analysis
The first stage of data processing was carried out as previously described(12). NextSeq-produced fastq files (two per sample) were directly mapped using the Bowtie 2(13) algorithm with -very-sensitive option to the human reference genome hg19 (GRCh37). Reads with mapping quality of 40 or higher were retained for further data processing. Length of a DNA fragment was determined as the difference of the left-most and the rightmost mapped base of the corresponding read pair.
As the first step we decided to calculate weighted median and mean of fragment lengths of the samples. We used the functions provided by the Weighted stats library (https://py-pi.org/project/weightedstats/).
As we can see from results, there is a  clear difference between oncologic and control samples in their length. Medians of both metrics are significantly lower (U=214.15, p=3.15 × 10-10) for oncologic samples (162-193 bp, mean 174.28 bp) than healthy (177-192 bp, mean 183.18 bp), suggesting that the overall length of fragments in oncologic samples is shorter than the length in control samples. The only statistic contradicting this conclusion is the maximum weighted median of fragment length in oncological samples, which is higher than the healthy one.
However this phenomena can be easily attributed to the existence of an outlier in oncologic samples. The difference between healthy and oncologic samples can be clearly seen on mean fragment length profiles shown in Figure 2.
After the initial analysis of median and mean fragment lengths suggested a clear difference between oncologic and control samples we decided to normalize the count of fragments of given lengths in the samples (we divided the number of fragments of every given length by the sum of all fragments in the sample in effort to ease comparison between the samples). Following the normalization we plotted all oncologic and all healthy fragment length profiles to allow for visual comparison.
The difference between Oncologic samples and Control samples is clear. Oncologic samples have very high and sharp peak in lengths between 155 bp and 165 bp (Figure 2 and 3(a)), which is completely absent in the control samples. On the other hand the control samples contain a higher number of fragments of length between 285 bp and 395 bp, which we can clearly see represented by the higher ridge on the right tail of the plot (Figure 2 and 3(b)).
We also compared the oncologic samples between each other in effort to find differences in their length profiles based on the grade of the tumour. We compared the median fragment lengths by the grade (Figure 4) and calculated euclidean distance of fragment length profiles from mean control healthy profiles (Figure 5).
We found that the G1 (the lowest tumour grade) samples were the most similar to control samples both in the median values and according to calculated euclidean distances. On the contrary the G4 (the highest tumour grade) samples proved to deviate from the control samples more significantly.
Machine learning
Based on the results from data analysis we decided to create a prototype of machine learning model which would differentiate the oncologic samples from healthy controls.
The crucial part of any machine learning is the feature selection. Based on the analysis results we were convinced that the calculated weighted median and weighted mean 35 had to be included as features. No matter how clear was the difference in weighted means and medians between oncologic samples and healthy controls these two features aren’t enough to show the whole characteristic of a length profile. We tested several different approaches to select the additional features:

• k-best – using the sklearn’s  univariate feature selection (https://scikit-learn.org/stable/modules/generated/skle-arn.feature_selection.SelectKBest.html) which selects the best features based on univariate statistical tests we chose the 10 best features which had the best results in the given tests. 12 features total.
• medians – we divided the fragment length profile of a sample into ten bins by the
• fragment length. Each bin had the same range (first bin: 1bp-100bp, second bin: 101bp-200bp and so on…). After the division into bins we calculated the weighted median of every bin and added it as a feature. This method produced 10 additional features. 12 features total.
• sums – we divided the fragment length profile into bins same as when we calculated the medians, however in this method we summed the number of fragments
• in given bin instead of calculating the weighted median of the length in the bin. This method also provided 10 additional features with 12 total.
• quantiles – when using this method we calculated the quantiles of the fragment length profile with the step 0.1 (cal-culating the Q(0.1), Q(0.2)…Q(0.9)). This resulted in 9 additional features, 11 total.
• peaks – last method we decided to test was splitting the fragment length profiles into bins with unequal range based on the occurrence of peaks in the mean plotted pro-files. The ranges we chose were:
  1. 1bp-159bp – the pre-peak area
  2. 160bp-174bp – main peak
  3. 175bp-189bp – secondary peak
  4. 190bp-229bp – downwards slope
  5. 230bp-279bp – trough
  6. 280bp-409bp – last low peak
  7. 410bp-1000bp – tail
  This method resulted in fewest additional features – 7, to taling only 9. All additional features were calculated from the normalized values.

We tested machine learning models based on Decision Trees, Random Forests, SVMs and XGBoosting with multiple different hyperparameter settings. We compared the models n combination with all feature selection models using the GridSearch method based on 10 fold cross validation with the deciding metric being the F1 score because of the unbalanced nature of our dataset. The selection process was done using 85% of our data as the training sub-dataset.
The SVM model combined with the “medians” feature selection method provided the best result of F1 Score equal to 0,9325. We used this model to predict the remaining 15% of the dataset with results captured in Figure 6.

Discussion

With the results we acquired during the research it is safe to claim that fragment length profiles are a viable indicator of oncologic disease in the organism. However no matter how promising the results may seem it is crucial to test this conclusion on more data, ideally from multiple different diagnoses. Oncologic disease show great variance in their behaviour and structure which is the main reason behind the need for more testing.
The scope of this work did not allow for testing of other machine learning algorithms and neural networks or deep learning algorithms, which could potentially bring even better results. However even without testing these methods we were able to prepare a machine learning model with results satisfactory enough to be used in combination with other partial predictors in a larger meta-predictor. This was the main goal of this study, which means it is safe to say we were successful.
During our research we also learned that samples with different tumour grades deviate in their fragment length profiles. The level of deviation varied, however it certainly showed a great potential for further research. The important finding was, that the Euclidean distance from mean control profile grew with the severity of the disease. Based on our analysis the biggest challenge, when solving this differentiation, will most likely be the differentiation between grades G2 and G3 since the samples of these grades had often over-lapping features.
What we deem as the biggest achievement of this study is that it showed a real possibility of liquid biopsy becoming a reality in the relatively near future. This would noticeably increase the quality of life for oncologic patients and also increase their chances of remission and curing.

Acknowledgment
This article was created with the support of the OP Integra-ted Infrastructure for the project: Long term strategic research and development focused on the occurrence of Lynch syndrome in the Slovak population and possibilities of prevention of tumors associated with this syndrome, ITMS: 313011V578, co-financed by the European Regional Development Fund.

Poďakovanie
Táto publikácia vznikla vďaka podpore v rámci Operačného programu Integrovaná infraštruktúra pre projekt: Dlhodobý strategický výskum a vývoj zameraný na výskyt Lynchovho syndrómu v populácii SR a možnosti prevencie nádorov spojených s týmto syndrómom , kód ITMS: 313011V578, spolufinancovaný zo zdrojov Európskeho fondu regionálneho rozvoja.

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