public IEnumerable CustomLabelsSource { get; set; }

Public Property CustomLabelsSource As IEnumerable

<Style TargetType="{x:Type dxga:ArcScale}">
    <Setter Property="CustomLabelsSource" Value="{Binding RomanLabels}"/>
    <Setter Property="CustomLabelTemplate">
        <Setter.Value>
            <DataTemplate>
                <dxga:ScaleCustomLabel Value="{Binding Hour}"
                                       Content="{Binding RomanHour}"
                                       Visible="{Binding Visible}"/>
            </DataTemplate>
        </Setter.Value>
    </Setter>
</Style>

public class WorldTimeViewModel {
    public IEnumerable<HourLabelData> RomanLabels { get; private set; }
}

public class HourLabelData : BindableBase {
    public int Hour { get; private set; }
    public string RomanHour { get; private set; }
    public bool Visible {
        get { return GetProperty(() => Visible); }
        set { SetProperty(() => Visible, value); }
    }

    public HourLabelData(int hour) {
        Hour = hour;
        RomanHour = romanHours[hour - 1];
    }
    static string[] romanHours = 
        new string[] { "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX", "X", "XI", "XII" };
}

Public Class WorldTimeViewModel
    Public Property RomanLabels As IEnumerable(Of HourLabelData)
End Class

Public Class HourLabelData
    Inherits BindableBase

    Public Property Hour As Integer
    Public Property RomanHour As String

    Public Property Visible As Boolean
        Get
            Return GetProperty(Function() Visible)
        End Get
        Set(ByVal value As Boolean)
            SetProperty(Function() Visible, value)
        End Set
    End Property

    Public Sub New(ByVal hour As Integer)
        Hour = hour
        RomanHour = romanHours(hour - 1)
    End Sub

    Shared romanHours As String() = 
        New String() {"I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX", "X", "XI", "XII"}
End Class