Multimodal Distribution of Human Cold Pain Thresholds
Publication Date
May 20, 2015
Journal
PLOS ONE
Authors
Jörn Lötsch, Violeta Dimova, Isabel Lieb, Michael Zimmermann, et al
Volume
10
Issue
5
Pages
e0125822
DOI
https://dx.plos.org/10.1371/journal.pone.0125822
Publisher URL
http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0125822
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/25992576
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4439151
Europe PMC
http://europepmc.org/abstract/MED/25992576
Web of Science
000354921400047
Scopus
84930623096
Mendeley
http://www.mendeley.com/research/multimodal-distribution-human-cold-pain-thresholds
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Mendeley | Further Information

{"title"=>"Multimodal distribution of human cold pain thresholds", "type"=>"journal", "authors"=>[{"first_name"=>"Jörn", "last_name"=>"Lötsch", "scopus_author_id"=>"7004589758"}, {"first_name"=>"Violeta", "last_name"=>"Dimova", "scopus_author_id"=>"36185080100"}, {"first_name"=>"Isabel", "last_name"=>"Lieb", "scopus_author_id"=>"56674449900"}, {"first_name"=>"Michael", "last_name"=>"Zimmermann", "scopus_author_id"=>"55704371600"}, {"first_name"=>"Bruno G.", "last_name"=>"Oertel", "scopus_author_id"=>"11141915400"}, {"first_name"=>"Alfred", "last_name"=>"Ultsch", "scopus_author_id"=>"55915441200"}], "year"=>2015, "source"=>"PLoS ONE", "identifiers"=>{"scopus"=>"2-s2.0-84930623096", "doi"=>"10.1371/journal.pone.0125822", "pui"=>"604612677", "issn"=>"19326203", "pmid"=>"25992576", "sgr"=>"84930623096"}, "id"=>"e718a0c7-49b1-3c5e-93d7-4eff7befb327", "abstract"=>"BACKGROUND: It is assumed that different pain phenotypes are based on varying molecular pathomechanisms. Distinct ion channels seem to be associated with the perception of cold pain, in particular TRPM8 and TRPA1 have been highlighted previously. The present study analyzed the distribution of cold pain thresholds with focus at describing the multimodality based on the hypothesis that it reflects a contribution of distinct ion channels.\\n\\nMETHODS: Cold pain thresholds (CPT) were available from 329 healthy volunteers (aged 18 - 37 years; 159 men) enrolled in previous studies. The distribution of the pooled and log-transformed threshold data was described using a kernel density estimation (Pareto Density Estimation (PDE)) and subsequently, the log data was modeled as a mixture of Gaussian distributions using the expectation maximization (EM) algorithm to optimize the fit.\\n\\nRESULTS: CPTs were clearly multi-modally distributed. Fitting a Gaussian Mixture Model (GMM) to the log-transformed threshold data revealed that the best fit is obtained when applying a three-model distribution pattern. The modes of the identified three Gaussian distributions, retransformed from the log domain to the mean stimulation temperatures at which the subjects had indicated pain thresholds, were obtained at 23.7 °C, 13.2 °C and 1.5 °C for Gaussian #1, #2 and #3, respectively.\\n\\nCONCLUSIONS: The localization of the first and second Gaussians was interpreted as reflecting the contribution of two different cold sensors. From the calculated localization of the modes of the first two Gaussians, the hypothesis of an involvement of TRPM8, sensing temperatures from 25 - 24 °C, and TRPA1, sensing cold from 17 °C can be derived. In that case, subjects belonging to either Gaussian would possess a dominance of the one or the other receptor at the skin area where the cold stimuli had been applied. The findings therefore support a suitability of complex analytical approaches to detect mechanistically determined patterns from pain phenotype data.", "link"=>"http://www.mendeley.com/research/multimodal-distribution-human-cold-pain-thresholds", "reader_count"=>14, "reader_count_by_academic_status"=>{"Librarian"=>1, "Researcher"=>3, "Student > Ph. D. Student"=>3, "Student > Postgraduate"=>1, "Student > Master"=>1, "Student > Bachelor"=>3, "Professor"=>2}, "reader_count_by_user_role"=>{"Librarian"=>1, "Researcher"=>3, "Student > Ph. D. Student"=>3, "Student > Postgraduate"=>1, "Student > Master"=>1, "Student > Bachelor"=>3, "Professor"=>2}, "reader_count_by_subject_area"=>{"Agricultural and Biological Sciences"=>5, "Medicine and Dentistry"=>2, "Neuroscience"=>1, "Pharmacology, Toxicology and Pharmaceutical Science"=>1, "Psychology"=>3, "Social Sciences"=>1, "Engineering"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>2}, "Neuroscience"=>{"Neuroscience"=>1}, "Social Sciences"=>{"Social Sciences"=>1}, "Psychology"=>{"Psychology"=>3}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>5}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>1}}, "reader_count_by_country"=>{"Germany"=>1, "Spain"=>1}, "group_count"=>1}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/2077049"], "description"=>"<p>Due to the data transformations, retransformation of the modes to <i>CPT</i> values is thus obtained as <i>CPT = 32°C—e</i><sup><i>LogSI</i></sup><i>+ 1</i>. This retransformation of the <i>m</i><sub><i>i</i></sub> values provides the modes of the three Gaussians in the linear temperature range over which <i>CPT</i> was measured, i.e., 23.6, 13.3 and 1.5°C for Gaussian number i = 1, 2 and 3, respectively.</p><p>Values of variables obtained following modeling of the cold pain thresholds (rescaled for stimulus intensity, <i>SI = 32°C - CPT</i> to accommodate the increasing perception with increasing stimulus strength and zero-invariant log-transformed as <i>LogSI = Ln(SI+1)</i>), by means of the Gaussian mixture model (GMM given as </p><p></p><p><mi>p</mi></p><p></p><p><mi>x</mi></p><p></p><mi> </mi><mo>=</mo><mi> </mi><p></p><p><mo stretchy=\"true\">∑</mo></p><p><mi>i</mi><mi> </mi><mo>=</mo><mi> </mi><mn>0</mn></p><p><mi>M</mi></p><p></p><p></p><p></p><p><mi>w</mi></p><p><mi>i</mi></p><p></p><p></p><p></p><mi>N</mi><mo>(</mo><mi>x</mi><mo>|</mo><p></p><p><mi>m</mi></p><p><mi>i</mi></p><p></p><mo>,</mo><p></p><p><mi>s</mi></p><p><mi>i</mi></p><p></p><mo>)</mo><p></p><p></p>, for which the optimum number of mixes was found to be <i>M</i> = 3 (Figs <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125822#pone.0125822.g002\" target=\"_blank\">2</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125822#pone.0125822.g003\" target=\"_blank\">3</a>), where <i>m</i><sub><i>i</i></sub>, <i>s</i><sub><i>i</i></sub> and <i>w</i><sub><i>i</i></sub> are the parameters mean, standard deviation and relative weight of each of the Gaussians, respectively, obtained for the <i>LogSI</i> data.<p></p>", "links"=>[], "tags"=>["cpt", "pain thresholds", "em", "Gaussian Mixture Model", "kernel density estimation", "Distinct ion channels", "gmm", "trpm", "trpa", "pde", "Human Cold Pain Thresholds BackgroundIt", "pain phenotype data", "Gaussian distributions", "ion channels.MethodsCold pain thresholds", "Pareto Density Estimation"], "article_id"=>1421693, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Jörn Lötsch", "Violeta Dimova", "Isabel Lieb", "Michael Zimmermann", "Bruno G. Oertel", "Alfred Ultsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0125822.t002", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Values_of_variables_obtained_following_modeling_of_the_cold_pain_thresholds_rescaled_for_stimulus_intensity_SI_32_176_C_CPT_to_accommodate_the_increasing_perception_with_increasing_stimulus_strength_and_zero_invariant_log_transformed_as_LogSI_Ln_SI_1_by_/1421693", "title"=>"Values of variables obtained following modeling of the cold pain thresholds (rescaled for stimulus intensity, <i>SI = 32°C - CPT</i> to accommodate the increasing perception with increasing stimulus strength and zero-invariant log-transformed as <i>LogSI = Ln(SI+1)</i>), by means of the Gaussian mixture model (GMM given as px = ∑i = 0MwiN(x|mi,si), for which the optimum number of mixes was found to be <i>M</i> = 3 (Figs 2 and 3), where <i>m</i><sub><i>i</i></sub>, <i>s</i><sub><i>i</i></sub> and <i>w</i><sub><i>i</i></sub> are the parameters mean, standard deviation and relative weight of each of the Gaussians, respectively, obtained for the <i>LogSI</i> data.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-05-20 04:34:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/2077050", "https://ndownloader.figshare.com/files/2077051", "https://ndownloader.figshare.com/files/2077052"], "description"=>"<div><p>Background</p><p>It is assumed that different pain phenotypes are based on varying molecular pathomechanisms. Distinct ion channels seem to be associated with the perception of cold pain, in particular TRPM8 and TRPA1 have been highlighted previously. The present study analyzed the distribution of cold pain thresholds with focus at describing the multimodality based on the hypothesis that it reflects a contribution of distinct ion channels.</p><p>Methods</p><p>Cold pain thresholds (CPT) were available from 329 healthy volunteers (aged 18 – 37 years; 159 men) enrolled in previous studies. The distribution of the pooled and log-transformed threshold data was described using a kernel density estimation (Pareto Density Estimation (PDE)) and subsequently, the log data was modeled as a mixture of Gaussian distributions using the expectation maximization (EM) algorithm to optimize the fit.</p><p>Results</p><p>CPTs were clearly multi-modally distributed. Fitting a Gaussian Mixture Model (GMM) to the log-transformed threshold data revealed that the best fit is obtained when applying a three-model distribution pattern. The modes of the identified three Gaussian distributions, retransformed from the log domain to the mean stimulation temperatures at which the subjects had indicated pain thresholds, were obtained at 23.7 °C, 13.2 °C and 1.5 °C for Gaussian #1, #2 and #3, respectively.</p><p>Conclusions</p><p>The localization of the first and second Gaussians was interpreted as reflecting the contribution of two different cold sensors. From the calculated localization of the modes of the first two Gaussians, the hypothesis of an involvement of TRPM8, sensing temperatures from 25 – 24 °C, and TRPA1, sensing cold from 17 °C can be derived. In that case, subjects belonging to either Gaussian would possess a dominance of the one or the other receptor at the skin area where the cold stimuli had been applied. The findings therefore support a suitability of complex analytical approaches to detect mechanistically determined patterns from pain phenotype data.</p></div>", "links"=>[], "tags"=>["cpt", "pain thresholds", "em", "Gaussian Mixture Model", "kernel density estimation", "Distinct ion channels", "gmm", "trpm", "trpa", "pde", "Human Cold Pain Thresholds BackgroundIt", "pain phenotype data", "Gaussian distributions", "ion channels.MethodsCold pain thresholds", "Pareto Density Estimation"], "article_id"=>1421694, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Jörn Lötsch", "Violeta Dimova", "Isabel Lieb", "Michael Zimmermann", "Bruno G. Oertel", "Alfred Ultsch"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0125822.s001", "https://dx.doi.org/10.1371/journal.pone.0125822.s002", "https://dx.doi.org/10.1371/journal.pone.0125822.s003"], "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Multimodal_Distribution_of_Human_Cold_Pain_Thresholds_/1421694", "title"=>"Multimodal Distribution of Human Cold Pain Thresholds", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2015-05-20 04:34:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/2077047"], "description"=>"<p>The plot clearly indicated that less than a mixture of three Gaussians provided an inadequate fit and more than three Gaussians did not further improve the fit.</p>", "links"=>[], "tags"=>["cpt", "pain thresholds", "em", "Gaussian Mixture Model", "kernel density estimation", "Distinct ion channels", "gmm", "trpm", "trpa", "pde", "Human Cold Pain Thresholds BackgroundIt", "pain phenotype data", "Gaussian distributions", "ion channels.MethodsCold pain thresholds", "Pareto Density Estimation"], "article_id"=>1421691, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Jörn Lötsch", "Violeta Dimova", "Isabel Lieb", "Michael Zimmermann", "Bruno G. Oertel", "Alfred Ultsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0125822.g002", "stats"=>{"downloads"=>1, "page_views"=>18, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Scree_plot_23_of_the_model_quality_for_the_EM_fit_of_the_Gaussian_mixture_illustrating_the_number_of_components_which_should_be_assessed_in_order_to_explain_a_high_degree_of_variation_in_the_data_/1421691", "title"=>"Scree plot [23] of the model quality for the EM fit of the Gaussian mixture, illustrating the number of components which should be assessed in order to explain a high degree of variation in the data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-20 04:34:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/2077048"], "description"=>"<p>The graph displays the data after rescaling for stimulus intensity as <i>SI = 32°C - CPT</i> (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125822#pone.0125822.g001\" target=\"_blank\">Fig 1</a>) and subsequent log transformation as <i>LogSI = ln(SI+1)</i>. The density distribution is presented as probability density function (PDF), estimated by means of the Pareto Density Estimation (PDE [<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125822#pone.0125822.ref021\" target=\"_blank\">21</a>]). A Gaussian mixture model (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125822#pone.0125822.e001\" target=\"_blank\">Eq 1</a>; GMM given as </p><p></p><p><mi>p</mi></p><p></p><p><mi>x</mi></p><p></p><mi> </mi><mo>=</mo><mi> </mi><p></p><p><mo stretchy=\"true\">∑</mo></p><p><mi>i</mi><mi> </mi><mo>=</mo><mi> </mi><mn>0</mn></p><p><mi>M</mi></p><p></p><p></p><p></p><p><mi>w</mi></p><p><mi>i</mi></p><p></p><p></p><p></p><mi>N</mi><mo>(</mo><mi>x</mi><mo>|</mo><p></p><p><mi>m</mi></p><p><mi>i</mi></p><p></p><mo>,</mo><p></p><p><mi>s</mi></p><p><mi>i</mi></p><p></p><mo>)</mo><p></p><p></p>), was fit to the data, for which the optimum number of mixes was found to be <i>M</i> = 3. Subject distribution among the obtained three Gaussians was n = 155, n = 61 and n = 113 for Gaussian 1–3, respectively, starting from the left.<p></p>", "links"=>[], "tags"=>["cpt", "pain thresholds", "em", "Gaussian Mixture Model", "kernel density estimation", "Distinct ion channels", "gmm", "trpm", "trpa", "pde", "Human Cold Pain Thresholds BackgroundIt", "pain phenotype data", "Gaussian distributions", "ion channels.MethodsCold pain thresholds", "Pareto Density Estimation"], "article_id"=>1421692, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Jörn Lötsch", "Violeta Dimova", "Isabel Lieb", "Michael Zimmermann", "Bruno G. Oertel", "Alfred Ultsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0125822.g003", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Distribution_of_the_cold_pain_thresholds_CPT_observed_in_n_329_subjects_pooled_from_previous_studies_Table_1_/1421692", "title"=>"Distribution of the cold pain thresholds (<i>CPT</i>) observed in n = 329 subjects pooled from previous studies (Table 1).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-20 04:34:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/2077046"], "description"=>"<p>The four different studies are drawn in different color to enhance the association of data subsets with the study in which they have been acquired. The graph displays the data after rescaling for stimulus intensity as <i>SI = 32°C - CPT</i> to provide increasing stimulus intensity along the abscissa with increasing x. The lower limit of the applied stimulus intensity by the Thermal Sensory Analyzer is marked with a perpendicular dashed line. Data is shown as histograms and superimposed probability density functions (pdf, Gaussian kernel), separately for men and women (columns). For the main analysis, all data subsets shown here were pooled, log-transformed and mathematically modeled for multi-modality (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125822#pone.0125822.g003\" target=\"_blank\">Fig 3</a>).</p>", "links"=>[], "tags"=>["cpt", "pain thresholds", "em", "Gaussian Mixture Model", "kernel density estimation", "Distinct ion channels", "gmm", "trpm", "trpa", "pde", "Human Cold Pain Thresholds BackgroundIt", "pain phenotype data", "Gaussian distributions", "ion channels.MethodsCold pain thresholds", "Pareto Density Estimation"], "article_id"=>1421690, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Jörn Lötsch", "Violeta Dimova", "Isabel Lieb", "Michael Zimmermann", "Bruno G. Oertel", "Alfred Ultsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0125822.g001", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Distribution_of_cold_pain_thresholds_as_observed_in_the_five_different_data_sets_rows_corresponding_to_the_four_studies_11_14_as_in_study_1_11_data_was_separated_to_accommodate_the_involvement_of_two_observers_in_contrast_to_the_other_three_studies_where/1421690", "title"=>"Distribution of cold pain thresholds as observed in the five different data sets (rows) corresponding to the four studies [11–14] as in study #1 [11], data was separated to accommodate the involvement of two observers in contrast to the other three studies where only a single observed had acquired the data (Table 1).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-05-20 04:34:12"}

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{"start_date"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}
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